Feedback gain in multiple antenna systems

Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel assumptions is large and most practical systems lie in between. Therefore, it is important to analyze multiple antenna systems in the presence of partial channel information. We upper bound the outage probability performance of multiple antenna systems with preamble-based channel estimation and quantized feedback. We design causal feedback and power control schemes to minimize this upper bound on outage probability. We consider the following practical issues in our analysis and design: (1) the channel information is imperfect both at the receiver and at the transmitter and (2) part of the total available resources for the system need to be used for estimation and feedback. Our results demonstrate that for block fading channels, sending a periodic preamble and causally receiving channel state information via a feedback channel can lead to substantial gains in the outage performance over any nonfeedback scheme. Most of the gains achieved by perfect feedback can be achieved by very few bits of feedback. Furthermore, it is demonstrated that these outage probability gains can be translated into improvements in frame error rate performance of systems using space-time codes. Thus, implementing a power control, even at the cost of reduced spectral resources for the forward channel is beneficial for block fading channels     

Limiting performance of block-fading channels with multipleantennas

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the “delay-limited” (or “nonergodic”) capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Approaching V-BLAST Capacity With Adaptive Modulation and LDPC Encoding

This paper presents a practical implementation of the vertical Bell Laboratories layered space-time (V-BLAST) type system, in which the multiple-input multiple-output (MIMO) open-loop capacity can be approached with conventional scalar coding, using adaptive modulation with appropriate channel codes, e.g., low-density parity-check (LDPC) codes and optimum successive detection (OSD). The density evolution (DE) technique is employed to determine the maximal achievable rate of an LDPC code for each transmit antenna for a given channel realization at a given SNR. Numerical results show that the average sum rate of the adaptively modulated LDPC-encoded system is quite close to the V-BLAST capacity with both rate and power adaptations. Considering the performing degradation caused by error propagation due to the imperfect feedback and relatively long decoding delay in the OSD, we use parallel interference cancellation (PIC) followed by minimum mean square error (MMSE) filtering in the bit error rate (BER) performance simulation. Simulation results show that a target BER of 10-5 can be achieved by the optimally designed LDPC codes. To simplify the code design, we replace the LDPC codes optimally designed for each channel realization with rate-compatible punctured LDPC codes, at the cost of a slight sum rate loss. If the fading process is nonergodic, the outage capacity corresponding to a given outage probability is used to measure the channel performance. As an example, we design the LDPC codes for an adaptively modulated 2 × 2 V-BLAST system to approach its outage capacity for a given outage probability.      

On low-complexity space-time coding for quasi-static channels

We propose a new space-time coding scheme for the quasi-static multiple-antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter. In our scheme, codewords produced by a trellis encoder are formatted into space-time codeword arrays such that decoding can be implemented efficiently by minimum mean-square error (MMSE) decision-feedback interference mitigation coupled with Viterbi decoding, through the use of per-survivor processing. We discuss the code design for the new scheme, and show that finding codes with optimal diversity is much easier than for conventional trellis space-time codes (STCs). We provide an upper bound on the word-error rate (WER) of our scheme which is both accurate and easy to evaluate. Then, we find upper and lower bounds on the information outage probability with discrete independent and identically distributed (i.i.d). inputs (as opposed to Gaussian inputs, as in most previous works) and we show that the MMSE front-end yields a large advantage over the whitened matched filter (i.e., zero-forcing) front-end. Finally, we provide a comprehensive performance/complexity comparison of our scheme with coded vertical Bell Labs layered space-time (V-BLAST) architecture and with the recently proposed threaded space-time codes. We also discuss the concatenation of our scheme with block space-time precoders, such as the linear dispersion codes.     

Energy‐efficient outage‐constrained power allocation based on statistical channel knowledge for dual‐hop cognitive relay networks

This paper investigates the power allocation problem in decode‐and‐forward cognitive dual‐hop systems over Rayleigh fading channels. In order to optimize the performance of the secondary network in terms of power consumption, an outage‐constrained power allocation scheme is proposed. The secondary nodes adjust their transmit power subject to an average interference constraint at the primary receiver and an outage probability constraint for the secondary receivers while having only statistical channel knowledge with respect to the primary nodes. We compare this approach with a power allocation scheme based on instantaneous channel state information under a peak interference constraint. Analytical and numerical results show that the proposed approach, without requiring the constant interchange of channel state information, can achieve a similar performance in terms of outage probability as that of power allocation based on instantaneous channel knowledge. Moreover, the transmit power allocated by the proposed approach is considerably smaller than the power allocated by the method based on instantaneous channel knowledge in more than 50% of the time. Copyright © 2015 John Wiley & Sons, Ltd.     

Coded modulation in the block-fading channel: coding theorems and code construction

We consider coded modulation schemes for the block-fading channel. In the setting where a codeword spans a finite number N of fading degrees of freedom, we show that coded modulations of rate R bit per complex dimension, over a finite signal set /spl chi//spl sube//spl Copf/ of size 2/sup M/, achieve the optimal rate-diversity tradeoff given by the Singleton bound /spl delta/(N,M,R)=1+/spl lfloor/N(1-R/M)/spl rfloor/, for R/spl isin/(0,M/spl rfloor/. Furthermore, we show also that the popular bit-interleaved coded modulation achieves the same optimal rate-diversity tradeoff. We present a novel coded modulation construction based on blockwise concatenation that systematically yields Singleton-bound achieving turbo-like codes defined over an arbitrary signal set /spl chi//spl sub//spl Copf/. The proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block-fading channel. We analyze the ensemble average performance under maximum-likelihood (ML) decoding of the proposed codes by means of upper bounds and tight approximations. We show that, differently from the additive white Gaussian noise (AWGN) and fully interleaved fading cases, belief-propagation iterative decoding performs very close to ML on the block-fading channel for any signal-to-noise ratio (SNR) and even for relatively short block lengths. We also show that, at constant decoding complexity per information bit, the proposed codes perform close to the information outage probability for any block length, while standard block codes (e.g., obtained by trellis termination of convolutional codes) have a gap from outage that increases with the block length: this is a different and more subtle manifestation of the so-called "interleaving gain" of turbo codes.     

Nakagami-m信道协作网络编码中断性能分析

无线网络编码是一项能极大提高无线网络流量的有用技术,而协作分集可以有效地克服无线衰落的影响。研究了Nakagami-m信道下协作网络编码系统中断性能,分析了不同协作策略下的互信息表达式,推导了协作网络编码中断概率闭式表达式,并对分析的结果进行了仿真。仿真结果显示,在高SNR和谱效率R〈4条件下,协作网络编码中断概率较分布式空时编码性能SNR增益有接近2 dB的提高,并且随分布参数m值的增大,协作网络编码中断概率性能逐步改善。     

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.     

Service outage based power and rate allocation for parallel fading channels

The service outage based allocation problem explores variable-rate transmission schemes and combines the concepts of ergodic capacity and outage capacity for fading channels. A service outage occurs when the transmission rate is below a given basic rate r/sub o/. The allocation problem is to maximize the expected rate subject to the average power constraint and the constraint that the outage probability is less than /spl epsi/. A general class of probabilistic power allocation schemes is considered for an M-parallel fading channel model. The optimum power allocation scheme is derived and shown to be deterministic except at channel states of a boundary set. The resulting service outage achievable rate ranges from 1-/spl epsi/ of the outage capacity up to the ergodic capacity with increasing average power. Two near-optimum schemes are also derived by exploiting the fact that the outage probability is usually small. The second near-optimum scheme significantly reduces the computational complexity of the optimum solution; moreover, it has a simple structure for the implementation of transmission of mixed real-time and non-real-time services.     

Power allocation in a transmit diversity system with mean channel gain information

We study the power allocation problem in a transmit diversity wireless system with mean channel gain information. In Rayleigh fading for a given set of mean channel gains and nodes, we seek to find the power allocation that minimizes the outage probability subject to a total power constraint. The optimal solution is shown to be computationally intensive when the number of channels is large. Instead, we derive a simple solution based on the upper bound to the outage probability which can be summarized as equal power allocation with channel selection. Numerical results show that the proposed solution is near-optimal over a wide range of parameter values. The problem addressed and the solution are relevant to a decode-and-forward cooperative relaying system with only partial channel information available to the relays.     

Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments     

Outage Probability in Mobile Telephony Due to Multiple Log-Normal Interferers

The mobile radio channel is characterized by three important factors: path losses larger than free space, fading typically taken as Rayleigh, and shadowing generally characterized as lognormal. For cellular systems, in order to determine acceptable reuse distances between base stations and to compare modulation methods, the probability of unacceptable cochannel interference (outage probability) has to be determined in the realistic situation where both fading and shadowing occur. In this paper, the average outage probability is computed for centrally located base stations when multiple log-normal interferers are present. This is done for both the mobile-to-base and base-to-mobile communication links. An unexpected result of this study is that the outage probabilities for the two cases do not differ in a significant way. Cumulative probability curves of the short-term average-signal-toaverage-interference ratio (SIR) are presented for a variety of system parameters: channel set number, propagation law exponent (γ), and dB spread (σ) of the log-normal distribution for the signal and interferers. An important observation is the large sensitivity of the performance curves to the propagation parameters: for a system with seven channel sets with a 10 dB SIR threshold, the average outage probability varies from 10 percent forgamma = 3.7, sigma = 6dB, to 70 percent forgamma = 3, sigma = 14dB. Alternatively, for a fixed outage objective of 10 percent, the required SIR threshold value ranges from -17 dB to 11 dB, depending on the propagation parameters. These variations make it imperative that accurate measurements of these parameters be obtained for the different service areas. Outage probabilities are also easily related to specific modulation methods and diversity approaches; detailed results are given for several representative cases.     

