CDMA Systems With Correlated Spatial Diversity: A Generalized Resource Pooling Result

This correspondence analyzes the behavior of code-division multiple-access (CDMA) systems with correlated spatial diversity. The users transmit to one or more antenna arrays. The centralized receiver employs a linear multiuser detector. We derive the performance of a large system with random spreading sequences and weak assumptions on the flat-fading channel gains-the fading may be correlated and contain line-of-sight components. We show that, as the number of users and the spreading factor grow large with fixed ratio, the performance of the system is fully characterized by a square matrix with size equal to the number of receiving antennas and multiuser efficiencies are not identical for all users. Our general result includes the analysis of CDMA systems with spatial diversity discussed by Hanly and Tse ('01) for independent channel gains in case of both micro-diversity and macro-diversity and provides a rigorous proof for the macro-diversity case missing in their work. We also show that to any scenario with correlated Rayleigh fading, there exists a macro-diversity scenario with independent Rayleigh fading which is characterized by the same signal-to-interference-and-noise ratio (SINR). Furthermore, sufficient conditions are given which force the multiuser efficiencies of all users to become identical also in case of statistically dependent channel gains     

Capacity of a mobile multiple-antenna wireless link with isotropically random Rician fading

We analyze the capacity of a multiple-antenna wireless link with M antennas at the transmitter and N antennas at the receiver in a Rician fading channel when the channel is unknown at both the transmitter and the receiver. The Rician model is a nonstandard model with a Rayleigh component and an isotropically random rank-one specular component. The Rayleigh and specular components remain constant for T symbol periods, after which they change to completely independent realizations, and so on. To maximize mutual information over the joint density of T/spl middot/M complex transmitted signals it is sufficient to maximize over a joint density of min{T,M} real transmitted signal magnitudes. The capacity-achieving signal matrix is equal to the product of two independent matrices, a T/spl times/T isotropically random unitary matrix and a T/spl times/M real nonnegative diagonal matrix. If M>T, optimum signaling uses only T out of the M transmit antennas. We derive a novel lower bound on capacity which enables us to compute achievable rate regions for many cases. This lower bound is also valid for the case of purely Rayleigh-fading channels, where it has not been feasible, in general, to compute capacity, or mutual information. Our numerical results also indicate that the Rayleigh model is surprisingly robust: under our Rician model, up to half of the received energy can arrive via the specular component without significant reduction in capacity compared with the purely Rayleigh case.     

Exact BER analyses of Nakagami/Nakagami CCI BPSK and Nakagami/Rayleigh CCI QPSK systems in slow fading

A recent letter presented an approximate bit error rate (BER) analysis of coherent binary phase-shift keying (BPSK) in cochannel interference with Nakagami faded desired and interfering signals. Here, the exact BER of coherent nonreturn-to-zero (NRZ) BPSK with cochannel interference in Nakagami fading is derived showing that the approximate analysis may be inaccurate. The exact BER of NRZ quaternary PSK (QPSK) with Nakagami faded desired user signal and Rayleigh faded interfering signals is also derived. Slow fading, asynchronous timing and independent fading gains are assumed.     

常见分集合并系统的性能分析

在移动通信中,分集技术是一种最有效的抗衰落技术。本文对3种常见的线性合并分集技术进行简要分析,给出它们的基带表示和合并器输出信噪比的概率密度函数(pdf),由此给出它们的合并增益。针对系统采用MPSK调制的情况,对瑞利衰落信道的3种合并分集系统的比特误码率(BER)性能进行理论研究,分别给出选择性合并(SC)和最大比率合并(MRC)系统的理论比特误码率表达式;对于等增益合并(EGC)分集,给出了一种近似的EGC系统的输出信噪比的pdf,由此导出EGC的一种近似的BER表达式,由蒙特卡罗仿真结果可以看出此近似的BER数值结果是准确的。数值结果显示:MRC性能最好,EGC性能稍差,而SC性能较差。文中给出的分析方法对于实际分集系统的理论研究具有普遍的指导意义。     

