Asymptotic behavior of the pairwise error probability with applications to transmit beamforming and rake receivers

We derive the precise asymptote of the pairwise error probability for high signal-to-noise ratio (SNR) and apply it to obtain new results concerning transmit beamforming and selective Rake receivers. For downlink beamforming (with N transmit antennas and independently identically distributed (i.i.d.) Rayleigh fading) based on quantized feedback from the mobile, we show that at least /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback (per coherence time) is required to obtain full diversity, and among all beamforming schemes using /spl lceil/log/sub 2/(N)/spl rceil/ bits of feedback, selection diversity is optimal. We give the exact expression for the SNR loss of selection diversity with respect to ideal beamforming based on perfect knowledge of fading coefficients. Further, we study selective Rake receivers for independent arbitrary fading distribution and arbitrary power delay profile (PDP). In particular, we show that the SNR loss of the SRake receiver with respect to the all-Rake receiver does not depend on the PDP, and we also propose a transformation to adapt the expressions known for the symbol error probability for the case of i.i.d. Rayleigh fading to the general case.     

Structures and performance of noncoherent receivers for unitary space-time modulation on correlated fast-fading channels

Fast fading used in this paper refers to multiple-input-multiple-output (MIMO) channels with channel gains changing from sample to sample, even within a block symbol. The impact of spatially correlated and sample-to-sample variant (SCSSV) fading channels on the design and error performance of noncoherent receivers is not yet clear in the literature. In this paper, we derive optimal and suboptimal noncoherent receivers for operating on SCSSV MIMO fading channels. The joint effect of spatial correlation and sample-to-sample variation of channel gains on various receivers in Rayleigh and Rician fading is investigated by the derivation of their pairwise error performance. Numerical and simulation results are also presented to illustrate the theory and to compare the performance of the optimal and suboptimal receivers.     

相关时变衰落信道中DSTM非相干接收机的结构与性能

针对空间相关时变衰落信道中的差分空时调制系统,推导得出了一种新的基于信道相关矩阵和时变衰落参数的最优非相干接收机结构,并针对几种特殊信道条件对该接收机进行了简化.实际应用该最优接收机时,基于判决反馈得到的数据,提出了一种次优的非相干接收机结构DF-NCR.理论分析和仿真结果表明,在相关时变衰落信道条件下,采用DF-NCR的差分空时调制系统的误码性能优于传统的差分传输模式.     

Pairwise error probability of space-time codes in Rician-Nakagami channels

In this letter, we investigate the shadowing effect on the performance of space-time codes, using the Rician-Nakagami channel model which has been recently introduced. Specifically, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the Rician-Nakagami channel, which is in the form of a simple single finite-range integral. We also present numerical results how the PEP expressions for the Rician-Nakagami channel can be related to those for the classical Rician-lognormal channel based on the parameter transformation between these two models.     

A unified approach to the probability of error for noncoherent anddifferentially coherent modulations over generalized fadingchannels

We present a unified approach to determine the exact bit error rate (BER) of noncoherent and differentially coherent modulations with single and multichannel reception over additive white Gaussian noise and generalized fading channels. The multichannel reception results assume independent fading in the channels and are applicable to systems that employ post-detection equal gain combining. Our approach relies on an alternate form of the Marcum Q-function and leads to expressions of the BER involving a single finite-range integral which can be readily evaluated numerically. Aside from unifying the past results, the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution. The best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions     

Pairwise error probability of space-time codes in frequency selective Rician channels

In this letter, we investigate the performance of space-time codes in frequency selective correlated Rician channels. An exact expression has been derived for the pairwise error probability (PEP) of space-time trellis codes over frequency selective Rician fading channel, which is in the form of a single finite range integral. We also obtain a closed form expression for the PEP when the signal matrices are drawn from some special design and the performance upper bound.     

Bit error probability analysis for FRAMES WCDMA downlink receivers

The wide-band code-division multiple-access (WCDMA) concept FMA2 developed in the European Future Radio Wide-Band Multiple-Access Systems (FRAMES) project supports variable-data-rate transmission. The data rate can be altered by changing either the spreading factor or by using multiple spreading codes in parallel. In order to facilitate flexible changing of the data rate, variable-length orthogonal Walsh codes are used for channel separation, followed by the scrambling code. Optional short scrambling codes can be used if interference suppression is used. The downlink performance of the FMA2 system using both the conventional RAKE and LMMSE-RAKE receivers is studied. According to the numerical results, the performance of the conventional RAKE receivers is significantly degraded at the highest data rates, whereas the LMMSE-RAKE performs well in those cases also     

An error probability analysis of the optimum noncoherent multiuser detector for multipath and multiantenna diversity communications over Rayleigh-fading channels

The optimum noncoherent multiuser detector is obtained for generalized diversity symbol-synchronous communication systems that employ nonorthogonal multipulse modulation. A unified approach is adopted to simultaneously address various forms of diversity such as time, frequency, multipath, and/or receiver-amenna diversity. Upper and lower bounds on the average bit-error probability of the optimum noncoherent detector are derived. While these bounds are numerically computable, they are too complicated to give insights about the relative influence of system parameters on the essential behavior of the bit-error rate. To address this issue, an asymptotic (low noise) analysis of the bit-error probability is undertaken. It is shown that the upper and lower bounds are indeed asymptotically convergent. A formula for the asymptotic efficiency of the optimum noncoherent detector is thereby derived. Interestingly, the asymptotic efficiency is found to be positive, and independent of the signal strengths of the interfering users.     