Outage capacities and optimal power allocation for fading multiple-access channels

We derive the outage capacity region of an M-user fading multiple-access channel (MAC) under the assumption that both the transmitters and the receiver have perfect channel side information (CSI). The outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given a required rate and average power constraint for each user, we find a successive decoding strategy and a power allocation policy that achieves points on the boundary of the outage probability region. We discuss the scenario where an outage must be declared simultaneously for all users (common outage) and when outages can be declared individually (individual outage) for each user.     

Adaptive Modulation over Nakagami Fading Channels

We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closed-form solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We then analyze the performance of practical constant-power variable-rate M-QAM schemes over NMF channels. We obtain closed-form expressions for the outage probability, spectral efficiency and average bit-error-rate (BER) assuming perfect channel estimation and negligible time delay between channel estimation and signal set adaptation. We also analyze the impact of time delay on the BER of adaptive M-QAM.     

Leveraging coherent space-time codes for noncoherent communication via training

Training codes are introduced for the multiple-antenna, noncoherent, multiple block-Rayleigh-fading channel in which the fading coefficients, which are constant over a fixed number of dimensions (coherence interval) for each block and then change independently to a new realization, are known neither at the transmitter nor at the receiver. Each codeword of a training code consists of a part known to the receiver-used to form a minimum mean-squared error (MMSE) estimate of the channel-and a part that contains codeword(s) of a space-time block or trellis code designed for the coherent channel (in which the receiver has perfect knowledge of the channel). The channel estimate is used as if it were error-free for decoding the information-bearing part of the training codeword. Training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable. Conditions for which the estimator-detector (E-D) receiver is equivalent to the optimal noncoherent receiver are established. A key performance analysis result of this paper is that the training codes when decoded with the E-D receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code. In some cases, the performance of training codes can be measured relative to coherent reception via "training efficiency," which is then optimized over the energy allocation between the training and data phases. In the limit of increasing block lengths, training codes always achieve the performance of coherent reception. The examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available, even though the latter require exponential decoding complexity.     

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。     

Path diversity for DS-SSMA communications in Nakagami fading channels

Average error probability and outage probability for an asynchronous direct sequence spread spectrum multiple access communications through slow nonselective Nakagami fading channels are evaluated for nondiversity and diversity receptions. Using the Gauss quadrature rule, the moments of the self-interference and the multiple access interferences are used to evaluate average error probability and outage probability. Combining the diversity technique and error correcting codes, comparisons between the uncoded nondiversity DS-SSMA system and that of the coded diversity system are shown for the Gold Code of codelength 127. Using fourth-order diversity and the Reed-Solomon code, the maximum achievable number of users is 12 percent of the codelength for Rayleigh fading, when the average probability is 10^–3. The corresponding outage probability is less than 5 percent. Performance comparisons between Rician and Nakagami fading channels are made. Since the system is interference limited, the performance seems to show no significant difference for the two fading channel models when the number of users is large.     

MIMO antenna subset selection with space-time coding

This paper treats multiple-input multiple-output (MIMO) antenna subset selection employing space-time coding. We consider two cases differentiated based on the type of channel knowledge used in the selection process. We address both the selection algorithms and the performance analysis. We first consider the case when the antenna subsets are selected based on exact channel knowledge (ECK). Our results assume the transmission of orthogonal space-time block codes (with emphasis on the Alamouti (see IEEE J. Select. Areas Commun., vol.16, p.1451-68, Oct. 1998) code). Next, we treat the case of antenna subset selection when statistical channel knowledge (SCK) is employed by the selection algorithm. This analysis is applicable to general space-time coding schemes. When ECK is available, we show that the selection algorithm chooses the antenna set that maximizes the channel Frobenius norm leading to both coding and diversity gain. When SCK is available, the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain. In case of ECK-based selection, we provide analytical expressions for average SNR and outage probability improvement. For the case when SCK-based selection is used, we derive expressions for coding gain. We also present extensive simulation studies, validating our results.     

Automatic design of orthogonal or near-orthogonal linear dispersive space-time block codes

This paper considers a wireless multiple-input multiple-output (MIMO) communication system in a frequency-nonselective scenario with spatially uncorrelated Rayleigh fading channel coefficients and investigates the design of linear dispersive (LD) space-time block codes. Efficient LD codes are obtained by optimizing the constituent weight matrices so that an upper bound on the union bound of the codeword error probability is minimized. Interestingly, the proposed design procedure automatically generates LD codes that either correspond to, or are close to, the well-known class of orthogonal space-time block (OSTB) codes. A theoretical analysis confirms this by proving that OSTB codes are indeed optimal, when the setup under study permits their existence. Simulation results demonstrate the excellent performance of the designed codes. In particular, the importance of the codes' near-orthogonal property is illustrated by showing that low-complexity linear equalizer techniques can be used for decoding purposes while incurring a relatively moderate performance loss compared with optimal maximum-likelihood (ML) decoding.