Flexible Transmission Scheme for 4G Wireless Systems with Multiple Antennas

New air interfaces are currently being developed to meet the high requirements of the emerging wireless communication systems. In this context, the combinations of the multicarrier (MC) and spread-spectrum (SS) technologies are promising candidates. In this paper, we propose a generic transmission scheme that allows to instantiate all the combinations of orthogonal frequency-division multiplexing (OFDM) and cyclic-preﬁxed single-carrier (SC) modulations with direct-sequence code-division multiple access (DS-CDMA). The generic transmission scheme is extended to integrate the space-division multiplexing (SDM) and the orthogonal space-time block coding (STBC). Based on a generalized matrix model, the linear frequency-domain minimum mean square error (MMSE) joint detector is derived. A mode selection strategy for up-and downlink is advised that e ﬃ ciently trades o ﬀ the cost of the mobile terminal and the achieved performance of a high-mobility cellular system. It is demonstrated that an adaptive transceiver that supports the proposed communication modes is necessary to track the changing communication conditions.


INTRODUCTION
Because of the limited frequency bandwidth, on the one hand, and the potential limited power of terminal stations, on the other hand, spectral and power efficiency of future systems should be as high as possible.New air interfaces need to be developed to meet the new system require-This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.ments.Combinations of the multicarrier (MC) and spreadspectrum (SS) modulations, named multicarrier spreadspectrum techniques, could be interesting candidates.They might benefit from the main advantages of both MC and SS schemes such as high spectral efficiency, multiple-access capabilities, narrowband interference rejection, simple one-tap equalization, and so forth.
Cellular systems of the third generation are based on the recently emerged direct-sequence code-division multiple-access (DS-CDMA) technique [1].Intrinsically, DS-CDMA has interesting networking abilities.First, the communicating users do not need to be time synchronized in the uplink.Second, soft handover is supported between two cells making use of different codes at the base stations.However, the system suffers from intersymbol interference (ISI) and multiuser interference (MUI) caused by multipath propagation, leading to a high loss of performance.
The use of the orthogonal frequency-division multiplexing (OFDM) modulation is widely envisaged for wireless local area networks [2].At the cost of the addition of a cyclic prefix, the time dispersive channel is seen in the frequency domain as a set of parallel independent flat subchannels and can be equalized at a low-complexity.An alternative approach to OFDM, that benefits from the same low complexity equalization property, is single-carrier block transmission (SCBT), also known as single-carrier (SC) with frequency-domain equalization.Since the SCBT technique benefits from a lower peak-to-average power ratio (PAPR), [3] encourages the use of SCBT in the uplink and OFDM in the downlink in order to reduce the constraints on the analog front end and the processing complexity at the terminal.
There are potential benefits in combining OFDM (or SCBT) and DS-CDMA.Basically the frequency-selective channel is first equalized in the frequency domain using the OFDM modulation technique.DS-CDMA is applied on top of the equalized channel, keeping the interesting orthogonality properties of the codes.The DS-CDMA signals are either spread across the OFDM carriers (referred to as intrablock spreading) leading to multicarrier CDMA (MC-CDMA) [4,5,6,7], or across the OFDM blocks (referred to as interblock spreading) leading to multicarrier block-spread CDMA (MCBS-CDMA) [8,9,10,11].The SCBT counterparts named here single-carrier CDMA (SC-CDMA) and single-carrier block-spread CDMA (SCBS-CDMA) have also been proposed in [12,13,14,15], respectively.The different flavors to mix the MC and SS modulations complement each other and allow to make an efficient tradeoff between the spectral and power efficiency according to the user requirements, channel propagation characteristics (time and frequency selectivity), and terminal resources.For example, it has been recently proposed, in [16] for the downlink, and in [17] for the uplink, to perform a two-dimensional spreading (combination of MC-CDMA with MCBS-CDMA) in order to cope with the time and frequency selectivity of the channels.The chips of a given symbol are mapped on adjacent channels where the fading coefficients are almost constant so that the orthogonality properties of the codes are preserved and a low-complexity single-user detector can be used.
To meet the data rate and quality-of-service requirements of future broadband cellular systems, their spectral efficiency and link reliability should be considerably improved, which cannot be realized by using traditional singleantenna communication techniques.To achieve these goals, multiple-input multiple-output (MIMO) systems, which deploy multiple antennas at both ends of the wireless link, exploit the extra spatial dimension, besides the time, frequency, and code dimensions, which allows to significantly increase the spectral efficiency and/or to significantly improve the link reliability relative to single-antenna systems [18,19,20].MIMO systems explicitly rely on the fact that the channels created by the additional spatial dimension are independent from each other.This is approximately true in rich scattering environments.However, when the channels are correlated, the gain obtained by the use of multiple antennas is limited.Until very recently, the main focus of MIMO research was on single-user communications over narrowband channels, thereby neglecting the multiple-access aspects and the frequency-selective fading channel effects, respectively.
First, if the multiantenna propagation channels are sufficiently uncorrelated, MIMO systems can create N min parallel spatial pipes, which allows to realize an N min -fold capacity increase, where N min = min {N T , N R } (N T and N R denote the number of transmit and receive antennas, resp.) is called the spatial multiplexing gain [18,19,20].Specifically, space-division multiplexing (SDM) techniques exploit this spatial multiplexing gain, by simultaneously transmitting N min independent information streams at the same frequency [21,22].In [23], SDM is combined with SC-CDMA to increase the data rate of multiple users in a broadband cellular network.
Second, MIMO systems can also create N T N R independently fading channels between the transmitter and the receiver, which allows to realize an N T N R -fold diversity increase, where N T N R is called the multiantenna diversity gain.Specifically, space-time coding (STC) techniques exploit diversity and coding gains, by encoding the transmitted signals not only over the temporal domain but also over the spatial domain [24,25,26].Space-time block coding (STBC) techniques, introduced in [25] for N T = 2 transmit antennas, and later generalized in [26] for any number of transmit antennas, are particularly appealing because they facilitate maximum-likelihood (ML) detection with simple linear processing.However, these STBC techniques have originally been designed for frequency-flat fading channels exploiting only multiantenna diversity of order N T N R .Therefore, timereversal (TR) STBC techniques, originally proposed in [27] for single-carrier serial transmission, have been combined with SCBT in [28,29] for signaling over frequency-selective fading channels.In [30,31], the TR-STBC technique of [28] is combined with SC-CDMA to improve the performance of multiple users in a broadband cellular network.Although this technique enables low-complexity chip equalization in the frequency domain, it does not preserve the orthogonality among users, and hence, still suffers from multiuser interference.The space-time coded multiuser transceiver of [32], which combines the TR-STBC technique of [29] with SCBS-CDMA, preserves the orthogonality among users as well as transmit streams, regardless of the underlying multipath channels.This allows for deterministic ML user separation through low-complexity code-matched filtering as well as deterministic ML transmit stream separation through linear processing.Another alternative to remove MUI deterministically in a space-time coded multiuser setup [33,34] combines generalized multicarrier (GMC) CDMA, originally developed in [35], with the STBC techniques of [26] but implemented on a per-carrier basis.