Timing error detector design and analysis for orthogonal space-time block code receivers

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.     

Bounds on the error probability of FSK and PSK receivers due to non-Gaussian noise in fading channels

This paper derives upper and lower bounds on binary error probability as a function of signal-to-noise ratio for several digital data systems operating over a complex Gaussian fading channel. Bounds of varying degrees of tightness are obtained by placing certain physically meaningful constraints on the allowable detected noise probability distributions. Detailed derivations are given for bounds corresponding to constraints on the "crest-factor" of the detected noise and on the ratio of peak noise power to average signal power. The calculations include the effects of diversity corn-billing and are applicable to frequency-shift keying (FSK), binary and quaternary phase-shift keying (PSK) using a pilot tone as reference, and binary and quaternary PSK using the previous signaling element as a phase reference. It is an interesting result of this paper that for moderate noise crest factors the upper and lower bounds can be rather close. In the particular case of nondiversity operation, for example, the lower bound actually becomes approximately equal to the upper bound at SNR's of30dB or greater for noises with a crest factor as high as20dB.     

Bit-error probability analysis of linear receivers for CDMA systemsin frequency-selective fading channels

The bit-error probability of a linear receiver for code-division multiple-access communications is analyzed. The analysis is presented for the additive white Gaussian noise and fading multipath channels also with data-aided channel estimation. Two ways to approximate the averaging over the interfering data symbol combinations are considered and compared. Numerical examples are presented to demonstrate the usefulness of the analysis methods     

Performance of the noncoherent biquadratic and GLRT receivers overtwo-path channels with known amplitudes and Rayleigh fading

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the “biquadratic” receiver, optimum at low signal-to-noise ratios (SNR's), and the “bilinear” receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the biquadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest     

Large-SNR error probability analysis of BICM with uniform interleaving in fading channels

This paper studies the average error probability of bit-interleaved coded modulation with uniform interleaving in fully-interleaved fading channels. At large signal-to-noise ratio, the dominant pairwise error events are mapped into symbols with Hamming weight larger than one, causing a flattening of the error probability. Closed-form expressions for the error probability with general modulations are provided. For interleavers of practical length, the flattening is noticeable only at very low values of the error probability.     

Error probability analysis of FFH/MFSK receivers over frequency-selective Rician-fading channels with partial-band-noise jamming

An optimum maximum-likelihood (ML) receiver structure for a fast frequency-hopped M-ary frequency-shift keying system over frequency-selective Rician-fading channels against partial-band-noise jamming and additive white Gaussian noise is proposed. In addition, we propose two suboptimum ML receivers and derive their corresponding analytical bit-error rate expressions.     

发射天线选择空时分组码的误符号率分析

研究瑞利衰落信道上使用发射天线选择和空时分组编码的多输入多输出系统的误码性能。使用矩生成函数法和Apell超几何函数、Lauricella多变量超几何函数,推导采用相干检测的M进制相移键控(MPSK)和广义矩形M进制正交幅度调制(GR-MQAM)的平均符号错误概率(SEP)的精确闭合表达式。数值计算结果表明:增加发射天线或/和接收天线数可以改善MIMO瑞利衰落上MPSK和GR-MQAM的平均SEP性能。     

On the probability of error of antenna-subset selection with space-time block codes

Orthogonal space-time block codes (OSTBCs) can obtain full diversity advantage with a simple, but optimal, receiver. Unfortunately, OSTBCs lack in array gain compared with beamforming techniques and suffer a rate loss for more than two transmit antennas. One simple method for improving the array gain and adapting OSTBCs to any number of transmit antennas is antenna-subset selection, where the OSTBC is transmitted on a subset of the transmit antennas. In this letter, we analyze the symbol-error rate performance of antenna-subset selection combined with OSTBCs.     

Models for channels with memory and their applications to error control

Errors encountered in digital transmission over most real communication channels are not independent but appear in clusters. Such channels are said to exhibit memory, i.e., statistical dependence in the occurrence of errors; and thus cannot be adequately represented by the classical memoryless binary symmetric channel. The existence of memory implies additional capacity. To exploit this through efficient coding schemes, it is necessary to describe and model the underlying statistical structure of the error process. This paper reviews various channel models, noting the interaction between channel modeling and error control.     

On improved bounds on the decoding error probability of block codesover interleaved fading channels, with applications to turbo-like codes

We derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved Rician fading channels, coherently detected and maximum-likelihood (ML) decoded. We assume that the fading coefficients during each symbol are statistically independent (due to a perfect channel interleaver), and that perfect estimates of these fading coefficients are provided to the receiver. The improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity, and are found by generalizing some previously introduced upper bounds for the binary-input additive white Gaussian nose (AWGN) channel. The advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low-density parity-check (LDPC) codes, and it is especially pronounced in a portion of the rate region exceeding the cutoff rate. Our generalization of the Duman and Salehi bound (Duman and Salehi 1998, Duman 1998) which is based on certain variations of Gallager's (1965) bounding technique, is demonstrated to be the tightest reported upper bound. We therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo-like codes, referring to the optimal ML decoding. For certain ensembles of uniformly interleaved turbo codes, the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms