An upper bound on turbo codes performance over quasi-static fading channels

This letter proposes an upper bound on the performance of turbo-codes over quasi-static fading channels. First an upper bound is derived for the case of a single-input single-output channel. The result is then extended to the case of a serial concatenation of a turbo-code and a space-time block code. Unlike a simple extension of the union bound, the derived upper bounds are shown to converge for all signal-to-noise ratios. Additionally the closed form upper bounds obtained confirm analytically that, unlike over additive white Gaussian noise channels, turbo-code performance does not improve by increasing frame length over quasi-static fading channels.     

On the performance of space-time codes over spatially correlated Rayleigh fading channels

We derive the exact pairwise error probability (PEP) for space-time coding over quasi-static Rayleigh fading channels in the presence of spatial fading correlation. We show that receive correlation always degrades the PEP for all signal-to-noise ratios (SNRs). We quantify the effect of receive correlation by employing the notion of "majorization". We show that the stronger the receive correlation, the worse the PEP for all SNRs. We show that at low SNR, depending on the codes, transmit correlation can either improve or degrade the PEP performance. We show that to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs.     

Distance spectra and performance bounds of space-time trellis codes over quasistatic fading channels

This correspondence presents a general approach to upper bounding coded system performance over quasistatic fading channels (QSFC). This approach has the advantage of yielding a closed-form upper bound that converge for all signal-to-noise ratios (SNRs). The proposed approach is used to upper-bound the performance of space-time trellis codes (STTC) over QSFCs. The resulting upper bounds for STTCs are better adapted to the QSFC and present an improvement over worst case pairwise error probability (PEP) analysis used so far. In its second part, this correspondence investigates several ways to reduce the complexity of computing the distance spectrum of STTCs. The combined result obtained from using the new upper bounds and the computed distance spectra are shown to be close to simulated performance for all SNRs.     

衰落信道上空频分组码的性能分析

对于任意抽头数的多输入多输出(MIMO)频率选择性Nakagami衰落信道,利用矩生成函数(MGF)方法和高斯Q函数的指数近似表达式,推导采用矩形M进制正交幅度调制(MQAM)的空频分组编码(SFBC)正交频分复用(OFDM)系统的平均误符号率(SER)性能的精确和近似解析表达式。数值计算和仿真结果证明了理论分析的正确性和近似分析的准确性。     

On CDMA with space-time codes over multipath fading channels

We explore code-division multiple-access systems with multiple transmitter and receiver antennas combined with algebraic constellations over a quasi-static multipath fading channel. We first propose a technique to obtain transmit diversity for a single user over quasi-static fading channels by combining algebraic constellations with full spatial diversity and spreading sequences with good cross-correlation properties. The proposed scheme is then generalized to a multiuser system using the same algebraic constellation and different spreading sequences. We also propose a linear multiuser detector based on the combination of linear decorrelation with respect to all users, and the application of the sphere decoder to decode each user separately. Finally, we consider the generalization to multipath fading channels where the additional diversity advantage due to multipath is exploited by the sphere decoder, and a method of blind channel estimation based on subspace decomposition is examined.     

On performance bounds for space-time codes on fading channels

We evaluate truncated union bounds on the frame-error rate (FER) performance of space-time (ST) codes operating over the quasi-static fading channel and compare them with computer simulation results. We consider both ST trellis and block codes. We make the following contributions. For the case of ST trellis codes, we develop a general method, which we denote as measure spectrum analysis, that characterizes ST codeword differences and accommodates the combined influences of the ST code and channel scenario. We propose a numerical bounding method that converges in the measure spectrum to within a very small fraction of a decibel to the simulated FER over the full range of signal-to-noise ratio. In addition, we demonstrate the existence of dominant quasi-static fading error events and detail a method for predicting them. Using only this set of dominant measure spectrum elements, very rapid and tight numerical estimation of FER performance is attained.     