Interblock spreading
IFFT redundancy We propose a transmission chain composed of generic blocks and able to instantiate all the communication modes combining OFDM/SCBT and DS-CDMA as special cases.In contrast with the transceiver proposed in [35,36,37] that relies on a sharing of the set of carriers to retain the orthogonality between the users, our transmission scheme relies on orthogonal CDMA, and thus inherits the nice advantages of CDMA related to universal frequency reuse in a cellular network, like increased capacity and simplified network planning.Furthermore, the focus is especially put on the communication modes emerging in the standards.We demonstrate the rewarding synergy between existing and evolving MIMO communication techniques and our generic transmission technique, which allows to increase the spectral efficiency and to improve the link reliability of multiple users in a broadband cellular network.Considering realistic propagation channels, we also advise a strategy for mode selection according to the communication conditions, making an efficient tradeoff between the desired performance and the required computational complexity.
The paper is organized as follows.In Section 2, the generic transmission scheme is presented that can capture the standard emerging communication modes as special cases.It is shown how the MC and SC modes can be instantiated.Section 3 is devoted to the extension of the transmission scheme introduced in Section 2 to multiple-antenna systems.Both SDM and STBC multiple-antenna techniques are considered.A low-complexity minimum mean square error (MMSE) receiver is designed in Section 4 based on a generalized matrix model.Finally, a strategy for communication mode selection is proposed in Section 5, based on the evaluation of the cost and performance of each mode in a highly mobile cellular environment.
In the sequel, we use single-and double-underlined letters for the vectors and matrices, respectively.Matrix I N is the identity matrix of size N and matrix 0 M×N is a matrix of zeros of size M × N. The operators (•) * , (•) T , and (•) H denote, respectively, the complex conjugate, transpose, and transpose conjugate of a vector or a matrix.The operator ⊗ is the Kronecker product between two vectors or matrices.We index the transmitted block sequence by i, the MIMO coded block sequence and the intrablock chip block sequence by j, and the interblock chip block sequence by n.