Error Rate Analysis for Coded Multicarrier Systems Over Quasi-Static Fading Channels

Several standards such as IEEE 802.11a/g, IEEE 802.16, and the European Computer Manufacturers Association (ECMA) multiband orthogonal frequency division multiplexing (MB-OFDM) for high data-rate ultra-wideband employ bit-interleaved convolutionally coded multicarrier modulation over quasi-static fading channels. Motivated by the lack of appropriate error rate analysis techniques for this popular type of system and channel model, we present two novel analytical methods for bit error rate (BER) estimation of coded multicarrier systems operating over frequency-selective quasi-static channels with nonideal interleaving. In the first method, the approximate performance of the system is calculated for each realization of the channel, which is suitable for obtaining the outage BER performance (a common performance measure for, e.g., MB-OFDM systems). The second method assumes Rayleigh distributed frequency-domain subcarrier channel gains and knowledge of their correlation matrix, and can be used to directly obtain the average BER performance. Both methods are applicable to convolutionally coded interleaved multicarrier systems employing quadrature amplitude modulation, and are also able to account for narrowband interference (modeled as a sum of tone interferers). To illustrate the application of the proposed analysis, both methods are used to study the performance of a tone-interference-impaired MB-OFDM system.     

A Closed-Form BER Expression for BPSK Using MRC in Correlated CCI and Rayleigh Fading

An exact closed-form expression for the average bit error rate (BER) of coherent BPSK using maximal ratio combining (MRC) with correlated branches in the presence of cochannel interference (CCI) and noise is derived. This expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix.     

Error rate performance of digital FM mobile radio withpostdetection diversity

An analysis of bit error rate (BER) in a binary digital FM system with postdetection diversity is presented. Expressions for the average BER due to additive white Gaussian noise (AWGN), random FM noise and delay-spread in the multipath channel are derived for reception using differential demodulation (DD), and frequency demodulation (FD) assuming independent fading signals. Calculated results for MSK show that the BER performance is strongly dependent on the RMS-delay/bit-duration ratio and that the delay-spectrum shape is of no importance when the receiver predetection filter product is optimized for the effect of AWGN. The effect of fading correlation on the diversity improvement is also analyzed for a two-branch case with multiplicative Rayleigh fading signals. Expressions for the average BER due to AWGN and random FM noise are derived. Calculated results are shown for the average BER due to random FM noise assuming a horizontally spaced antenna system at a mobile station. It is shown that the use of small antenna spacings leads to a diversity improvement greater than that obtainable for the case of independent AWGN     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

Performance analysis of multi‐input multi‐output systems with maximum likelihood detection over shadowed fading channels

Multiple‐input multiple‐output (MIMO) transmission techniques constitute an important technology in modern wireless communication. Hence, performance analysis methods for such systems are of considerable interest. This paper considers first the average pairwise error probability for uncoded MIMO systems employing maximum likelihood detection over a composite Rayleigh‐Lognormal fading channel with spatial correlation. It provides general results, applicable also to a wider class of shadowing models, concerning asymptotical diversity gains and shows that they are not changed by such shadowing. Then, analytical evaluation techniques for bit‐error‐rate (BER) over composite Rayleigh‐Lognormal fading channels, based on the truncated union bound and the transfer function, are considered. Furthermore, these techniques are modified for applications over spatially correlated channels. This paper shows that such performance evaluation techniques provide good approximations to BER of spatially uncorrelated MIMO systems and also in the presence of moderate spatial correlation, over Rayleigh‐Lognormal fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

Unified BER and optimum threshold analysis of binary modulations in simple and cascaded Rayleigh fading channels with switched combining

