Interference Cancellation Based Spectrum Sharing for Massive MIMO Communication Systems

Cellular network operators are predicting an increase in space of more than 200 percent to carry the move and tremendous increase of total users in data traffic. The growing of investments in infrastructure such as a large number of small cells, particularly the technologies such as LTE-Advanced and 6G Technology, can assist in mitigating this challenge moderately. In this paper, we suggest a projection study in spectrum sharing of radar multi-input and multi-output, and mobile LTE multi-input multi-output communication systems near m base stations (BS). The radar multi-input multi-output and mobile LTE communication systems split different interference channels. The new approach based on radar projection signal detection has been proposed for free interference disturbance channel with radar multi-input multi-output and mobile LTE multi-input multi-output by using a new proposed interference cancellation algorithm. We chose the channel of interference with the best free channel, and the detected signal of radar was projected to null space. The goal is to remove all interferences from the radar multi-input multi-output and to cancel any disturbance sources from a chosen mobile Communication Base Station. The experimental results showed that the new approach performs very well and can optimize Spectrum Access.

due to its high frequency range. At the same time, delicate analyses have to be performed so that losses on the radar side can be reduced significantly by thoroughly choosing the best channel and preserving the i th mobile communication base station. Through a systematical inquiry and analytical results, we demonstrate that the dropping of the radar scheme is smaller when it comes to choosing the appropriate channel of interference and handed down to choose the good channel that the radar signals' detection is estimated. Secondly, we have discussed the challenges of localizing a targeted point of a radar that has spread its waves in the null space interference channel. Obviously, our objective here is to reduce interference on the LTE cellular network. Our scenario is a radar massive multiple-input multiple-output and an LTE mobile massive multiple-input multiple-output. We consider that the wireless mobile cellular system has many base stations. Two spectrum access methods were selected for this purpose. First, we consider the case where on the radar side the accessible degrees of freedom are not sufficient to localize the chosen targeted point and reduce the interferences of the mobile base stations at the same time. Here, we chose one cellular mobile base station as a sample, to do our projection optimization, with a consideration of maintaining as little degradation as possible. Secondly, we considered a scenario where on the radar side, the accessible degrees of freedom are sufficient to localize the chosen targeted point and reduce the interferences of the mobile base stations at the same time. We analyzed the proficiency of the chosen target detection projection wave and performed hand-to-hand comparisons of the two waves. We get the advantage of the use of the generalized likelihood ratio (GLR) for its flexibility and less computation to perform the detection and to obtain test statistics of the null space projection and orthogonal wave signal. The signal target detector execution for both waves was investigated based on theoretical level as well as practical level throughout Monte Carlo simulations.
The present work is organized as follows. In Section 2 we talk about massive multiinput multi-output (MIMO) radar, selection of channel target, orthogonal waves signal, channel interference, the chosen mobile system model, the cooperative RF environment, and architecture. We have analyzed spectrum sharing for both massive MIMO radar and mobile communications systems. Its performance includes matrix projection and a target Detection Decision Test.
In Section 3, we talk about numerical results and analyses. In Section 4, we talk about projection algorithm and discussion. Section 5 is the conclusion of the paper.

System Model
In this section, we presented the chosen detection point target of MIMO radar, in a far-end site, the orthogonal waves, interference channel, and massive mobile cellular network. In the present work, we have considered a radar that is a colocation massive multiinput multi-output radar with M variable of transmitter and receiver antennas grouped inside a military base station. We consider that our colocated multi-input multi-output radar antenna array is half observation of the wave. An additional study of the massive multi-input multi-output radar is deeply placed where components are well-positioned, which produces strength to the spatial distinctiveness [29,30]. The colocated scanned massive radar brings a very good spatial intent parameter point of the target recognition analysis if we tried to compare it with wide-spaced radar [31]. Consider x(t) to be the signal transmitted by M massive multi-input multi-output radar input presented here, Then, the transmit-receive steering matrix can be written as, By considering M transmitter and receiver, we can then define, a T (θ) a(θ) a R (θ).
For flexible reasoning, we assume that the path attenuation of the wave α is the same for the transmitter and receivers' antennas; we use this inference because of the backside site [32]. The tilt θ represents the angular azimuth of the chosen point. A summary of notations presented in this paper can be found in Table 1. The signal received from a single point, in far-end with constant velocity υ r at an angle θ can be written as, where α is the loss path as well as the breeding loss and the reflection measurement, and n(t) represents additive complex Gaussian noise. On the receiver side, we set the following inference: Channel between j th UE and i th BS r i (t) Received Signal at i th BS P i Projection Matrix for the i th Channel −θ and α are deterministic unknown parameters and is the entrance orientation of the chosen target and complex magnitude of the target, respectively. We denote the move of trajectory noise by n(t), and is independent, zero-mean, we consider it to be well-known, complex Gaussian and converged matrix, R n = σ 2 n I M , i.e., n(t)~N c (0 M , σ 2 n I M ), where N c represents the CGND (Complex Gaussian Normally Distributed). By Considering Equation (4) hypothesis, the receiver signal can be represented, And the orthogonal waveforms transmitted by the massive MIMO radars can be written, The quadratic transmission signals of massive MIMO radars advantages in context of selecting one specific receiver from the transmission side and generate end-to-end inclusion system to ameliorate the angle of resolution, increase the cluster hole more on virtualization, also enlarge the number of solvable targets, reduces earlobes [33], and decrease the probability of head off if we tried to compare it to the rational signal waves [34].