SINGLE-ANTENNA GENERIC TRANSMISSION SCHEME
The transmission scheme for the mth user (m = 1, . . ., M) is depicted in Figure 1.Since we focus on a single-user transmission, the transmission scheme applies to both the up-and downlink.In the uplink, the different user's signals are multiplexed at the receiver, after propagation through their respective multipath channels.In the downlink, the different user signals are multiplexed at the transmitter, before the inverse fast Fourier transform (IFFT) operation.The transmission scheme comprises four basic operations: intrablock spreading, interblock spreading, IFFT, and adding transmit redundancy.The symbols s m [ j] are first serial-to-parallel converted into blocks of B symbols, leading to the sequence The blocks s m [ j] are linearly precoded with a Q × B (Q ≥ B) matrix, θ m , which possibly introduces some redundancy and spreads the symbols in s m [ j] with length-Q codes as follows: ( We refer to this first operation as intrablock spreading, since the information symbols s m [ j] are spread within a single precoded block sm [ j].The precoded block sequence sm [ j] is then block spread with the elements c m [n] of a length-N inter code sequence, leading to N inter successive chip blocks: where j = n/N inter .We refer to this second operation as interblock spreading, since the information symbols s m [ j] are spread along N inter different chip blocks.The third operation involves the transformation of the frequency-domain chip block sequence xm [n] into the time-domain chip block sequence: where F H Q is the Q×Q IFFT matrix.Finally, the K×Q (K ≥ Q) transmit matrix T possibly adds some transmit redundancy to the time-domain chip blocks: With , and transmitted over the air at a rate 1/T c (T c stands for the chip duration).
In the following, we will detail how our generic transmission scheme instantiates different communication modes, and, thus, supports different emerging communication standards.We distinguish between the MC modes, on the one hand, and the SC modes, on the other hand.In Figure 2, the principle of CDMA spreading in two possible dimensions is illustrated.

Instantiation of the multicarrier modes
The MC modes always comprise the IFFT operation, and add transmit redundancy in the form of a cyclic prefix (T = T cp ).The MC modes comprise MC-CDMA and MCBS-CDMA as particular instantiations of the generic transmission scheme.

MC-CDMA
As we have indicated in the introduction, MC-CDMA first performs classical DS-CDMA symbol spreading, followed by OFDM modulation, such that the information symbols are spread across the different subcarriers located at different frequencies and characterized by a different fading coefficient [4,5,6].With Q = BN intra and N intra the intrablock spreading code length, the Q × B intrablock spreading matrix θ m = β m spreads the chips across the subcarriers, where the mth user's Q × B spreading matrix β m is defined as with The interblock spreading operation is discarded by setting N inter = 1.Since intrablock spreading does not preserve the orthogonality among users in a frequency-selective channel, MC-CDMA requires advanced multiuser detection for uplink reception in the base station, and frequency-domain chip equalization for downlink reception in the mobile station.MC-CDMA has been proposed as a candidate air interface for future broadband cellular systems [7].

MCBS-CDMA
The MCBS-CDMA transmission scheme is the only MC mode that comprises the interblock spreading operation N inter > 1.Since the CDMA spreading is applied on each carrier independently, which can be seen as a constant fading channel if the propagation environment is static, MCBS-CDMA retains the orthogonality among users in both upand downlink [11].Hence, it has the potential to convert a difficult multiuser detection problem into an equivalent set of simpler and independent single-user equalization problems.However, it will be shown in Section 5 that the performance of MCBS-CDMA is highly degraded under mediumto-high mobility conditions since the orthogonality between the users is lost in that case.In case no channel state information (CSI) is available at the transmitter, it performs linear precoding to robustify the transmitted signal against frequency-selective fading.In case CSI is available at the transmitter, it allows to optimize the transmit spectrum of each user separately through adaptive power and bit loading.Note that classical MC-DS-CDMA can be seen as a special case of MCBS-CDMA, because it does not include linear precoding, but, instead, only relies on bandwidth-consuming forward error correction (FEC) coding to enable frequency diversity [8,10,38].

Instantiation of the single-carrier modes
The SC modes employ a fast Fourier transform (FFT) as part of the intrablock spreading operation to annihilate the IFFT operation.For implementation purposes, however, the IFFT is simply removed (and not compensated by an FFT), in order to minimize the implementation complexity.The SC modes rely on cyclic prefixing (T = T cp ) to make the channel appear circulant.The SC modes comprise SC-CDMA and SCBS-CDMA as particular instantiations of the generic transmission scheme.