Construction of block modulation codes over rings for fading channels

A new methodology is described for construction of block coded modulation (BCM) over modulo-8 rings for fading channels. Code construction criteria are defined to obtain the maximum use of channel characteristics and to achieve the phase invariance property. Some code examples are presented.<>     

Tree-structured oversampled filterbanks as joint source-channel codes: application to image transmission over erasure channels

This paper studies oversampled filterbanks for robust transmission of multimedia signals over erasure channels. Oversampled filterbanks implement frame expansions of signals in l/sup 2/(Z). The dependencies between the expansion coefficients introduced by the oversampled filterbank are first characterized both in the z-domain and in the time-domain. Conditions for recovery of some typical erasure patterns like bursty erasure patterns are derived. The analysis leads to the design of two erasure recovery algorithms that are first studied without quantization noise. The reconstruction algorithm derived from the time-domain analysis exploits the fact that an oversampled filterbank represents signals with more than one set of basis functions. The erased samples are first reconstructed from the received ones, and then, signal space projection is applied. The effect of quantization noise on the reconstructed signal is studied for both algorithms. Using image signals, the theoretical results are validated for a number of erasure patterns, considering unequal error protection enabled tree-structured decompositions.     

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.     

双瑞利衰落信道下最大比合并性能研究

基于接收信噪比的统计特性,研究了双瑞利衰落条件下各分集支路衰落幅度不平衡时最大比合并MRC接收系统的差错和分集性能。采用基于矩生成函数的方法导出了涵盖多种调制方式的平均误符号率ASER的通用公式,并得到了其Chernoff一致界。仿真结果表明:双瑞利衰落下采用MRC接收技术可以大大减小传输系统的ASER且能获得与瑞利衰落时相同的渐进分集增益,但在实际可接收到的信噪比范围内可获得的分集增益与满分集增益具有明显的差距;相对于单支路接收系统,双瑞利衰落下的MRC系统可近似得到满的相对分集增益。     

Asymptotic performance of space-frequency codes over broadband channels

We show that when the number of receive antennas is large, the Euclidean distance among codewords dominates the performance of space-frequency codes, the same result as for space-time codes. Therefore, in the presence of a large number of receive antennas, space-frequency codes can be optimized by using the Euclidean-distance criterion valid for additive white Gaussian noise channels. Simulation results show that this conclusion is also valid when the number of antennas is small.     

Progressive transmission of images over fading channels using rate-compatible LDPC codes.

In this paper, we propose a combined source/channel coding scheme for transmission of images over fading channels. The proposed scheme employs rate-compatible low-density parity-check codes along with embedded image coders such as JPEG2000 and set partitioning in hierarchical trees (SPIHT). The assignment of channel coding rates to source packets is performed by a fast trellis-based algorithm. We examine the performance of the proposed scheme over correlated and uncorrelated Rayleigh flat-fading channels with and without side information. Simulation results for the expected peak signal-to-noise ratio of reconstructed images, which are within 1 dB of the capacity upper bound over a wide range of channel signal-to-noise ratios, show considerable improvement compared to existing results under similar conditions. We also study the sensitivity of the proposed scheme in the presence of channel estimation error at the transmitter and demonstrate that under most conditions our scheme is more robust compared to existing schemes.     

MIMO-assisted space-code-division multiple-access: linear detectors and performance over multipath fading channels

In this contribution, we propose and investigate a multiple-input-multiple-output space-division, code-division multiple-access (MIMO SCDMA) scheme. The main objective is to improve the capacity of the existing direct-sequence (DS)-CDMA systems, for example, for supporting an increased number of users, by deploying multiple transmit and receive antennas in the corresponding systems and by using some advanced transmission and detection algorithms. In the proposed MIMO SCDMA system, each user can be distinguished jointly by its spreading code signature and its unique channel impulse response (CIR) transfer function referred to as spatial signature. Hence, the number of users might be supported by the MIMO SCDMA system and the corresponding achievable performance are determined by the degrees of freedom provided by both the code signatures and the spatial signatures, as well as by how efficiently the degrees of freedom are exploited. Specifically, the number of users supported by the proposed MIMO SCDMA can be significantly higher than the number of chips per bit, owing to the employment of space-division. In this contribution, space-time spreading is employed for configuring the transmitted signals. Three types of low-complexity linear detectors, namely, correlation, decorrelating, and minimum mean-square error (MMSE) are considered for detecting the MIMO SCDMA signals. The bit-error rate performance of the MIMO SCDMA system associated with these linear detectors are evaluated by simulations, when assuming that the MIMO SCDMA signals are transmitted over multipath Rayleigh-fading channels. Our study and simulation results show that MIMO SCDMA assisted by multiuser detection is capable of facilitating joint space-time despreading, multipath combining, and receiver diversity combining, while simultaneously suppressing the multiuser interfering signals.     