. Mobile Communication System
A TDD massive multi-input multi-output mobile LTE communications system has been considered for Ҡbase stations; each is supplied by an N BS transmitter and receiver element, shielded by i th base station and L UE i user equipment. The user equipment likewise are multi-input and output systems categorized by N UE transmitter and receiver element. By conceding that s UE i (t) is the transmitted signal of j th user equipment to the i th unit, the receiver signal at the end base station can be described, where H j represents the matrix in j th user equipment communication system, w j (t) represents the white additive Gaussian noise. Q c,j , P c,j represents the linear decoding and precoding matrices. The goal of designing the j th precoder and decoder is to find a null space spanned by the columns of a decoder matrix in order to align the interfering signals [11,[35][36][37].

Co-Existence RF Environment
In communication wireless system model theory, we generally assumed that the transmission (which is from the base station) carried the States Space Channel Information (SSCI) from the receiver (known as the user equipment) in Frequency Division Duplex communication systems. On the other hand, they can exchange each other's transmission channel in Time Division Duplex communication systems [38]. Response and exchange traffic are well-grounded, feasible as much as the response has an understandable and consistent time and radio frequency channel and greater than the reciprocity traffic time, respectively. For instance, when radar channels are sharing spectrum with mobile cellular structure, one way for getting the SSCI is that the radar shall measure H i according to the estimation sent from the base station (BS) [39]. A different method is that the radar gets the advantage of mobile cell concerning carrier estimation, assisted by the low-power signal, and the carrier estimation is filtered to the radar. For instance, by considering radar detected signal as an interference on the mobile cellular side, the channel can be classified as an intrusion channel and consider the internal information as intrusion channel state information. The propagation of the spectrum between radar and LTE mobile cellular system networks can be visualized in two main ways, first as the radars' military network system. Splitting their spectrum within military base stations, we denote it Mil-to-Mil spectrum sharing. The second way is the radars' military base station sharing their spectrum with a business or mobile cellular commercial network. This was denoted as the Mil-to-Com spectrum sharing. In this paper, we focused more on the Mil-to-Com case. The intrusion channel state information can be obtained by allowing impulse of commercial network. The largest impulse scheme is the null-pilot and shelter that came from the radar interference. In the two scenarios, notwithstanding the sharing scheme, Mil-to-Mil or Mil-to-Com, we have the intrusion channel state information for the reason of reducing radar interference at the mobile commercial network.

Construction
We harmonized the coexistence between the two schemes as illustrated in Figure 1, in which the military-based massive radar multi-input multi-output is splitting Ҡinterference carriers with its neighbor mobile system. By considering this scenario, the detected signal on the receiver side at the i th base station can be represented as, H i represents interference channel between mobile Cellular base station and the radar. And i = 1,2, . . . , k, where H i can be written, Here h (l,k) i denotes the coefficient carrier of k th radar's base station antenna to the l th LTE mobile antenna of the i th base station. The components of H i are independent, identically distributed, moreover annular proportional and randomly distributed equivalent to complex Gaussian with zero-mean, hence accepting Rayleigh dispersion. Furthermore, meticulous and comprehensive analysis of interference channel for radar and mobile communications systems, along with more than two special channels, are presented in [28,33,40]. Our goal here is to map x(t) toward null space interference H i , by canceling interference at i th base station, such as H i x(t) = 0, so that r i (t) should be Equation (7) instead of Equation (8).

Radar Mobile System Spectrum Sharing
In this section, we deal with spectrum sharing of radar multi-input multi-output and that of mobile communication, and included Ҡbase stations. Both systems share the same numbers of interferences (Ҡ) that lead us to H i (i = 1, 2, . . . , k). The detected signal of radar is estimated by projecting it to the map of zero interference channel and connecting the two communications systems (radar and mobile) by utilizing our suggested interference-channel-collection inference, in sequence of having removed all interferences from the radar multi-input multi-output. The selection of interference channel is done with respect on maximizing zero map projection, represented as argmax 1≤i≤K dim[N(H i )] and project the detected signal of the radar in null space of this scheme.

Performance
We used theorem of Cramer bound and the maximum likelihood estimation to evaluate the slope of the targeted point of entrance as our statistical scheme of the network. Attention also was put on analyzing the deterioration approximation of the arrival angle of the chosen point, suitable to project the wave of the radar in null space. Cramer bound of an isolated chosen point study was well analyzed in [40], For instance, the maximum likelihood of no interference of a single targeted point can be represented as, where τ r is the two-way breeding hold up connecting the chosen point and the reference point, and we denote ω D as the Doppler frequency transfer. Furthermore, we consider the performance measurement such as the Cramer bound and maximum likelihood; we are more concerned with the constant changes that occurred in the beampattern of radar wave projection. The response of beampattern measurement for a chosen point is controlled by θ as presented in [40], Here Ω represents the constant of harmonization, and θ D is the processor-driving rudder of the primary beam. In this research, we studied two spectrum-sharing methods and analyzed them as follows: Case 1 (M < ҠN BS and M > N BS ). A case where the radar has only a few beam antennas in comparison with the interconnected, which is Ҡ-BS where M <ҠN BS . On the other hand, radar antennas are greater than the base station antennas beam, where M > N BS . In a situation like this, it is impossible for the radar to reduce interferences at once in all the antennas as Ҡ-Base station inside the system structure are due to poor applicable degrees of freedom. Moreover, the accessible degrees of freedom can grant us target detection and interference reduction at once, and that means only upon one selected base station inside the network of Ҡbase stations. For the selection of the base station by the radar, this will depend on the optimization operation of the radar. This paper seeks to study how to reduce interference in a maximum manner on the side of the mobile base station with the least possible deterioration performance of the radar operation. The defect is that the interferences cannot significantly be reduced by removing one base station on the network; therefore, the radar will have to use a very high-power level in order to have a good performance. However, this can increase the probability gain of interference on the mobile base stations which are not included in the mitigation study scenario. In [41,42], the technique explained that by applying resource allocation and dual-cell approaches we can change Ҡ -1 base stations to nonradar frequency ranges. In M <ҠN BS conventional colocated multi-input multi-output radar and cellular system, applying the Zero Interference Projection (ZIP) technique, is not an effective way of reducing significant interference because ZIP has a limited number of parameters to stabilize the two systems. By so doing, it will lead to low performance of the radar. Although we can also modify the structure of the radar system into a superposed multi-input multi-output radar structure, the transmitted wave range of colocated radar will have to be divided into numerous sub-rages which can be acceptable by superposed. A superposed radar waves structure increases the degree of freedom of the transmitted wave, and as result the massive multiinput multi-output radar can perform very well. At the same time, we have significantly reduced interferences at the LTE mobile base station without compromising the radar's transmitted parameters requirement. Case 2 Where M >ҠN BS . Let us examine a case where the massive multi-input multioutput radar has many antenna elements and this increases the beam, in comparison with a mixed antenna element with Ҡbase stations. In such a situation, it is possible that the massive multi-input multi-output radar can reduce considerable interference to every single K base station in the network, while ensuring good signal detection of the chosen targets. Here we have enough degree of freedom which makes our scenario possible. In this case, the mixed interference shared in the networks between massive multi-input multi-output radar and LTE mobile base stations system can be written as;

Matrix Projection
At this point, we structure the prediction array for Scenarios 1 and 2.
1st Prediction Scenario, where M <ҠN BS and M > N BS : Here, the prediction algorithm for the first scenario is presented. At this point, the schemes of radar detection are estimated over null space of interference transmission trajectory H i . We suppose that the MIMO radar has the information of each channel state of H i interference channels, over the response, in Mil-to-Mil or Mil-to-Com scheme, considering the performance of a unique evaluation of decomposition (UED) to estimate the interference cancellation and therefore build the projection matrix. Let us estimate first EUD of H i , And, where p min (N BS , M) and σ i1 > σ i2 > · · · > σ iq > σ iq+1 = σ iq+2 = · · · = σ ip = 0 are the singular values of H i . From here we can define, where, Given aforementioned definitions, we are able to determine projection matrix, In order to verify that P i is a suitable matrix projection, these two conditions have to be met:   (19) is follows that, P i = P H i = P 2 i . We can also show P i is a projector matrix if ∀ v ∈ rang (P i ), then P i v = v; and w, v = P i w, then, This confirms our first property. Condition 2 P i ∈ C M×M is the null space orthogonally projected matrix H i ∈ C N BS ×M . Proof, P i = P H i ,we can write, In 'Prediction Scenario 1 , we have a total of Ҡinterference channels. Hence, we must choose the channel that leads to a minimum deterioration of radar wave in the lowest level as possible, P i min P After the projection matrix has been determined, we can now estimate the signal of radar over the null space of intrusion channel, The statistical matrix between the two waves can be written as, The projection does not preserve its perpendicularity, which means it is not identical anymore and is classified according to the projection matrix.
2nd Prediction Scenario, where M > K N BS : Here, the prediction algorithm for the second scenario is presented. At this point, the schemes of radar detection are estimated over null space of mixed interference trajectory H. It can be written as, And, where p min (N BS , M) and σ 1 > σ 2 > · · · > σ q > σ q+1 = σ q+2 = · · · = σ p = 0 are the singular values of H. We define, where, Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis σ′ ≜ { 0 , ∀ u ≤ q , 1, ∀ u > q, Considering the present assumption, we can then extend the projection matrix as follows, ≜ Σ ′ (27) At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), associating the case where the target is absent, and hypothesis Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, Considering the present assumption, we can then extend th lows, ≜ Σ ′ At this point we can now conclude that P is an accurate pr Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to im respect to orthogonal wave of radar, including Null-space projec here is a comparative test scheme of the waveforms through an tistics, that is, if the targeted point is present or not in the scope By considering the target detection and evaluation we analyze pothesis estimation test, wherefrom we decide to pick between hypothesis Ԣ 0 associating the case where the target is absent, a ciating the case where the target is present. For one model, the h tion (4) can be presented as, We used the generalized likelihood ration test because rameters but deterministic. The benefit of utilizing the generaliz is that we can substitute the hidden parameters with their maxim tion. The maximum likelihood estimations of and can be f schemes, point targets, and noise sources here in [40,43] where t used. In this paper, we examine a system with one target, and source of interference so we can better analyze the effect of NSP quently, we put forward an easier method of the maximum lik likelihood ration test estimation. The detection scheme of Equat sented, ( ) = ( , ) + ( )

And, ( , ) = ( ) ( )
We take the advantage of Karhunen-Loève algorithm to d function on evaluating and . We consider to be the {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal fu requirement, where zz ′ represents a function of Krönecker. This next series expressed to develop the system, y(t), Q(t, )}, and n(t), Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed.
By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), We used the generalized likelihood ration test because α and θ are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of α and θ can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating α and θ. We consider Ω to be the set, where elements are {y(t),Q(t, θ),n(t)}. We denote ψ z , z = 1, 2, . . . , are the orthonormal function of Ω meeting the requirement, where δ zz represents a function of Krönecker. This next series of elements of Ω, can be expressed to develop the system, y(t), Q(t, θ)}, and n(t), Here y z , Q z , and n z repesent weighed rate of Karhunen-Loève estimation in the view of the process gained by considering the matching internal production through the basic function ψ z (t). Therefore, a corresponding discrete scheme of Equation (29) can be written as, Considering the white annular complex Gaussian can be represented as: Here y z , Q z ,and n z repesent weighed rate of Karhunen-Loève estimation in the view of the process gained by considering the matching internal production through the basic function ψ z ( ). Therefore, a corresponding discrete scheme of Equation (29) can be written as, Considering the white annular complex Gaussian can be represented as: Ḓ[n(t)nt-nτ(t)] =σ n 2 I M (τt), [2] the array is i.i.d and n z~ ℕ c (0 M , σ n 2 I M ). From here, the function of log-likelihood can be expressed, By Maximizing Equation (34), where, It must be noted that Equation (35), aside of the constant , the other additions lead to infinite. However, because of the noncontribution of highest rank condition, the evaluation of θ and α their total sum can be finite by applying the equality, We can describe f th element of e Qy , after bringing Q (t, θ) to Equation (30).
where, = ∫ y(t) (t) T 0 , the same way, we can describe f th element of written here, Since, ⅇ and does not depend on the receiver, then the statistical estimation of θ and α can be taken from Equations (36) and (37). Now the maximum log-likelihood function can be represented as a vector estimation, And our hypothesis testing model as in Equation (28), it becomes then, where ( , , ; Ԣ 1 ) and ( ; Ԣ 0 ) are the result of the hypothesis test Ԣ 0 and Ԣ 1 respectively, which is the probability density functions of the receiver. Hence, the generalized likelihood ration test can be expressed as, [n(t)nt-nτ(t)] = σ 2 n I M δ(τt), [2] the array is i.i.d and n z~N c (0 M , σ 2 n I M ). From here, the function of log-likelihood can be expressed, By Maximizing Equation (34), where, It must be noted that Equation (35), aside of the constant Γ, the other additions lead to infinite. However, because of the noncontribution of highest rank condition, the evaluation of θ and α their total sum can be finite by applying the equality, We can describe f th element of e Qy , after bringing Q (t, θ) to Equation (30).
where, E = T 0 y(t)x H (t)dt, the same way, we can describe f g th element of E QQ written here, Since, e Qy and E QQ does not depend on the receiver, then the statistical estimation of θ and α can be taken from Equations (36) and (37). Now the maximum log-likelihood function can be represented as a vector estimation, And our hypothesis testing model as in Equation (28), it becomes then, Considering the present assumption, we can then extend the projection matrix as folws, At this point we can now conclude that P is an accurate projection matrix based on onditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with spect to orthogonal wave of radar, including Null-space projection waves. Our objective re is a comparative test scheme of the waveforms through analyzing decision test statics, that is, if the targeted point is present or not in the scope of Doppler shift needed. considering the target detection and evaluation we analyzed by considering the hythesis estimation test, wherefrom we decide to pick between two hypotheses: the zero pothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 assoating the case where the target is present. For one model, the hypothesis test as in Equan (4) can be presented as, We used the generalized likelihood ration test because and are unknown pameters but deterministic. The benefit of utilizing the generalized likelihood ration test that we can substitute the hidden parameters with their maximum likelihood computan. The maximum likelihood estimations of and can be found for different signal hemes, point targets, and noise sources here in [40,43] where the orthogonal signals are ed. In this paper, we examine a system with one target, and we did not consider the urce of interference so we can better analyze the effect of NSP on target sensing. Conseently, we put forward an easier method of the maximum likelihood and generalized elihood ration test estimation. The detection scheme of Equation (4)

Target Detection
In this point, we expended a numerical detecti respect to orthogonal wave of radar, including Null-s here is a comparative test scheme of the waveforms tistics, that is, if the targeted point is present or not By considering the target detection and evaluation pothesis estimation test, wherefrom we decide to pi hypothesis Ԣ 0 associating the case where the targe ciating the case where the target is present. For one m tion (4) can be presented as, We used the generalized likelihood ration test rameters but deterministic. The benefit of utilizing is that we can substitute the hidden parameters with tion. The maximum likelihood estimations of and schemes, point targets, and noise sources here in [40 used. In this paper, we examine a system with one source of interference so we can better analyze the ef quently, we put forward an easier method of the m likelihood ration test estimation. The detection schem sented, Considering the present assumption, we lows, ≜ At this point we can now conclude that Conditions 1 and 2.

Target Detection
In this point, we expended a numerical respect to orthogonal wave of radar, including here is a comparative test scheme of the wav tistics, that is, if the targeted point is present By considering the target detection and eval pothesis estimation test, wherefrom we decid hypothesis Ԣ 0 associating the case where th ciating the case where the target is present. Fo tion (4) can be presented as, We used the generalized likelihood rati rameters but deterministic. The benefit of ut is that we can substitute the hidden paramete tion. The maximum likelihood estimations o schemes, point targets, and noise sources her used. In this paper, we examine a system w source of interference so we can better analyz quently, we put forward an easier method o likelihood ration test estimation. The detectio sented, Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be repre-δ (38) where f y y, θ, α;

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σ′ ≜ { 0 , ∀ u ≤ q , 1, ∀ u > q, ent assumption, we can then extend the projection matrix as fol- now conclude that P is an accurate projection matrix based on ended a numerical detection test to improve the decision with e of radar, including Null-space projection waves. Our objective scheme of the waveforms through analyzing decision test staed point is present or not in the scope of Doppler shift needed. detection and evaluation we analyzed by considering the hyherefrom we decide to pick between two hypotheses: the zero g the case where the target is absent, and hypothesis Ԣ 1 assotarget is present. For one model, the hypothesis test as in Equas, n(t) ∶ Ԣ 0 (Absent) 0 ≤ t ≤ T 0 ( ) ( ) + ( ) ∶ Ԣ 1 (Present)0 ≤ t ≤ T 0 ized likelihood ration test because and are unknown pac. The benefit of utilizing the generalized likelihood ration test e hidden parameters with their maximum likelihood computahood estimations of and can be found for different signal d noise sources here in [40,43] where the orthogonal signals are xamine a system with one target, and we did not consider the e can better analyze the effect of NSP on target sensing. Conse-and f y; Considering the present assumption, we can then extend the projection ma lows, ≜ Σ ′ At this point we can now conclude that P is an accurate projection matrix Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the dec respect to orthogonal wave of radar, including Null-space projection waves. Ou here is a comparative test scheme of the waveforms through analyzing decisio tistics, that is, if the targeted point is present or not in the scope of Doppler sh By considering the target detection and evaluation we analyzed by consideri pothesis estimation test, wherefrom we decide to pick between two hypothese hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis ciating the case where the target is present. For one model, the hypothesis test a tion (4) can be presented as, We used the generalized likelihood ration test because and are unk rameters but deterministic. The benefit of utilizing the generalized likelihood is that we can substitute the hidden parameters with their maximum likelihood tion. The maximum likelihood estimations of and can be found for diffe schemes, point targets, and noise sources here in [40,43] where the orthogonal used. In this paper, we examine a system with one target, and we did not co source of interference so we can better analyze the effect of NSP on target sensi are the result of the hypothesis test

Target Detection
In this point, we expended a num respect to orthogonal wave of radar, inc here is a comparative test scheme of th tistics, that is, if the targeted point is p By considering the target detection an pothesis estimation test, wherefrom w hypothesis Ԣ 0 associating the case wh ciating the case where the target is pres tion (4) can be presented as, We used the generalized likeliho rameters but deterministic. The benefi is that we can substitute the hidden par tion. The maximum likelihood estimat schemes, point targets, and noise sourc used. In this paper, we examine a sys source of interference so we can better Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Conse-respectively, which is the probability density functions of the receiver. Hence, the generalized likelihood ration test can be expressed as,

Target Detection
In this point, we expended a numerical de respect to orthogonal wave of radar, including N here is a comparative test scheme of the wavefo tistics, that is, if the targeted point is present or By considering the target detection and evalua pothesis estimation test, wherefrom we decide t hypothesis Ԣ 0 associating the case where the t ciating the case where the target is present. For o tion (4) can be presented as, We used the generalized likelihood ration rameters but deterministic. The benefit of utiliz is that we can substitute the hidden parameters Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown pa-δ The statistic of L θ ML for both the hypotheses can be found in [44].

Target Detection
In this point, we expended a numerical detection test to respect to orthogonal wave of radar, including Null-space proj here is a comparative test scheme of the waveforms through tistics, that is, if the targeted point is present or not in the scop By considering the target detection and evaluation we analyz pothesis estimation test, wherefrom we decide to pick betwee hypothesis Ԣ 0 associating the case where the target is absent ciating the case where the target is present. For one model, the tion (4) can be presented as, We used the generalized likelihood ration test because rameters but deterministic. The benefit of utilizing the genera is that we can substitute the hidden parameters with their max tion. The maximum likelihood estimations of and can b schemes, point targets, and noise sources here in [40,43] where used. In this paper, we examine a system with one target, an source of interference so we can better analyze the effect of NS quently, we put forward an easier method of the maximum likelihood ration test estimation. The detection scheme of Equ sented,

( , ) = ( ) ( )
We take the advantage of Karhunen-Loève algorithm t function on evaluating and . We consider to be th {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal requirement, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, < ψ z ( ), ψ z ′ ( ) >= ∫ ψ z ( ), where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), : X 2 2 (ρ) (40) Whereby, -X 2 2 (ρ) represents the chi-squared noncentral dispensations, having 2 as degrees of freedom (DoF), -X 2 2 represents centralized chi-squared dispensations, having 2 as degrees of freedom (DoF). ρ represents the noncentral parameter; it can be written as, Based on a chosen probability of false alarm, for a given signal detection, a ration δ must be generated, Considering the present assumption, we can then ext lows, ≜ Σ ′ At this point we can now conclude that P is an accu Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection te respect to orthogonal wave of radar, including Null-space here is a comparative test scheme of the waveforms thro tistics, that is, if the targeted point is present or not in the By considering the target detection and evaluation we a pothesis estimation test, wherefrom we decide to pick be hypothesis Ԣ 0 associating the case where the target is ab ciating the case where the target is present. For one model tion (4) can be presented as,

(Presen
We used the generalized likelihood ration test beca rameters but deterministic. The benefit of utilizing the ge is that we can substitute the hidden parameters with their tion. The maximum likelihood estimations of and c schemes, point targets, and noise sources here in [40,43] w used. In this paper, we examine a system with one targe source of interference so we can better analyze the effect o quently, we put forward an easier method of the maxim likelihood ration test estimation. The detection scheme of sented, ( ) = ( , ) + ( )

And, ( , ) = ( ) ( )
We take the advantage of Karhunen-Loève algorith function on evaluating and . We consider to b {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonor requirement, represents a function of Krönecker. This next expressed to develop the system, y(t), Q(t, )}, and n(t), represents the inverse dispensations function with 2 as DoF. Then the signal detection estimation can be presented as, Considering the present assumption, we can then extend the projection matrix as follows, ≜ Σ ′ (27) At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, ( ) = ( , ) + ( ) And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, < ψ z ( ), ψ z ′ ( ) >= ∫ ψ z ( ), where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), Whereby F X 2 2 (ρ) is the noncentral dispensations function including its parameter ρ.

P D for Orthogonal Waveforms
For orthogonal waveforms R T x = I M , therefore, the generalized likelihood ration test can be expressed as, Considering the present assumption, we can the lows, ≜ Σ ′ At this point we can now conclude that P is an Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detecti respect to orthogonal wave of radar, including Null-s here is a comparative test scheme of the waveforms tistics, that is, if the targeted point is present or not By considering the target detection and evaluation pothesis estimation test, wherefrom we decide to pi hypothesis Ԣ 0 associating the case where the targe ciating the case where the target is present. For one m tion (4) can be presented as, y(t)={ n(t) ∶ Ԣ 0 (A ( ) ( ) + ( ) ∶ Ԣ 1 (P We used the generalized likelihood ration test rameters but deterministic. The benefit of utilizing is that we can substitute the hidden parameters with tion. The maximum likelihood estimations of and schemes, point targets, and noise sources here in [40 used. In this paper, we examine a system with one source of interference so we can better analyze the ef quently, we put forward an easier method of the m likelihood ration test estimation. The detection schem sented, ( ) = ( , ) +

And, ( , ) = ( )
We take the advantage of Karhunen-Loève al function on evaluating and . We consider {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the ort requirement, Considering the present assumption, we can then extend the projection matrix as follows, ≜ Σ ′ (27) At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, y(t)={ n(t) ∶ Ԣ 0 (Absent) 0 ≤ t ≤ T 0 ( ) ( ) + ( ) ∶ Ԣ 1 (Present)0 ≤ t ≤ T 0 (28) We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, ( ) = ( , ) + ( ) And, ( , ) = ( ) ( ) We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the δ O and the estimation of L θ ML for this scheme can be written, Considering the present assumption, we can then extend lows, ≜ Σ ′ At this point we can now conclude that P is an accurate Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to respect to orthogonal wave of radar, including Null-space pro here is a comparative test scheme of the waveforms through tistics, that is, if the targeted point is present or not in the sco By considering the target detection and evaluation we analy pothesis estimation test, wherefrom we decide to pick betwe hypothesis Ԣ 0 associating the case where the target is absen ciating the case where the target is present. For one model, th tion (4) can be presented as, We used the generalized likelihood ration test because rameters but deterministic. The benefit of utilizing the gener is that we can substitute the hidden parameters with their ma tion. The maximum likelihood estimations of and can b schemes, point targets, and noise sources here in [40,43] wher used. In this paper, we examine a system with one target, a source of interference so we can better analyze the effect of NS quently, we put forward an easier method of the maximum likelihood ration test estimation. The detection scheme of Equ sented, Considering the present assumption, we can then extend the projection matrix as follows, At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, ( ) = ( , ) + ( ) And, where, δ O is defined following a required probability of false alarm, And then we can determine the detection for orthogonal waves as follows,

P D for NSP Waveforms
For spectrum-sharing waveforms R T x = R Ť x , therefore, the generalized likelihood ration test can be expressed as, At this point we can now conclude that P is an Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detecti respect to orthogonal wave of radar, including Nullhere is a comparative test scheme of the waveforms tistics, that is, if the targeted point is present or not By considering the target detection and evaluation pothesis estimation test, wherefrom we decide to pi hypothesis Ԣ 0 associating the case where the targe ciating the case where the target is present. For one m tion (4) can be presented as, n(t) ∶ Ԣ 0 (A ( ) ( ) + ( ) ∶ Ԣ 1 (P We used the generalized likelihood ration test rameters but deterministic. The benefit of utilizing is that we can substitute the hidden parameters with tion. The maximum likelihood estimations of and schemes, point targets, and noise sources here in [40 used. In this paper, we examine a system with one source of interference so we can better analyze the ef quently, we put forward an easier method of the m likelihood ration test estimation. The detection sche sented,

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) can then be represented, And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, < ψ z ( ), ψ z ′ ( ) >= ∫ ψ z ( ), where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), δ NSP and the estimation of L θ ML for this scheme can be written, Here, Considering the present assumption, we can then exten lows, ≜ Σ ′ At this point we can now conclude that P is an accurat Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test t respect to orthogonal wave of radar, including Null-space pr here is a comparative test scheme of the waveforms throug tistics, that is, if the targeted point is present or not in the sc By considering the target detection and evaluation we anal pothesis estimation test, wherefrom we decide to pick betw hypothesis Ԣ 0 associating the case where the target is abse ciating the case where the target is present. For one model, th tion (4) can be presented as, We used the generalized likelihood ration test because rameters but deterministic. The benefit of utilizing the gene is that we can substitute the hidden parameters with their m tion. The maximum likelihood estimations of and can schemes, point targets, and noise sources here in [40,43] whe used. In this paper, we examine a system with one target, source of interference so we can better analyze the effect of N quently, we put forward an easier method of the maximum likelihood ration test estimation. The detection scheme of Eq sented, ( ) = ( , ) + ( )

And, ( , ) = ( ) ( )
We take the advantage of Karhunen-Loève algorithm function on evaluating and . We consider to be {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonorm requirement, < ψ z ( ), ψ z ′ ( ) >= ∫ ψ z ( ), where zz ′ represents a function of Krönecker. This next se expressed to develop the system, y(t), Q(t, )}, and n(t), Considering the present assumption, we can then extend the projection matrix as follows, ≜ Σ ′ (27) At this point we can now conclude that P is an accurate projection matrix based on Conditions 1 and 2.

Target Detection
In this point, we expended a numerical detection test to improve the decision with respect to orthogonal wave of radar, including Null-space projection waves. Our objective here is a comparative test scheme of the waveforms through analyzing decision test statistics, that is, if the targeted point is present or not in the scope of Doppler shift needed. By considering the target detection and evaluation we analyzed by considering the hypothesis estimation test, wherefrom we decide to pick between two hypotheses: the zero hypothesis Ԣ 0 associating the case where the target is absent, and hypothesis Ԣ 1 associating the case where the target is present. For one model, the hypothesis test as in Equation (4) can be presented as, We used the generalized likelihood ration test because and are unknown parameters but deterministic. The benefit of utilizing the generalized likelihood ration test is that we can substitute the hidden parameters with their maximum likelihood computation. The maximum likelihood estimations of and can be found for different signal schemes, point targets, and noise sources here in [40,43] where the orthogonal signals are used. In this paper, we examine a system with one target, and we did not consider the source of interference so we can better analyze the effect of NSP on target sensing. Consequently, we put forward an easier method of the maximum likelihood and generalized likelihood ration test estimation. The detection scheme of Equation (4) And, We take the advantage of Karhunen-Loève algorithm to derive the log-likelihood function on evaluating and . We consider to be the set, where elements are {y(t),Q(t, ),n(t)}.We denote ψ z , z=1,2,…, are the orthonormal function of meeting the requirement, < ψ z ( ), ψ z ′ ( ) >= ∫ ψ z ( ), T 0 ψ ′ * ( ) = zz ′ where zz ′ represents a function of Krönecker. This next series of elements of , can be expressed to develop the system, y(t), Q(t, )}, and n(t), δ NSP is also defined following a required probability of false alarm, And we can then determine the detection for orthogonal waves as follows,

Numerical Results
For better analysis of the detection sequence execution of each spectrum propagation for the massive multi-input multi-output radars, the Monte Carlo execution was performed by simulation on manipulating radar's parameter as presented in [45].

Analysis of Scenario 1
For this scenario, we generated ҠRayleigh channels interference at every run of the Monte Carlo simulation. We have the dimensions N BS × M, and computed the null spaces and built matching projection matrix by applying Algorithm 2. We decided the finest channel to carry out projection of radar signal scheme on applying Algorithm 1, transmit Null Space Projection signal scheme based on the received signal detection. We calculated the parameters estimation of θ, α, and estimated the detection signal sequence for orthogonal and NSP waves.
We performed Algorithm 1 and 2. In Figures 2 and 3, we demonstrate the importance of the two algorithms (1 and 2), in enhancing the detection target point where many BSs are in use on the detection scheme of the radar. It has to correctly detect the target point while not disturbing the sensing signal environment of the mobile LTE system scheme concerned. A summary of test environment parameters are presented in Table 2. For instance, we examined the case with five base stations (BSs) and the radar will have to choose the best projection channel with a minimum degradation scheme waveform within, while consequently maximizing the contingency of target detection.
In the scenario with N(H i ) = 1 as shown in Figure 2, we presented results of five different Null Space Projection detection signals. This means that radar's waves are projected with five base station signals at the same time. Here we noticed that for a good detection scheme of 90%, we will need from 3 dB to 6 dB of more gain of signal-to-noise ratio. This is by comparing with the orthogonal wave, and depending on the chosen channel. With the use of Algorithms 1 and 2, we can choose the interference channel that leads to a least deterioration of the radar wave and produce a better output by improving the execution of the detection. At the same time, minimizing additional gain in SNR is needed. In this instance, the two algorithms (1 and 2) will choose BS3 and because of this condition, the NSP wave needs the lowest gain of signal-to-noise ratio to reach a perfection detection, probably over 90 percent in comparison to the other base stations.   Another scenario is with dim N(H i ) = 6, as shown in Figure 3. We presented a performance of five different NSP signals scheme, but in this instance the MIMO radar has a bigger antenna set if we compare it to the earlier scenario. In the present scenario, to obtain the best signal detection probability of 90%, we will have to reach 2.3 to 3.3 dB of more gain on SNR in comparison to orthogonal wave. Similar to the earlier scenario, by applying Algorithms 1 and 2, we will be able to choose an interference channel scheme that leads to a minimum deterioration of radar wave. This shows a high performance of target detection scheme with the lowest additional gain in SNR of interest. In addition, Algorithms 1 and 2 will choose Base Station No. 4. This is because the NSP waveform needs a very low gain of signal-to-noise ratio performance detection sequence of 0.9%, if compared with other base stations. These two cases show the significance of Algorithms 1 and 2 on projection probability of the radar by proving its performance in the selection of the channel. That leads to a least interference scheme and improves the coexistence of the two communications systems (Radar-Mobile LTE). This reduces significantly the gain in signal-to-noise ratio needed for null space projection of radar waves.
In Figure 4, we show the alterations of probability of detection P D in the form of SNR for different probability of false alarm P f . Every figure shows the probability of detection P D for a fixed point; P D against P f has been evaluated for 10 −2 , 10 −4 , 10 −6 , 10 −8 , respectively, with the dimension 2 × 4 of interference channel, which implies antennas radar M = 4, and N BS = 2 for base station antennas, with the dimension N(H i ) = 2 of null-space.  In the first scenario, as observed, the two signal waveforms increased simultaneously, where the signal-to-noise ratio increases. Despite this, comparing the two waves for a chosen point of signal-to-noise ratio, we can observe that orthogonal signal waves showed a very good performance compared to the null space projection wave. This means that the waves transmitted are no longer orthogonal, which also means that we can no longer get the benefit of orthogonal waves when we are using massive multi-input multioutput radar, as we have highlighted in Section 3.1. The good news is that we have canceled all interferences at the base station level. In addition, in Scenario 1 as shown in Figure 2, for us to execute the needed signal detection for a settled P , we will need more signal-to-noise ratio for null space projection as compared with Figure 4. This is due to many radar antennas that we used, while the antennas of the base station remain at the same point in Figure 4, which increases the aspect of the NSP channel. This results in a very good signal operation for null space projection wave. As we are interested in reducing the bad impact of the null space projection on radar in order to optimize its operation, While comparing the sensing operation, the observation of the two waveforms brings clarity. In order to get a better detection probability in a fixed point of P f , we will need more gain level for signal-to-noise ratio for the null space project if we compare it with the orthogonal waves. By considering P D = 0.9 as best detection probability or 90%, we will need 1.8 to 4.1 dB of extra gain on the null space project waveform in order to perform similar results with the orthogonal wave signal.
In the first scenario, as observed, the two signal waveforms increased simultaneously, where the signal-to-noise ratio increases. Despite this, comparing the two waves for a chosen point of signal-to-noise ratio, we can observe that orthogonal signal waves showed a very good performance compared to the null space projection wave. This means that the waves transmitted are no longer orthogonal, which also means that we can no longer get the benefit of orthogonal waves when we are using massive multi-input multi-output radar, as we have highlighted in Section 3.1. The good news is that we have canceled all interferences at the base station level. In addition, in Scenario 1 as shown in Figure 2, for us to execute the needed signal detection for a settled P f , we will need more signal-to-noise ratio for null space projection as compared with Figure 4. This is due to many radar antennas that we used, while the antennas of the base station remain at the same point in Figure 4, which increases the aspect of the NSP channel. This results in a very good signal operation for null space projection wave. As we are interested in reducing the bad impact of the null space projection on radar in order to optimize its operation, it is better to make use of more radar antennas transmitter array.