SC-CDMA
The SC-CDMA transmission scheme, which combines SCBT with DS-CDMA, can be interpreted as the SC counterpart of MC-CDMA [12,13].This mode is captured through our general transmission scheme, by setting Q = BN intra .The intrablock spreading matrix θ m = F Q • β m , with β m defined in (5), performs symbol spreading on the B information symbols, followed by an FFT operation to compensate for the subsequent IFFT operation.Like MC-CDMA, SC-CDMA does not preserve the orthogonality among the users in a frequency-selective channel.It requires advanced multiuser detection for uplink reception at the base station and chip equalization for downlink reception at the mobile terminal.On the contrary to MC-CDMA, each user symbol is spread amongst multiple subchannels of the same power attenuation.The interblock spreading operation is left out by setting N inter = 1.

SCBS-CDMA
The SCBS-CDMA transceiver can be considered as the SC counterpart of MCBS-CDMA.It is the only SC mode that entails the interblock spreading operation (N inter > 1).The intrablock spreading matrix θ m = F Q only performs an FFT operation to compensate for the subsequent IFFT operation.
If the propagation channels are static, SCBS-CDMA retains the orthogonality among users in both the up-and downlink, even after propagation through a frequency-selective channel (like MCBS-CDMA).It also converts a difficult multiuser detection problem into an equivalent set of simpler and independent single-user equalization problems.The orthogonality property is however lost in time-selective channels, as studied numerically in Section 5.

EXTENSION TO MULTIPLE ANTENNAS
The generic transmission model is extended in Figure 3 to include two types of MIMO techniques.We assume N T antennas at the transmit side and N R antennas at the receive side.The information symbols d m nT [i], which are assumed independent and of variance equal to σ 2 d , are first serial-toparallel converted into blocks of B symbols, leading to the block sequence A MIMO coding operation is performed across the different transmit antenna streams, that results into the N T antenna sequences s m nT [ j] input to the generic transmission scheme.The overall rate increase obtained by the use of multiple antennas is either 1 or N T depending on the MIMO technique that is selected.

Space-division multiplexing
In this section, we combine our generic transmission scheme with SDM, which allows to instantiate all combinations of SDM with OFDM/SCBT and CDMA as special cases.The SDM technique is implemented by sending independent streams on each transmit antenna n T , as expressed in where j = i.

Space-time block coding
In this section, we combine our generic transmission scheme with STBC, which allows to instantiate all combinations of STBC with OFDM/SCBT and CDMA as special cases.For conciseness, we limit ourselves to the case of N T = 2 transmit antennas (Alamouti scheme [25,27]).The STBC coding is implemented by coding the two antenna streams across two time instants, as expressed in , where i = j/2 and In the case of the MC modes, the STBC coding is applied in the frequency domain on a per-carrier basis so that In the case of the SC modes, the STBC coding is applied in the time domain by further permuting the vector elements so that is a B × B permutation matrix implementing a time reversal.It is easily checked that the transmitted block at time instant j + 1 from one antenna is the time-reversed conjugate of the transmitted symbol at time instant j from the other antenna (with possible permutation and sign change).As we will show later, this property allows the deterministic transmit stream separation at the receiver, regardless of the underlying frequency-selective channels.

Cyclostationarization of the channels
Adopting a discrete-time baseband equivalent model, the chip-sampled received signal at antenna n R (n R = 1, . . ., N R ), v nR [n], is the superposition of a channel-distorted version of the MN T transmitted user signals, which can be written as where h m nR,nT [l] is the chip-sampled finite impulse response (FIR) channel of order L m that models the frequencyselective multipath propagation between the mth user's antenna n T and the base station antenna n R , including the effect of transmit/receive filters and the remaining asynchronism of the quasisynchronous users, and w nR [n] is additive white Gaussian noise (AWGN) at the base station antenna n R with variance σ 2 w .Furthermore, the maximum channel order L, that is, L = max m {L m }, can be well approximated by L ≈ (τ max,a + τ max,s )/T c + 1, where τ max,a is the maximum asynchronism between the nearest and the farthest user of the cell, and τ max,s is the maximum excess delay within the given propagation environment [35].
Assuming perfect time and frequency synchronization, the sequence From the scalar input/output relationship in (11), we can derive the corresponding block input/output relationship: where else, and H m nR,nT [1] is a K × K upper triangular Toeplitz matrix with entries [H m nR,nT [1]] and [H m nR,nT [1]] p,q = 0 else (see, e.g., [35] for a detailed derivation of the single-user case).The delay-dispersive nature of multipath propagation gives rise to so-called interblock interference (IBI) between successive blocks, which is modeled by the second term in (12).The Q × K receive matrix R removes the redundancy from the chip blocks, that is, R again discards the length-L cyclic prefix.The purpose of the transmit/receive pair is twofold.First, it allows for simple block-by-block processing by removing the IBI, that is, R•H m nR,nT [1]•T = 0 Q×Q , provided the CP length to be at least the maximum channel order L. Second, it enables low-complexity frequency-domain processing by making the linear channel convolution to appear circulant to the received block.This results in a simplified block input/output relationship in the time domain: where [n] is the corresponding noise block sequence.Note that circulant matrices can be diagonalized by FFT operations, that is, where Λ m nR,nT is a diagonal matrix composed of the frequencydomain channel response between the mth user's antenna n T and the base station antenna n R .

Matrix model
Based on (13), a generalized matrix model is developed that relates the vector of transmitted user's symbols to the vector of received samples.It encompasses all the combinations of OFDM/SCBT with CDMA considered in this paper as special cases.Based on this model, a multiuser joint detector optimized according to the MMSE criterion will be derived and its complexity will be reduced by exploiting the cyclostationarity properties of the matrices.
The generalized input/output matrix model that relates the MIMO-coded symbol vector defined as T T (14) with for m = 1, . . ., M to the received and noise vectors defined as for n R = 1, . . ., N R , is given by ȳ where the channel matrix is defined as with for m = 1, . . ., M and n R = 1, . . ., N R , and the intrablock spreading, Fourier, and interblock spreading matrices are defined, respectively, as in which Note that the model ( 18) only holds for static channels.In case of time-selective channels, the channel matrices Ḣm nR,nT cannot be diagonalized anymore and are different from one chip block to the next one.

Space-division multiplexing
Taking (6) into account, the model ( 18) is instantiated to the SDM input/output matrix model where the vector of transmitted symbols is defined as with T T (25) for m = 1, . . ., M, and the received and noise vectors are defined as The MIMO encoding, intrablock spreading, channel, Fourier, and interblock spreading matrices are, respectively, given by

Space-time block coding
Taking (7) into account, the model ( 18) is instantiated to the STBC input/output matrix model where the vector of transmitted symbols is given in (25) assuming that N T = 2, the received and noise vectors are defined as The MIMO encoding, intrablock spreading, channel, Fourier, and interblock spreading matrices are, respectively, given by (30)

Multiuser joint detector
In order to detect the transmitted symbol block of the pth user dp [i] based on the received sequence of blocks within the received vector ȳmode [i] ("mode" stands for "sdm" or "stbc"), a first solution consists of using a single-user receiver that inverts successively the channel and all the operations performed at the transmitter.The single-user receiver relies implicitly on the fact that CDMA spreading has been applied on top of a channel equalized in the frequency domain.After CDMA despreading, each user stream is handled independently.However the single-user receiver fails in the uplink where multiple channels have to be inverted at the same time.
The optimal solution is to jointly detect the transmitted symbol blocks of the different users within the transmitted vector d[i] based on the received sequence of blocks within the received vector ȳmode [i].The optimum linear joint detector according to the MMSE criterion is computed in [39].At the output of the MMSE multiuser detector, the estimate of the transmitted vector is where The MMSE linear joint detector consists of two main operations [39,40].(i) First, a filter matched to the composite impulse responses multiplies the received vector in order to minimize the impact of the white noise.The matched filter consists of the CDMA interblock despreading, the FFT operator to move to the frequency domain, the maximum ratio combining (MRC) of the different received antenna channels, the CDMA intrablock despreading, the IFFT to go back to the time domain in case of the SC modes, and the STBC decoding.
(ii) Second, the output of the matched filter is still multiplied with the inverse of the composite impulse response autocorrelation matrix of size MN T B that mitigates the remaining intersymbol, interuser, and interantenna interference.
In the case of interblock spreading (MCBS and SCBS-CDMA), the spreading matrix C has the property that C H C = I NRQM if the CDMA codes are chosen orthogonal.When the propagation channels are static, the different user streams are perfectly separated at the output of the interblock despreading operation and further treated independently.The MMSE multiuser joint detector exactly reduces to independent single-user detectors.In case of time-varying propagation channels, model ( 18) is not valid anymore and the multiuser MMSE joint detector cannot be simplified to single-user detectors.
In the case of intrablock spreading (MC-and SC-CDMA), however, the linear MMSE receiver is different from the single-user receiver, and suffers from a higher computational complexity.Fortunately, both the initialization complexity, which is required to compute the MMSE receiver, and the data processing complexity can be significantly reduced for MC-and SC-CDMA, by exploiting the initial cyclostationarity property of the channels.Based on a few permutations and on the properties of the block circulant matrices given in [12], it can be shown that the initial inversion of the square autocorrelation matrix of size MN T B can be replaced by the inversion of B square autocorrelation matrices of size MN T .