Following a unified analytical framework, the bit error rate (BER) of several coherent and non‐coherent binary modulation schemes is derived for a switched diversity system. The two variants of switched combining that have been investigated are switch and stay combining and switch and examine combining. For channel modelling, at first a simple slow flat fading channel is assumed, where the amplitude attenuation obeys the Rayleigh distribution. Later the BER calculations are repeated for cascaded Rayleigh fading channel case. Rayleigh fading is the most popular model for electromagnetic signal propagation in wireless media when both or either of the transmitter/receiver is fixed. On the other hand, when both the transmitter and the receiver are mobile, a cascaded (or double) Rayleigh fading model is better suited. The applicability of these two models, namely simple and cascaded Rayleigh model, has been indicated by several theoretical studies and their suitability is established by various field measurements. In our paper, simple closed‐form BER expressions as a function of switching threshold have been found and optimum switching thresholds have been computed for both these models as well as for both types of diversity combining described earlier. The results presented in this paper can be very useful for communication system designers to analyze link quality of switched diversity assisted systems in various wireless environments. Copyright © 2010 John Wiley & Sons, Ltd.     

SIR-optimized weighted linear parallel interference canceller on fading channels

In this letter, we present a weighted linear parallel interference canceller (LPIC) where the multiple access interference (MAI) estimate in a stage is weighted by a factor before cancellation on Rayleigh fading and diversity channels. We obtain exact expressions for the average signal-to-interference ratio (SIR) at the output of the cancellation stages which we maximize to obtain the optimum weights for different stages. We also obtain closed-form expressions for the optimum weights for the different stages. We show that this SIR-optimized weighted LPIC scheme clearly outperforms both the matched filter (MF) detector as well as the conventional LPIC (where the weight is taken to be unity for all stages), in both near-far as well as non-near-far conditions on Rayleigh fading and diversity channels.     

Explicit Analytical Expressions for Outage and Error Rate of Diversity Cellular Systems in the Presence of Multiple Interferers and Correlated Rayleigh Fading

The outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. Further, the average bit-error rate of a coherent binary phase-shift keying (BPSK)-modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated Rayleigh fading is derived. The effects of the average signal-to-noise ratio (SNR) and the average signal-power-to-interference-power ratio on the system performance are examined.     

Implementation of space-time equalizer using multiplesingle-constrained SMI array processors and MLSE

We implemented a space-time equalizer using two sets of single-constrained sample matrix inversion array processors and a maximum-likelihood sequence estimator by using digital signal processors and field-programmable gate arrays. One of the array processors constrains the direct path, sends the one-symbol-delayed path component to the array output, and suppresses the paths with longer delays. The other array processor constrains the one-symbol-delayed path, sends the direct path component to the array output, and also suppresses the paths with longer delays. The desired paths, thus, extracted, whose signal-to-interference-plus-noise-ratios are improved in both path-diversity branches, are then combined by using a branch-metric-combining Viterbi equalizer. We implemented a receiver equipped with this equalizer and evaluated its bit-error rate performance by using a channel emulator. Experimental results indicate that the space-time equalizer provides both space diversity gains and path diversity gains while suppressing signals on paths with long delays     

分布式残余频偏信道中的Alamouti STBC-OFDM功率分配

在具有不同残余频偏的分布发射天线多径瑞利衰落信道中,该文使用Cholesky判决反馈检测的Alamouti STBC-OFDM链路,提出了一种抑制残余频偏影响的发射功率分配方法:以最小化残余频偏下链路的平均误比特率下界为准则,为发射天线分配功率。首先推导了残余频偏下链路的平均误比特率下界,然后给出了发射天线间最优功率分配因子的闭合解。仿真结果表明,与传统的假设频率理想同步的功率分配方法相比,在残余频偏对性能影响占主导作用的场景中,该文方法提升了链路性能,提升程度随着两根发射天线到接收机间平均信道功率增益之比的增加而增大。     

