Carrier frequency offsets problem in recent DST-SC-FDMA system: Investigation and compensation

Carrier frequency offset (CFO) is a challenging problem in the uplink of the single-carrier frequency division multiple access (SC-FDMA) system. CFOs effect on the orthogonality between subcarriers and cause inter-carrier interference (ICI) and multiple access interference (MAI). This paper, analyzes the impact of the CFOs on the performance of the Discrete Sine Transform (DST) SC-FDMA (DST-SC-FDMA) system and investigates with different wireless channels, different modulation schemes and different subcarriers mapping schemes. Furthermore, an efﬁcient equalization and CFOs compensation scheme is proposed to enhance the performance of the DST- SC-FDMA system and transmit images efﬁciently over DST- SC-FDMA system. The proposed scheme combines the minimum mean square error (MMSE) equalizer and the parallel interference cancellation (PIC). The combined method is referred to as MMSE + PIC. The results show that CFOs degrades the DST-FDMA performance. The obtained results show a noticeable performance improvement of the proposed MMSE-PIC scheme over the conventional MMSE equalizer. More-over, it is found that it is possible to efﬁciently transmit wireless image using the proposed MMSE + PIC scheme,

(ICI) and Multiple Access Interference (MAI) among users [8]. Hence, the system performance gets deteriorated in the presence of ICI and MAI [9]. CFOs problem in multicarrier systems was extensively studied in the literature [10][11][12]. Feedback and compensation approaches have been proposed to reduce and mitigate the impacts of CFO when used for uplink transmission [13][14][15]. In our previous work [16], the impacts of CFO on SC-FDMA performance was investigated and analyzed with consideration of different subcarriers mapping schemes where the localized subcarrier mapping (LFDMA) and interleaved subcarrier mapping (IFDMA) schemes are used. In [17], the effect of CFOs on SC-FDMA-IDMA was investigated with considering an uncoded system and an additive white Gaussian noise channel model.
The issue of the CFOs compensation for Discrete Fourier Transform SCFDMA (DFT-SC-FDMA) and the discrete cosine transform SC-FDMA (DCT-SC-FDMA) systems was investigated in [11] and [18]. To the best of the author's knowledge, the issue of CFOs compensation for the DST-SC-FDMA system is not studied until the time of writing this paper. Moreover, image Frequency domain linear equalization and compensation are used in our scheme. For future works, it is possible to use frequency domain decision feedback equalizer (DFE) for further improvements [19]. It is also possible to extend our work for multi-input multi-output (MIMO) SC-FDMA and use DFE [20,21]. 2. The CFOs impacts on the performance of the DST-SC-FDMA system are investigated on the basis of SNR versus BER with different wireless channels, different modulation schemes, different subcarriers mapping schemes, and the proposed MMSE+PIC and MMSE compensation techniques. 3. The peak signal to noise ratio (PSNR) and the mean square error (MSE) performances of the received image over DST-SC-FDMA system with CFO presence are studied, compared and investigated with consideration of Vehicular A channel, different modulation schemes, different subcarriers mapping schemes, and MMSE and the proposed MMSE+PIC CFO compensation techniques.
The remainder of this paper is organized as follows. In Section 2, DST-SC-FDMA system model in the presence of CFOs is introduced. In section 3, the MMSE scheme is presented. Section 4 illustrates MMSE+PIC scheme. Section 5 discusses image transmission over DST-SC-FDMA system. In Section 6, simulation results are discussed. The conclusion is presented in section 7.

