Tradeoff between diversity gain and interference suppression in a MIMO MC-CDMA system

In this paper, the uplink of an asynchronous multi-carrier direct-sequence code-division multiple-access (MC-DS-CDMA) system with multiple antennas at both the transmitter and the receiver is considered. We analyze the system performance over a spatially correlated Rayleigh fading channel with multiple-access interference (MAI), and evaluate the antenna array performance with joint fading reduction and MAI suppression. Assuming perfect channel knowledge available at the transmitter, maximal ratio transmission is employed to weight the transmitted signal optimally in terms of combating signal fading. At the receiver, adaptive beamforming reception is adopted to both suppress MAI and combat the fading. Note that while correlations among the fades of the antennas in the receive array reduce the diversity gain against fading, the array still has the capability for interference suppression. We examine the effect of varying the number of transmit and receive antennas on both the diversity gain and the interference suppression.     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

Antenna selection for multiple-antenna transmission systems: performance analysis and code construction

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.     

The diversity gain of transmit diversity in wireless systems withRayleigh fading

In this paper, we study the ability of transmit diversity to provide diversity benefit to a receiver in a Rayleigh fading environment. With transmit diversity, multiple antennas transmit delayed versions of a signal to create frequency-selective fading at a single antenna at the receiver, which uses equalization to obtain diversity gain against fading. We use Monte Carlo simulation to study transmit diversity for the case of independent Rayleigh fading from each transmit antenna to the receive antenna and maximum likelihood sequence estimation for equalization at the receiver. Our results show that transmit diversity with M transmit antennas provides a diversity gain within 0.1 dB of that with M receive antennas for any number of antennas. Thus, we can obtain the same diversity benefit at the remotes and base stations using multiple base-station antennas only     

A space-time coding modem for high-data-rate wirelesscommunications

This paper presents the theory and practice of a new advanced modem technology suitable for high-data-rate wireless communications and presents its performance over a frequency-flat Rayleigh fading channel. The new technology is based on space-time coded modulation (STCM) with multiple transmit and/or multiple receive antennas and orthogonal pilot sequence insertion (O-PSI). In this approach, data is encoded by a space-time (ST) channel encoder and the output of the encoder is split into N streams to be simultaneously transmitted using N transmit antennas. The transmitter inserts periodic orthogonal pilot sequences in each of the simultaneously transmitted bursts. The receiver uses those pilot sequences to estimate the fading channel. When combined with an appropriately designed interpolation filter, accurate channel state information (CSI) can be estimated for the decoding process. Simulation results of the proposed modem, as applied to the IS-136 cellular standard, are presented. We present the frame error rate (FER) performance results as a function of the signal-to-noise ratio (SNR) and the maximum Doppler frequency, in the presence of timing and frequency offset errors. Simulation results show that for a 10% FER, a 32-state eight-phase-shift keyed (8-PSK) ST code with two transmit and two receive antennas can support data rates up to 55.8 kb/s on a 30-kHz channel, at an SNR of 11.7 dB and a maximum Doppler frequency of 180 Hz. Simulation results for other codes and other channel conditions are also provided. We also compare the performance of the proposed STCM scheme with delay diversity schemes and conclude that STCM can provide significant SNR improvement over simple delay diversity     

Diversity-multiplexing tradeoff in multiple-access channels

In a point-to-point wireless fading channel, multiple transmit and receive antennas can be used to improve the reliability of reception (diversity gain) or increase the rate of communication for a fixed reliability level (multiplexing gain). In a multiple-access situation, multiple receive antennas can also be used to spatially separate signals from different users (multiple-access gain). Recent work has characterized the fundamental tradeoff between diversity and multiplexing gains in the point-to-point scenario. In this paper, we extend the results to a multiple-access fading channel. Our results characterize the fundamental tradeoff between the three types of gain and provide insights on the capabilities of multiple antennas in a network context.     