Exact expression and tight bound on pairwise error probability for performance analysis of turbo codes over nakagami-m fading channels

This letter presents derivation for an exact and efficient expression on pairwise error probability over fully interleaved Nakagami-m fading channels under ideal channel state information at the decoder. As an outcome, this derivation also leads to a tight upper bound on pairwise error probability which is close to the exact expression. Pairwise error probability plots for different values of Nakagami parameter m along with an already existing numerically computable expression are provided. As an application of pairwise error probability, average union upper bounds for turbo codes having (1,7/5,7/5) and (1,5/7,5/7) generator polynomials employing transfer function approach are presented to illustrate the usefulness of the new efficient results     

Analysis and performance of bidirectional decoding of convolutionalcodes over fading channels

The performance of suboptimal convolutional decoding over fading channels is explored. The suboptimal decoding algorithm used is the bidirectional algorithm. By estimating a “decoder weight spectrum” for the decoder, an “equivalent free distance” may be observed. Furthermore, by using this “decoder weight spectrum”, useful estimations of the error probabilities are obtained and compared to computer-simulation results in the case of very slow and very fast fading. The resultant curves are shown to be very tightly related. Computer-simulation results are also shown for various signal-to-noise ratios, normalized Doppler spreads, and frame length on three typical fading channels: the Rayleigh fading channel with exponential and Bessel autocorrelation functions and the Rician fading channel with exponential autocorrelation function. We show that considerable gains (up to 4 dB) can be obtained with respect to a similar-complexity Viterbi decoder at a frame error probability P_e =10^-3 and a slightly smaller gain (up to 1.8 dB) at a bit error probability P_b=10^-5     

Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels

In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.     

Performance of Reed-Solomon codes for hybrid-ARQ over Rayleigh fading channels under imperfect interleaving

We present a new method to analyze the performance of Reed-Solomon codes for hybrid automatic-repeat-request (ARQ) over Rayleigh fading channels with imperfect interleaving. Using the asymptotic results of level crossings of the faded envelope, we characterize the packet-error probability as a function of the Doppler frequency and mean signal-to-noise ratio. We then use the notion of equivalent Doppler frequency to include the effect of imperfect interleaving on performance. This approach allows us to directly evaluate the throughput of hybrid-ARQ schemes and also specify minimum interleaving depths for achieving optimum throughput on correlated Rayleigh channels.     

Asymptotic performance analysis of arbitrary rectangular QAM over fading channels

In this paper, the asymptotic performance of arbitrary rectangular Quadrature Amplitude Modulation (QAM) signals over fading channels is investigated. A novel unified asymptotic average Symbol Error Probability (SEP) expression is derived in terms of diversity and coding gain. The validity and accu-racy of the analytical result are verified by means of computer simulations. Furthermore, the results pre-sented are very easy to be extended to the systems with multi-channel diversity receivers.     

Multidimensional M-PSK trellis codes for fading channels

This paper investigates the code search problem for trellis-coded multidimensional phase modulation for Rayleigh fading channels. New set partitionings for multiple phase-shift keying (M-PSK) are proposed using the effective code length (ECL) and the minimum product distance (PD) as the code design criteria. By using these set-partitionings rules, new multidimensional codes which are optimum for Rayleigh fading channels are constructed. The proposed codes compare favorably with the existing multidimensional trellis codes on fading channels in terms of bit error performance. The bit error performance is evaluated by simulation