Fast turbo codes with space‐time block codes in fast fading channels

In this paper, space‐time block coding has been used in conjunction with Turbo codes to provide good diversity and coding gains. A new method of dividing turbo encoder and decoder into several parallel encoding and decoding blocks is considered. These blocks work simultaneously and yield a faster coding scheme in comparison to classical Turbo codes. The system concatenates fast Turbo coding as an outer code with Alamouti's G2 space‐time block coding scheme as an inner code, achieving benefits associated with both techniques including acceptable diversity and coding gain as well as short coding delay. In this paper, fast fading Rayleigh and Rician channels are considered for discussion. For Rayleigh fading channels, a fixed frame size and channel memory length of 5000 and 10, respectively, the coding gain is 7.5 dB and bit error rate (BER) of 10^?4 is achieved at 7 dB. For the same frame size and channel memory length, Rician fading channel yields the same BER at about 4.5 dB. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimum selection diversity for BPSK signals in Rayleigh fadingchannels

We propose a new selection diversity scheme, called |ar|-selection diversity, that selects the branch providing the largest magnitude of log-likelihood ratio (LLR). The LLR for BPSK signals in fading channels is found to be proportional to the product of the fading amplitude and the matched filter output after phase compensation. The proposed |ar|-selection diversity scheme is shown to be optimal in the sense of minimizing the bit error rate (BER), and outperform existing selection diversity schemes. We also propose a suboptimal selection diversity scheme, called |aw|-selection diversity, that does not require a phase compensation in the selection process, thereby significantly reducing implementation complexity. We show that the proposed |ar|-selection and |aw|-selection diversity schemes exhibit significant power gains over existing selection diversity schemes in Rayleigh fading channels     

迭代子空间跟踪和结构约束的自适应波束形成算法

自适应波束形成(adaptive beam-forming:ABF)方法通过对阵列数据进行加权处理来获得最大的输出信干噪比,对采样协方差矩阵依赖性较大.在小快拍和通道随机响应误差条件下,采样协方差矩阵的估计值与真实值通常存在较大差异,严重恶化了基于线性约束最小均方误差准则的自适应波束形成方法的干扰抑制性能.针对该问题,本文基于子空间投影类波束形成方法的思想,提出采用迭代子空间跟踪和结构约束的自适应波束形成方法.该方法首先利用clearing技术在训练样本集上依次跟踪主特征矢量并构成信号子空间;然后根据子空间投影类波束形成权矢量的结构特性计算自适应加权矢量.仿真结果表明本文方法能有效提高自适应波束算法的输出信干噪比.     

Distributed beamforming in wireless relay networks with quantized feedback

This paper is on quantized beamforming in wireless amplify-and-forward (AF) relay networks. We use the generalized Lloyd algorithm (GLA) to design the quantizer of the feedback information and specifically to optimize the bit error rate (BER) performance of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedback scheme based on relay selection can achieve full diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by any approximations or modified forwarding schemes. Then, for highrate feedback, we find an upper bound on the average signalto- noise ratio (SNR) loss. Using this result, we demonstrate that both the average SNR loss and the capacity loss decay at least exponentially with the number of feedback bits. In addition, we provide approximate upper and lower bounds on the BER, which can be calculated numerically.We observe that our designs can achieve both full diversity as well as high array gain with only a moderate number of feedback bits. Simulations also show that our approximate BER is a reliable estimation on the actual BER. We also generalize our analytical results to asynchronous networks, where perfect carrier level synchronization is not available among the relays.     

一种基于STBC的SC-FDE系统双天线联合检测算法

针对双发双收的基于空时分组编码的单载波频域均衡(STBC-SC-FDE)系统,研究了一种双天线联合检测算法,通过信道估计、导频干扰消除、加权联合均衡等过程重构发送的信息。并根据信噪比对频域信号与均衡矩阵进行加权处理,使联合检测算法适用于2路接收信号信噪比不同的情况。仿真结果表明,所提出的双天线联合检测算法在SUI-3信道下最大可获得约8dB的接收分集增益。与时域最大比合并(MRC)算法相比,由于采用联合检测,该算法能有效改善系统在多径衰落信道下的误码率。