MODE SELECTION STRATEGY
In this section, a cost and performance comparison between the different communication modes is made, which can serve as an input for an efficient mode selection strategy.

Complexity
To evaluate the complexity of the different receivers, we distinguish between the initialization phase, when the receiver is calculated, and the data processing phase, when the received data is actually processed.The rate of the former is related to the channel's fading rate, whereas the latter is executed continuously at the symbol block rate.The complexity will be described in terms of complex multiply/accumulate cycle (MAC) operations.It is assumed that 2N 3 complex MAC operations are required to invert a matrix of size N, and that N log 2 (N) complex MAC operations are required to compute an FFT of size N.

Initialization complexity
The complexity required to compute the MMSE receiver is given in Table 1 for the base station and for the terminal, respectively.It has been assumed that the inversion of the MMSE equalizer block diagonal inner matrix is dominant.Since the size of each block is equal to the number of interfering users times the number of interfering antennas, the computation of the equalizer is more complex in case of intrablock spreading (number of interfering users equal to the number of users) than in case of interblock spreading (number of interfering users equal to one), and in case of SDM (number of interfering antennas equal to the number of transmit antennas) than in case of STBC (number of interfering antennas equal to one).

Data processing complexity
The complexity needed during the data processing phase to transmit and receive each user's transmitted complex symbol is further given in the Table 2.The computational effort is almost equally shared between the transmitter and the receiver in the case of the MC-based modes.In the case of the SCbased modes, all the computational effort has been moved to the receiver.From a terminal complexity point of view, it is clearly advantageous to use the SC-based modes in uplink and the MC-based modes in downlink.Both the transmission and the reception are less complex in case of interblock spreading than in case of intrablock spreading, because the (I) FFT operators can be executed at a lower rate in the former case (namely, before the spreading at the transmitter and after the despreading at the receiver).Since STBC combines N T successive symbol blocks, it is on the overall more complex than the SDM scheme.

Peak-to-average power ratio
The PAPR is illustrated in Figure 4 for each mode as a function of the spreading factor.The user signals are spread by periodic Walsh-Hadamard codes for spreading, which are overlaid with an aperiodic Gold code for scrambling.QPSK modulation is assumed with Q = 128 subchannels, and a cyclic prefix length of L = 32.The PAPR is defined as the maximum instantaneous peak power over all combinations of the transmitted symbols divided by the average transmit power.
While the MC-based communication modes feature a very large PAPR, the SC-based communication modes have Table 2: Data processing complexity, M users (M = 1 at the terminal), N T transmit antennas, N R receive antennas, Q carriers/subchannels, B complex symbols per block.a PAPR close to 0 dB.MC-CDMA has a PAPR improving for an increasing spreading factor due to the fact that the total number of possible chip combinations at the output of the spreading operation is decreasing.The use of the SC-based communication modes is encouraged in the uplink to reduce the power amplifier backoff at the mobile terminal and, thus, to increase its power efficiency (even if the power amplifier backoff is not directly settled based on the low probability power peak values in the MC-based systems, it is expected that the variation in instantaneous transmitted power is much lower in the SC-based systems).

Goodput performance
We consider a mobile cellular system which operates in an outdoor suburban macrocell propagation environment.The channel model is largely inspired from the 3 GPP TR25.996 geometrical spatial channel model [41].The radius of the cell is equal to 3 km.The mobile terminals are moving at a speed ranging from 0 (static) to 250 km/h (highly mobile).
The system operates at a carrier frequency of 2 GHz, with a system bandwidth of 5 MHz.Linear antenna arrays are assumed at the mobile terminals and at the base station.An antenna spacing equal to 0.5 wavelength is selected at the mobile terminals, which results in a correlation equal to 0.2 between the antennas, and an antenna spacing equal to 5 wavelengths is selected at the base station, which results in a correlation smaller than 0.1 between the antennas.We assume a six-sector antenna at the base station and omnidirectional antennas at the mobile terminals.The propagation environment is characterized by a specular multipath composed of 6 paths (each path represents the reflection on a scatterer) and 10 subpaths per path (each subpath represents the reflection on a specific part of the scatterer).For each path, the excess delay standard deviation is equal to 238 nanoseconds, the angle spread standard deviation at the base station and that at the mobile terminals are equal to 6 and 68 degrees, respectively.For each subpath, the angle spread standard variation at the base station and that at the mobile terminals are equal to 2 and 5 degrees, respectively.The computation of the path loss is based on the COST231 Hata urban propagation model.
Monte Carlo simulations have been performed to average the bit error rate (BER) over 500 stochastic channel realizations, and to compute the corresponding goodput, defined as the throughput offered to the user assuming a retransmission of the erroneous packets until they are correctly received.The information bandwidth is spread by the spreading factor equal to 8. The user signals are spread by periodic Walsh-Hadamard codes for spreading, which are overlaid with an aperiodic Gold code for scrambling.QPSK, 16-QAM, or 64-QAM modulation is used with Q = 128 subchannels, and a CP length of L = 32.We assume a packet size of 512 complex symbols (4 blocks of 128 symbols in case of MCBS/SCBS-CDMA or 32 blocks of 16 symbols in case of MC/SC-CDMA).Convolutional channel coding in conjunction with frequency-domain interleaving is employed according to the IEEE 802.11a/g standard.The code rate varies from 1/2, 2/3, to 3/4.At the receiver, soft-decision Viterbi decoding is used.
We distinguish between the uplink and the downlink.In the uplink, transmit power control is applied such that the received symbol energy is constant for all users.The power transmitted by each terminal depends on the actual channel experienced by it.The BER (or the goodput) is determined as a function of the received bit energy, or, equivalently, as a function of the transmit power averaged over the different channel realizations.In the downlink, no transmit power control is applied.For a constant transmit power at the base station, the received symbol energy at each terminal depends on the channel under consideration.The BER (or the goodput) is determined as a function of the transmit power, or, equivalently, as a function of the received bit energy averaged over the channel realizations.For a given received symbol energy, the required transmit powers for the different communication modes appear to be very similar.
Rather than comparing all possible modes for the two link directions, we only consider the relevant modes for each direction.For the uplink, the SC modes demonstrate two pronounced advantages compared to MC modes [3].First, the SC modes exhibit a smaller PAPR than the MC modes, which leads to increased terminal power efficiency.Second, the SC modes allow to move the IFFT at the transmitter to the receiver, which results in reduced terminal complexity.For the downlink, the MC modes are the preferred modulation schemes, since they only incur a single FFT operation at the receiver side which also leads to reduced terminal complexity.
Figure 5 illustrates the user's goodput in the downlink of a MCBS-CDMA-based static communication system for different combinations of the constellation size and channel coding rate.The signal is received at the terminal through 2 antennas.A typical user's load of 5 users has been assumed.Looking to those combinations that give the same asymptotic goodput (16-QAM and CR 3/4 compared to 64-QAM and CR 1/2), it is always preferable to combine a high constellation size with a low code rate.The same conclusion holds in order to select the combination constellation-coding rate that maximizes the goodput for each SNR value.The envelope is obtained by progressively employing QPSK, 16-QAM, 64-QAM constellations and a code rate equal to 1/2, and then by increasing the code rate progressively to the values 2/3, 3/4 while keeping the constellation size fixed to 64-QAM.The gain in communication robustness provided by the use of more channel coding exceeds the loss in communication  robustness due to the use of a higher constellation.As it will be shown later, the conclusion may be reversed in a mobile environment due to better robustness of lower-order mappings to changing channel conditions.
Figures 6 and 7 illustrate the gain obtained by the use of different multiple-antenna techniques in the downlink of an MCBS-CDMA-based static system and in the uplink of an SCBS-CDMA-based static system, respectively.Four different system configurations are considered (1×1, 1×2, 2×1, 2× 2).A typical user's load is assumed (number of users equal to 5).Two optimal combinations of the constellation and channel coding rate are considered (16-QAM with coding rate 1/2, 64-QAM with coding rate 3/4).Exploiting the spatial diversity at the mobile terminal or at the base station by the use of two antennas (1 × 2 or 2 × 1 configurations), MRC reception, or STBC transmission enables a significant gain in transmit power (up to 12 dB gain is achieved in the downlink, up to 7 dB gain is achieved in the uplink).However, the additional gain obtained by combining STBC transmission with MRC reception (2 × 2 configuration) is relatively small (less than 2 dB).SDM suffers from a high 8 dB loss in the goodput regions that can also be reached by a single-antenna system (this loss can be reduced if more complex nonlinear receivers are considered).One can only achieve an increase of capacity by the use of multiple antennas at very high signalto-noise ratio (SNR) values.As a result, we advise to use one directive antenna at the base station to exploit the very small angle spread and increase the cell capacity, and two diversity antennas at the mobile terminal to improve the link reliability.The receive MRC technique is performed in the downlink, while the STBC coding scheme is applied in the uplink.Figures 8 and 9 illustrate the system performance sensitivity to the user's load assuming static channels.Interblock spreading (MCBS-CDMA and SCBS-CDMA) is compared to intrablock spreading (MC-CDMA and SC-CDMA).The number of users ranges from 1 to 8. Again the same two combinations of the constellation and channel coding rate have been selected (16-QAM with coding rate 1/2, 64-QAM with coding rate 3/4).In case of interblock spreading, the MMSE multiuser receiver reduces to an equivalent but simpler    single-user receiver, which performs channel-independent block despreading followed by MMSE single-user equalization.MCBS-CDMA and SCBS-CDMA are MUI-free transmission schemes, such that their user's goodput remains unaffected by the user's load.In case of intrablock spreading, the MMSE multiuser receiver outperforms the single-user detector.In the downlink, the performance of the MMSE multiuser joint detector is slightly decreasing for an increasing number of users and converges to the one of the single-detector at full user load.MMSE multiuser reception is especially needed in the uplink, since a single-user receiver cannot get rid of the MUI, and features a BER curve flattening already at low SNRs.The impact of the user's load is much more pronounced in the SC-CDMA uplink than in the MC-CDMA downlink since the signals propagate through different channels, which is more difficult to compensate for.In the downlink, MC-CDMA always outperforms MCBS-CDMA since it benefits from the frequency diversity offered by the CDMA spreading.In the uplink, the performance of SCBS-CDMA is equivalent to the one of SC-CDMA for a typical user's load, worse for a small user's load and better for a high user's load.
Figures 10 and 11 compare the effect of the terminal speed on the user's goodput in case of intrablock and interblock spreading.A typical user's load of 5 users has been assumed, which makes MC-CDMA (SC-CDMA) and MCBS-CDMA (SCBS-CDMA) perform equally well in static conditions.For each combination of the constellation and coding rate, the SNR value corresponding to the maximum slope in the goodput curves has been chosen (realistic working point in the curves illustrated in Figures 8 and 9).Since the symbol block duration is higher in case of interblock spreading than in case of intrablock spreading, the performance of MCBS-CDMA (SCBS-CDMA) is significantly reduced, while the performance of MC-CDMA (SC-CDMA) remains acceptable when the speed of the mobile terminals increases.Since the orthogonality between the users is lost when the speed increases, the impact is more severe in the uplink than in the downlink.If a 10-percent performance loss is acceptable, interblock spreading should be used up to 60 km/h in the downlink or 10 km/h in the uplink for detection complexity reasons, while intrablock spreading should  be used for higher speeds.This conclusion is in line with the two-dimensional spreading strategy proposed in [16,17] for a MC-based system, that prioritizes the spreading in the time domain rather than in the frequency domain, for the sake of complexity and performance.It is also interesting to note that the goodput achieved with high constellations at high speed is smaller than the goodput achieved with low constellations.