Analysis of Scenario 2
Here, for every run of the Monte Carlo simulation, we generate interference channel with ҠRayleigh signal. Each sequence has a dimension of ҠN BS × M. We compute null spaces and generate matching matrix projection according to Algorithm 4, and project the radar signal detection by applying Algorithm 3. We transmit the NSP signal detection, evaluate the parameters θ and α from the receiver, and estimate orthogonal and NSP waves signal detection.
In Figure 5, we have a scenario where the radar wave signal has a considerable antenna array, if we compare it with Ҡmobile base stations antenna array. In such a case, we have so much degree of freedom (DoF) for a good target detection at the radar and at the same time canceling interference to all base stations present in the network. Here we examined M = 100, Ҡ= 4, and N = {1,3,5}. We analyzed P D against P f = 10 −4 for a mixed disturbances channel H, considering the dimensions ҠN BS × M, where we equalize signal detection performance of primary wave and the null space projection wave inside channel interferences. It was observed that for us to obtain the probability of detection that we need for a fixed probability of false alarm, we will need more signal-to-noise ratio compared to the orthogonal waves. If we need a detection performance of P D = 0.90, we need 0.6,1 and 2.5 dB of extra signal-to-noise ratio for the null space projection wave, where N is 1,5 and 3 accordingly to obtain exactly the same result.

Discussion
Cognitive radio-based spectrum sharing is a new opportunity to face spectrum shortage in a world where everything tends to convert into a co-existence sharing. In this study, we analyzed spatial technique on spectrum access for massive MIMO radar and massive mobile communication systems, by considering numerous numbers of base stations. Our objective here is the cancellation of all interference schemes on the space. The selection of the best cancellation channel is made possible based on the maximum estimation and projection algorithm scheme, for a complete cancellation of disturbance to the cooperative radio frequency of existence.
1st Projection Algorithms Scenario, where M <ҠN BS but M > N BS : In this scenario, spectrum is spitted on setting up a projection matrix, then choosing an interference channel which is carried by the support of Algorithms 1 and 2. Primarily, on each and every impulse recurrence time (IRT), the radar receives its SSCI for the whole Ҡintrusion channels. The prediction matrix is created by the data transmitted through Algorithm 2 and the process of null spaces. In the first Algorithm, we showed the prediction arrays which are represented by Ҡ, obtained based on Algorithm 2, to get the forecast matrix which leads to minimum deterioration of radar waves and it is typical to improve the system. The present action goes alongside with the null space of chosen base stations through radar waves for matching chosen projection array and waveform transfer. Define P i min =P to be the desired projection. Implement the null space projector:x(t) =Px(t) End 2nd Projection Algorithm Scenario, where M > K N BS : Here, the spectrum sharing is performed throughout Algorithm 3 and 4. Initially, we considered that at each impulse recurrence time (IRT), SSCI of the total Ҡinterference channels has been received from the radar. And the data are forwarded to Algorithm 4 for the computation of null space which will result in H and create the matrix projection we called P. Algorithm 3 performs radar's wave projection into the null space. Algorithm 2. Projection for Algorithm 2 on 1st Scenario.

If Algorithm 1 received interferences H
Send P i to Algorithm 1. End Algorithm 3. Projection Algorithm 3 on 2nd Scenario.

Iterate
By observation from Ҡbase stations obtain SSCI of H.
Forward Interference H to Algorithm 4 and create matrix P. After Receiving matrix projection P through Algorithm 4. Execute zero interference projection,x(t) = Px(t) End Algorithm 4. Projection Algorithm 4 on 2nd Scenario.

Conclusions
In the future, spectrum sharing of radar radio frequency will be definitely shared with advanced evolution mobile communication systems (without mentioning the huge demand of Internet of Everything). This will curtail the escalation of bandwidth demand and reduce bad consequences of spectrum blockage for business and commercial communications platforms. In this paper, we studied a comparative spectrum-sharing scheme for radars and LTE mobile communications systems. An approach based on spatial technique was proposed to reduce signal interference of the radar at the mobile cellular communication environment. Our attention was more on reducing interferences on the radar side, where our target was to cancel and eliminate all forms of interferences, especially from the radar scheme, in a way that there is no more source of disturbance to the mobile base station of interest. We have expanded the concept by projecting signal detection of one radar system to null space interference channel of LTE mobile communication with numerous BSs. The parameter of a chosen target point was estimated and we trained the detection performances of the spectrum sharing for massive multi-input multi-output radars. We generated a statistical sensing detection estimation for targeted sensing point. We also applied the generalized likelihood ratio test (GLR) for determining whether the target point is present or not, while applying orthogonal waves and null space projection waves. The suggested spectrum-sharing algorithm can be applied in different scenarios, where massive multi-input multi-output of the radar is sharing spectrum environment with mobile LTE communications, by canceling and minimaxing all deterioration schemes in its operation.
Author Contributions: M.M.J. conceived this study and was involved in the data processing and writing of the manuscript. B.G. was involved in the data analysis and supervised the research. C.Z. and X.B. were involved in review and editing the data. All authors have read and agreed to the published version of the manuscript.