Exploiting Multipath Diversity in Multiple Antenna OFDM Systems With Spatially Correlated Channels

Multiple antennas are useful in orthogonal frequency division multiplexing (OFDM) systems for providing transmit and receive diversity to overcome fading. Typically, these designs require considerable separation between the antennas. Spatial correlation is introduced when antennas are not well separated, and it often leads to performance degradation in a flat fading environment. However, in frequency selective fading channels with rich multipath diversity, OFDM receivers can overcome this performance degradation due to antenna correlation. This is due to transformation of a highly spatially correlated channel impulse response to a less spatially correlated channel frequency response inherently by an OFDM system in the presence of rich multipath diversity. We illustrate this for a simple receive diversity OFDM system and hence introduce the concept of space sampling at the receiver where antennas are placed relatively close to each other. The minimum separation required between the antennas under such circumstances is derived analytically, and it is shown that even with a separation of only$0.44lambda$, the required spatial correlation in the channel frequency response becomes sufficiently low. Simulated performance results with such spacing for various multiple antenna OFDM systems corroborate the analytical results.     

MIMO Channels in the Low-SNR Regime: Communication Rate, Error Exponent, and Signal Peakiness

We consider multiple-input multiple-output (MIMO) fading channels and characterize the reliability function in the low signal-to-noise (SNR) regime as a function of the number of transmit and receive antennas. For the case when the fading matrix H has independent entries, we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate. Further, by considering a correlated channel model, we show that the maximum performance gain (in terms of the error exponent and communication rate) is achieved when the entries of the channel fading matrix are fully correlated. The results we presented in this work in the low-SNR regime can also be applied to the infinite bandwidth regime     

Frequency acquisition synchronization for multiple antenna systems

In this paper, we consider the problem of frequency acquisition synchronization by using multiple antennas over wireless fading channels. We introduce frequency synchronization with different combining schemes including space diversity and time diversity. Their performance is estimated for a Rayleigh fading channel with an analysis both theoretically and by simulation. We investigate the relationship between the mean squared error (MSE) and the average signal‐to‐noise ratio (SNR) for combining of different blocks and antennas. Both the carrier frequency offset and the sampling frequency offset are estimated when multiple antennas are utilized for signal transmission. The estimation with maximum ratio combining (MRC) scheme is presented in detail, and the estimation with selection combining scheme and equal gain combining scheme are introduced briefly. The simulation results explicitly show that the performance of the frequency acquisition synchronization with MRC scheme is better than that of others and that the MSE at low SNR is not very close to the Cramér–Rao low bound in multiblock combining frequency synchronization. Furthermore, the results address that in order to improve the performance, the total number of receive antennas will be increased exponentially. Copyright © 2013 John Wiley & Sons, Ltd.     

非相干天线选择算法

基于广义似然比检验(GLRT)与天线选择相结合,提出了平瑞利衰落信道的非相干天线选择(NON-AS)算法,天线选择和信号检测无需信道状态信息.NON-AS算法适用于多输入多输出(MIMO)系统的接收端,接收天线选择是基于每个天线瞬时接收到信号矢量的F-2范数.与相干检测的天线选择相比,NON-AS算法不需要估计信道,大大降低了系统复杂性.成对错误概率分析和仿真结果表明:在高信噪比情况下,选择有最大范数的接收天线,系统能实现和使用全部接收天线相同的分集增益.     

Transmit diversity over quasi-static fading channels using multiple antennas and random signal mapping

We introduce a scheme that achieves a diversity gain for coded systems under static fading conditions by using multiple antennas and random signal mapping. In a two-antenna system, the bit-error rate performance of the proposed scheme approaches that of Alamouti's scheme when the channel is perfectly known. In the presence of channel mismatch, the proposed scheme outperforms Alamouti's scheme significantly. It is shown that, as the number of transmit antennas N goes to infinity, the effective channel for the introduced scheme behaves as if it were perfectly interleaved (i.e., as if the fading was independent). When N is small, further performance gain can be achieved by expanding the original signal constellation.     

相关衰落信道上WCDMA系统的安全性能分析

对多输入多输出（MIMO）相关衰落信道上宽带码分多址接入（WCDMA）的安全性能进行评估,一种省时高效的解决方案是理论分析法。推导了相关 Nakagami 衰落信道上采用空时分组码和二维瑞克接收机（2D-Rake）的 WCDMA 系统的非零安全容量概率和安全中断概率的精确解析表达式。利用上述表达式,可以快速地评估收发天线数、天线相关系数、Nakagami衰落系数、平均路径衰减系数等参数对WCDMA系统安全性能造成的影响。数值计算和仿真结果相吻合,证明了以上理论分析的正确性。推导了WCDMA系统渐近安全中断概率的解析表达式。结果表明,WCDMA 系统的安全分集增益为主信道各个可分离路径上的分集增益之和,与窃听信道无关;对于恒定多径强度轮廓的同分布Nakagami衰落信道,WCDMA系统的安全分集增益为主信道的收/发天线数、多径个数以及Nakagami衰落系数四者之积。     

异步V-BLAST中基于功率扩展的迭代并行干扰消除

在平坦瑞利衰落信道下,异步V-BLAST系统中,现有检测算法随信噪比提高误码率性能改善缓慢。为此,该文提出一种基于预处理矩阵的迭代检测算法:在发射端,通过预处理矩阵将发射信号扩展到整个数据帧上,以获取空时分集度;在接收端,采用低复杂的迭代并行干扰消除方法,由于在迭代过程中干扰重建基于预处理矩阵,所以上次迭代的检测误差被扩展,降低了迭代过程中的误差传播。仿真验证了所提方法的有效性,在8发4收场景下,误码率为10-3时,与现有串行干扰消除方法相比,带来了约7 dB信噪比增益。     

Error probability performance for W-CDMA systems with multiple transmit and receive antennas in correlated Nakagami fading channels

The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m (1960) fading channel framework. The impact of the array configuration (e.g., the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as the fading severity, angular spread and path delay profile) on the overall space-path diversity gain can be directly evaluated. In addition, the exact pairwise error probability of a convolutional coded system is obtained, and the coding gain of a space-path diversity receiver is quantified.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

在频率选择性相关信道中的空频分组编码技术

本文提出了频率选择性瑞利衰落信道中的对角空频分组码(DSF)，研究了码的性能。分析表明，在各天线对间的信道相互独立，系统有NT个发射天线，NR个接收天线和信道冲击响应长度是L时，DSF码可实现分集增益NRNTL。此外，相关的发射天线阵列会使DSF码分集增益下降，但是对码的性能影响不大，特别是在较长的多路径信道上。因此，DSF码对于相关的衰落信道显示出优越的鲁棒性能。最终仿真结果证实了本文的分析。     

基于Schmidt正交化的多天线选择复用

该文从提高信道传输有效性的角度,提出了一种新的多天线选择发送策略--贪婪搜索(GS)法,使用这种方法挑选出使容量最大化的发送天线组合作为传输信号的天线。此法在结合注水(waterfilling)法进行天线功率分配的情况下,与理想的全天线注水法相比,可以减小发射机的复杂度,在独立信道下传输容量略有损失,在相关信道下可以提高传输容量,并且所付出的代价是仅需要对信道矩阵进行Schmidt正交化变换。这种方法一般用于信道矩阵列不满秩,即发送端天线数大于接收端天线数,发送端已知信道矩阵的情况(与注水法结合)或者接收端已知信道矩阵的情况(等功率分配)。     

Degrees of freedom in some underspread MIMO fading channels

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.     

Performance analysis for V‐BLAST system using OSIC receiver in correlated channel

Vertical‐Bell Labs Layered Space–Time (V‐BLAST) system is an emerging spatial multiplexing scheme that can achieve high spectral efficiency. Ordered successive interference cancellation (OSIC) detection algorithm is suitable for V‐BLAST system because it can afford a reasonable trade‐off between complexity and performance. However, the correlation of a real‐world wireless channel may result in a substantial degradation of the OSIC performance. In this paper, the performance of OSIC under correlated fading is analyzed. We obtain the closed‐form expression of post‐processing signal‐to‐noise ratio (SNR) for each sub‐stream based on V‐BLAST architecture, and then derive the distribution of post‐processing SNR based on multivariate statistical theory. The upper bound of the average probability of error (APE) is derived by the nearest neighbor union bound theory. From the expression of APE for each sub‐stream, it is shown that the diversity gain at the ith processing step is (N ? M + i), where N and M are the number of receive and transmit antennas, respectively. Correlation can decrease the effective post‐processing SNR rather than the diversity gain, and the decreased amount of the effective post‐processing SNR is accurately measured by the corresponding diagonal element of the inverse of the transmit correlation matrix. The optimal ordering can improve the performance and this advantage vanishes gradually as the scattering angle decreases. Copyright © 2010 John Wiley & Sons, Ltd.