CONCLUSIONS
A generic transmission scheme has been designed that allows to instantiate all the combinations of OFDM and cyclic-prefixed SC modulations with DS-CDMA.The SDM and STBC multiple-antenna techniques have been integrated in the generic transmission scheme.For each resulting mode, the optimal linear MMSE multiuser receiver has been derived.
A mode selection strategy has also been proposed that trades off efficiently the communication performance in a typical suburban dynamic outdoor environment with the complexity and PAPR at the mobile terminal.
(i) A hybrid modulation scheme (MC in the downlink, SC in the uplink) should be used in order to minimize the mobile terminal PAPR and data processing power.
(ii) Under low-to-medium mobility conditions, it is better to use a high constellation and a low channel coding rate to achieve the maximum goodput for a given SNR value.However, the lowest constellation order should be selected under high mobility conditions.
(iii) One directive antenna should be used at the base station to increase the cell capacity and multiple antennas should be used at the mobile terminal in combination with diversity techniques like MRC reception and STBC transmission to improve the link reliability.
(iv) Since interblock and intrablock spreading perform equally well in typical user loads, interblock spreading should be used at low terminal speeds to minimize the data processing complexity while intrablock spreading should only be used at high terminal speeds.
It has been demonstrated that an adaptive transceiver is interesting to support different communication modes and to efficiently track the changing communication conditions.

Figure 4 :
Figure 4: PAPR as a function of the spreading factor, QPSK, 128 carriers.

Figure 10 :
Figure 10: Impact of the terminal speed on the downlink, MCBS-CDMA (IE stands for interblock spreading) and MC-CDMA (IA stands for intrablock spreading), using MRC.

Figure 11 :
Figure 11: Impact of the terminal speed on the uplink, SCBS-CDMA (IE stands for interblock spreading) and SC-CDMA (IA stands for intrablock spreading), using STBC.
where I cp consists of the last L rows of I Q , T

Table 1 :
Initialization complexity, M users, N T transmit antennas, Q carriers/subchannels, and B complex symbols per block.