DST-SC-FDMA SYSTEM MODEL IN THE PRESENCE OF CFOS
In this section, we describe the uplink DST-SC-FDMA system model in presence of CFOs.
We assume U users communicating at the same time with a fixed base station (BS) through independent multipath Rayleighfading channels as shown in Figure 1. The signals that are received at BS from all users are assumed to be synchronized in the time domain. The data is modulated then N-points DST is performed at the transmitter.
The output symbols of DST are mapped using interleaved and localized mapping schemes. Afterwards, an M-points Inverse DST (IDST) is performed and a cyclic prefix (CP) of length N C is added to the resulting signal that is eventually transmitted over the wireless channel. The transmitted signal from the uth user (u = 1; 2, ….., U) can be given by [18] where S N and S −1 M are an N × N DST and an M × M IDST matrices, respectively. B u T is an M × N matrix that describes the subcarriers mapping of the uth user. M = Q.N, where Q is the maximum number of users that can transmit, simultaneously. x u is an N × 1 vector that contains the modulated symbols of the uth user. P add is an (M + N C ) × M matrix, which adds a CP of length N C . as in [18], the inputs of B u T matrix for both DST-LFDMA and DST-IFDMA can be expressed in (2) and (3), respectively. ) where I N and 0 Q×N matrices refers N×N identity matrix and Q×N all-zero matrix, respectively. u l (l = 1, 2, 3, …., N) denotes the unit column vector, of length N, with all zero entries except at l. P add can be given as follows: where At the receiver side, the received signal can be expressed as follows:r where p rem is an M × (M + N C ) matrix that removes the CP and is expressed by E u is an M × M diagonal matrix, which describes the CFO of the uth user after the CP removal.ñ = P rem n andX u = P remx u are the noise and the transmitted signal after the CP removal, respectively. H u C is an M × M circulant matrix describing the channel of the uth user.
A receiver transforms the received signal into the frequency domain via an M-points DFT as follows: where Γ u cir = F M E u F −1 M is a circulant matrix that represents the interference from the uth user,X u = F MX u is an M × 1 vector that describes the transmitted samples from the uth user after the mapping process. N is the DFT ofñ. The next step is the estimation of the modulated symbols by performing demodulation processes of the FDE, the M-points IDFT and the DST-SC-FDMA. This estimation can be given bŷ wherex u is a vector N × 1 that contains the modulated symbols estimation. B u R is an N × M subcarriers demapping matrix of the uth user. The entries of B u R for both DST-LFDMA and DST-IFDMA systems are determined by using the transpose of Equations (2) and (3), respectively. W u is an M × M matrix that represents FDE of the uth user. In the last step, the decoding and the demodulation processes are performed.

THE MMSE SCHEME
MMSE scheme is shown in Figure 2. The MMSE matrix of the joint scheme can be expressed in the frequency domain by using [18]: where Γ k cir is the N × N circulant CFOs interference matrix of the kth user. The error e between the estimated symbolŝ x k = W k R and the transmitted symbolsX k can be defined as follows: The equalizer matrix of the kth user is obtained by cost function of the minimization of the mean square error (MSE) as follows: where E refers to expectation of ‖W k R −X k ‖ 2 term. The MMSE is determined by solving ∂J/∂W k = 0 as follows: where Γ k P = Γ k cir Λ k . The estimated frequency domain symbols of the kth user are transformed into time domain symbols as follows: For the proposed MMSE scheme, the inversion of an M × M matrix for each user is required, which is practically difficult for a large N. The required complexity on the order of O(M 3 ), which is large for a large number of subcarriers. However, It is important to note that most of the elements in Γ k P are zeros and this matrix can be approximated as a banded matrix [11]. Thus, the total number of operations required in the banded matrix implementation for the DST-SC-FDMA system is approximately M [16r 2 + 26r + 5], where r is the bandwidth of a banded matrix.

MMSE+PIC SCHEME
In this section, we propose a MMSE+PIC scheme which is the combination of joint MMSE equalizer and CFOs with PIC to further reduce the effect of the residual MAI on the DST-SC-FDMA system. The structure of the proposed MMSE+PIC scheme for DST-SC-FDMA system is shown in Figure 3. In this scheme, the MMSE equalizer is used to estimate the MAI interference, which is regenerated and removed from the original received signal using the PIC in the frequency domain.
The algorithm of the proposed MMSE+PIC scheme for uplink DST-SC-FDMA system can be summarized as follows: Algorithm: 1. Remove CP from the received signal by using (7). 2. Apply DFT to the output signal using (9). 3. Apply joint MMSE scheme to estimate the samples for each user using (10). 4. Transform frequency domain estimates of the interfering users' samples into time domain symbols and M-point DST, subcarrier demaping, N-point IDST and the decision function f dec , hard decision function, is applied as follows: 5. Regenerate MAI in the frequency domain as follows: 6. Subtract MAI from Rto get the frequency domain interference-free signal as follows: 7. Estimate the frequency domain samples by applying the MMSE scheme, N-point IDFT, M-point DST, subcarrier demapping and N-point IDST on the interference-free signal R u free as follows: 8. Finally, apply the demodulation, and decoding processes to provide a better estimate of the desired data.
The main advantage of the proposed MMSE+PIC scheme is its better BER performance, even at high CFOs. However, the complexity of the receiver as compared with the MMSE receiver, which is the base station, will be increased.

IMAGE TRANSMISSION
For more investigation and in order to evaluate the proposed cancellation technique over DST-SC-FDMA, multi-user image transmission has been conducted in terms MSE and PSNR metrics. The quality of the reconstructed image with the original transmitted image is compared. The standard image "Cameraman image" will be transmitted over DST-SC-FDMA system with different basis functions, different subcarriers mapping schemes, different modulation schemes, and MMSE and MMSE+PIC compensation techniques. PSNR is the ratio between the maximum possible power of a signal and the power of the corrupting noise that affects the fidelity of this signal. It can be given by the following formula [12]: where f 2 max is the maximum pixel value in the image. On the other hand, the MSE is can be obtained as follows [12]: where M is number of pixels and I o and I r are the transmitted and the received images, respectively. The transmitted Cameraman image for all users of size 256 × 256 is shown in Figure 4.

SIMULATION RESULTS
Experiments and results have been carried out by using MAT-LAB simulator to mainly study the effectiveness of CFOs on

Simulation parameters
Uplink DST-SC-FDMA system with 128 subcarriers are considered. In these systems, four users are assumed with 32 subcarriers allocation to each user. QPSK and 16-QAM mapping are employed for data symbols of all users. The vehicular A and SUI3 models are used as channel models. The channel code that is used for the simulation is convolutional code with memory length 7 and octal generator polynomials (133,171). The simulation parameters are listed in Table 1.      better BER performance than the MMSE scheme and its performance is close to the system without CFOs. This is due to the ability of the MMSE+PIC scheme to effectively eliminate the MAI. It can be also seen that the MMSE+PIC scheme for the DST-LFDMA system that shown in Figure 8 provides the same BER performance as without CFOs, while  for the DST-IFDMA system it suffers 1.5 dB loss in the BER performance at (10 −4 ) as compared to that without CFOs shown in Figure 7. Furthermore, it is noted that MMSE scheme suffers 2 and 3.5 dB loss in the BER performance at (10 −4 ) for the DST-LFDMA and DST-IFDMA systems, respectively, as compared to that without CFOs. In the DST-IFDMA system that are shown in Figure 7, for BER = 10 −4 , the SNR values equal 20 and 22 dB for MMSE+PIC and MMSE, respectively whereas in the DST-LFDMA system shown in Figure 8, the SNR value equals 21.8 and 25 dB for MMSE+PIC and MMSE respectively, so the DST-IFDMA system is better than the DST-LFDMA system.

BER versus SNR simulation
For comparison purposes, the performance of the DST-IFDMA and DST-LFDMA system over SUI3 channel are simulated in Figures 9 and 10, respectively. It is clear that the DST-SC-FDMA system performance by using SUI3 channel is better than using a Vehicular A channel. In the DST-IFDMA system that are shown in Figure 9, for BER = 10 −4 , the SNR values equal 14 dB and 19 dB for MMSE+PIC and MMSE, respectively, whereas in the DST-LFDMA system that shown in Figure 10, the SNR values equal 17 dB for both schemes which is more better than that in a Vehicular A channel.  The performance of the DST-IFDMA and DST-LFDMA system over a Vehicular A channel for 16-QAM Modulation scheme are shown in Figures 11 and 12, respectively. From Figure 12, it can be observed that the MMSE+PIC scheme for the DST-LFDMA system provides the same BER performance as without CFOs, while for the DST-IFDMA system it suffers 2 dB loss in the BER performance at BER = 10 −2 as compared to that without CFOs as shown in Figure 11. Furthermore, it is noted that the MMSE scheme suffers 0.3 dB loss in the BER performance at BER = 10 −2 for the DST-LFDMA and about 4 dB loss in the BER performance at BER = 10 −1 and more than that at BER = 10 −2 for the DST-IFDMA systems as compared to that without CFOs. As compared to QPSK modulation that is shown in Figures 7  and 8, it is clear that the QPSK modulation type has the best BER performance but it is known that the data rate of 16-QAM modulation is the best. So, there is a trade-off between the high data rate and the good performance. At an SNR = 20 dB, the BER = 3 × 10 −2 and 10 −1 for the MMSE+PIC and MMSE scheme in the DST-IFDMA system as shown in Figure 11, respectively. For the DST-LFDMA system that is shown in Figure 12, the BER for the MMSE+PIC scheme is equal to  2.5×10 −2 but for the MMSE scheme it is equal to 3 × 10 −2 so the localized system is better than the interleaved system. Figures 13 and 14 show the performance of the DST-IFDMA and DST-LFDMA systems for 16-QAM modulation scheme over SUI3 channel, respectively. It is noted that the performance of the DST-SC-FDMA system over SUI3 channel is better than that in the Vehicular A channel. At an SNR = 20 dB, the BER = 4 × 10 −3 and 3 × 10 −2 for the MMSE+PIC and MMSE scheme in the DST-IFDMA system, respectively. For the DST-LFDMA system the BER for the MMSE+PIC scheme is the same as that in the DST-IFDMA system but for the MMSE scheme it is equal to 6 × 10 −3 which is better than in a Vehicular A channel that shown in Figures 11 and 12.

PSNR performance
As mentioned, for more investigation and in order to evaluate the proposed cancellation technique over DST-SC-FDMA, image transmission has been conducted in terms of MSE and PSNR metrics. For this purpose, Cameraman image has been transmitted over the coded DST-SC-FDMA system in the presence of CFOs with considering Vehicular A channel model, dif-  Tables 2 and 3 for QPSK and 16-QAM modulation schemes and illustrated in Figures 15 and 16, respectively. Figures 15 and 16 show the relationship between PSNR and SNR when Cameraman image is transmitted through the DST-SC-FDMA system for different subcarriers mapping schemes when QPSK and 16-QAM modulation schemes are used, respectively. As illustrated in both figures, it is observed that PSNR increased as SNR increased. Clearly, it is observed that the interleaved system gives better PSNR performance than the localized system for both CFOs compensation schemes when the QPSK is used as shown in Figure 15. Adversely, it is noted that the localized system gives better PSNR performance than the interleaved system when 16-QAM is used as shown in Figure 16. It can be also seen that the MMSE+PIC scheme provides better performance than the MMSE scheme. As compared to the 16-QAM modulation scheme, the QPSK modulation scheme has the best PSNR performance.

MSE performance
In this section, the MSE performance is examined and investigated. As in PNSR performance evaluation, Cameraman image has been transmitted over the coded DST-SC-FDMA system in the presence of CFOs with considering Vehicular A channel model, different subcarriers mapping schemes, QPSK and 16-QAM modulation schemes, and MMSE and MMSE+PIC compensation techniques. The obtained values of MSE are tabulated in Tables 4 and 5 and illustrated in Figures 17 and 18, respectively. Figures 17 and 18 illustrate the relationship between MSE and SNR when Cameraman image is transmitted through the considered system. It is observed that the MSE decreases when SNR increases. However, it is observed that the interleaved systems give lower values of MSE than the localized systems when the QPSK is used. In contrary, it is observed that the localized systems give lower values of MSE than the interleaved systems when the 16-QAM is used. It can be also seen that the MMSE+PIC scheme gives better performance than the MMSE scheme. As compared to the 16-QAM modulation scheme, the QPSK modulation scheme has the best MSE performance.

Clarity investigation
To investigate the clarity of the received images over the considered system, the received images at an SNR = 25 dB are selected. Figure 19 shows the received images of the DST-SC-FDMA system without CFOs for QPSK and 16-QAM.
To clarify the quality of the received image over the system, the reconstructed images at an SNR = 25 dB with QPSK and 16-QAM are shown in Figures 20 and 21, respectively. By comparing the received images with the images shown   Figure 19, it is concluded that the quality of the received image by using the MMSE-PIC scheme to compensate the CFOs is better than those images that are received by using the MMSE scheme. It is clear that the QPSK modulation scheme has better quality than the 16-QAM modulation scheme. It can be also seen that the interleaved system is better than the localized system when the QPSK is used but the localized system is better than the interleaved system when the 16-QAM is used.

CONCLUSION
This paper investigated the performance of the DST-SC-FDMA system in the presence of CFOs for different wireless channels, QPSK and 16-QAM modulation schemes, and different subcarriers mapping. CFOs compensation scheme has also been proposed that are referred to as MMSE+PIC. For more comparison, the obtained results with the MMSE scheme, without CFO and without CFO compensation have been simulated. It has been found that the performance of the DST-SC-FDMA degrades due to the CFOs and an efficient CFOs compensation scheme must be used. Simulation results have shown that the proposed MMSE+PIC improves the performance of the DST-SC-FDMA system for different modulation schemes, different wireless channels and different subcarriers mapping. Results also showed that the performance of the DST-IFDMA system is better than that of the DST-LFDMA system when QPSK is used but when 16-QAM is used, the performance of the DST-LFDMA system is better than that of the DST-IFDMA system. For more evaluation, the performance of the DST-SC-FDMA system in the presence of CFOs has been tested with image transmission over a Vehicular A channel for different scenarios. The obtained results show a noticeable performance improvement of the proposed MMSE+PIC scheme over the conventional MMSE scheme. This indicates that it is possible to efficiently transmit images over DST-SC-FDMA using the proposed MMSE+PIC scheme.

FIGURE 19
Received Images for DST-SC-FDMA system without CFOs at an SNR = 25 dB