A comparison of two combining techniques for equal gain, trelliscoded diversity receivers

Trellis coded modulation is widely used for digital transmission over fading channels. Classical diversity techniques are also frequently employed to combat fading. In this paper two different strategies for equal gain combining are compared, One scheme is based on an interleaved code combining technique. The alternative scheme is based on averaged diversity combining. The well known transfer function bounding technique for trellis codes is used to obtain: expressions for the bit error rate performance of the two trellis coded diversity receivers over a slowly fading Rayleigh channel. The analysis of interleaved code combining is a straightforward modification of the analysis for multiple trellis coded modulation. The analysis of averaged diversity combining is accommodated through a more involved, novel modification of the branch labeling of the error state diagram. The analytic techniques presented in this paper are supported by simulation results using a TCM scheme based on QPSK modulation and a rate-l/2 linear convolution code     

Maximum-likelihood differential detection of uncoded and trelliscoded amplitude phase modulation over AWGN and fading channels-metricsand performance

This paper derives metrics for maximum-likelihood differential detection of uncoded and trellis coded MPSK and QAM transmitted over Rayleigh and Rician fading channels. Receiver structures based on these metrics are proposed and their error probability performance analyzed and/or simulated. The results represent a generalization of the notion of multiple symbol differential detection, previously introduced by the authors for MPSK over an AWGN, to the fading channel and other modulations. For the coded cases, ideal interleaving/deinterleaving is assumed and furthermore the presence or absence of channel state information. An interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly-varying phase error (the other extreme to the slowly-varying phase error case normally assumed for differential detection), under certain practical assumptions, it is shown that the optimum receiver is of the limiter-discriminator type     

Impact of diversity reception on fading channels with codedmodulation. I. Coherent detection

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system)     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Bit-interleaved coded differential space-time modulation

Bit-interleaved coded differential space-time modulation for transmission over spatially correlated Ricean flat fading channels is discussed. For improved noncoherent detection without channel state information at the receiver, iterative decoding employing hard-decision feedback and prediction-based metric computation is applied. The performance is assessed based on the associated cutoff rate, analytical expressions for the bit error rate and the outage probability, respectively and simulations. It is shown that the proposed scheme offers high power efficiency exploiting both space and time diversity, while the computational complexity is kept at a relatively low level.     

Joint MAP equalization and channel estimation forfrequency-selective and frequency-flat fast-fading channels

This paper presents a new fractionally-spaced maximum a posteriori (MAP) equalizer for data transmission over frequency-selective fading channels. The technique is applicable to any standard modulation technique. The MAP equalizer uses an expanded hypothesis trellis for the purpose of joint channel estimation and equalization. The fading channel is estimated by coupling minimum mean square error techniques with the (fixed size) expanded trellis. The new MAP equalizer is also presented in an iterative (turbo) receiver structure. Both uncoded and conventionally coded systems (including iterative processing) are studied. Even on frequency-flat fading channels, the proposed receiver outperforms conventional techniques. Simulations demonstrate the performance of the proposed equalizer     

Design, analysis, and performance evaluation for BICM-ID withsquare QAM constellations in Rayleigh fading channels

We consider bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth-efficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a low-rate code and a new labeling technique designed specifically for fading channels. This results in a large coding gain over noniterative coded modulation and performance close to that of “turbo” coded modulation with less complexity. We also show that BICM-ID designed for fading channels usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICM-ID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10^-6 can be achieved with 16-QAM, a four-state rate 1/2 code at E_b/N₀ of about seven dB. We also derive performance bounds for BICM-ID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels     

Maximum likelihood decoding of uncoded and coded PSK signalsequences transmitted over Rayleigh flat-fading channels

The problem of maximum likelihood (ML) detection for uncoded and coded M-PSK signals on Rayleigh fading channels is investigated. It is shown that, if the received signal is sampled at baud-rate, a ML receiver employing per-survivor processing can be implemented. The error rate performance of this receiver is evaluated by means of computer simulations and its limitations are discussed. In addition, it is shown that, on a fast fading channel, the error floor in the BER curve can be appreciably lowered if more than one received signal sample per symbol interval is processed by the receiver algorithm, Finally, a sub-optimum two-stage receiver structure for interleaved coded PSK systems is proposed. Its error rate performance is assessed for simple trellis-coded modulation schemes and compared to that provided by other receiver structures     

Multidimensional Subcarrier Mapping for Bit-Interleaved Coded OFDM With Iterative Decoding

A power and bandwidth-efficient bit-interleaved coded modulation (BICM) with orthogonal frequency-division multiplexing (OFDM) and iterative decoding (BI-COFDM-ID) using combined multidimensional mapping and subcarrier grouping is proposed for broadband transmission in a frequency-selective fading environment. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence, they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multidimensional mapping for bit-interleaved coded modulation with iterative decoding (BICM-ID) in frequency-flat Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with linear constellation preceding (LCP). Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using LCP and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth, and receiver complexity.     

Coding for a coherent DS-CDMA system employing an MMSE receiver ina Rayleigh fading channel

This paper analyzes the performance of a convolutionally coded code-division multiple-access system, which employs a linear, minimum mean-square error (MMSE) receiver for interference suppression. A flat, Rayleigh fading channel is considered, where convolutional encoding and interleaving are employed in order to combat the effects of the fading. Theoretical results are derived for the average bit-error probability of the MMSE receiver, where the optimum tap weights for the adaptive filter are determined by the solution of the Wiener-Hopf equations. Simulation results showing the average bit-error rate of the MMSE receiver are also presented, which incorporate the effects of recursive least squares adaptation, channel estimation using pilot symbol-assisted modulation, and finite interleaving. Results show that the MMSE receiver with coding can provide a substantial gain over the matched-filter receiver in a rapidly varying, Rayleigh fading channel. The results also reiterate the fact that lower rate codes are not necessarily the best choice when used with the MMSE receiver     

RS-MPSK编码调制在传输压缩图像的Rayleigh衰落信道中的性能

本文研究了两种结构的ＲＳ－ＭＰＳＫ编码调制方案在传输压缩图像的Ｒａｙｌｅｉｇｈ衰落信道中的性能。采用计算机仿真的方法得到了该方案在Ｒａｙｌｅｉｇｈ衰落信道中的误比特率,并与理论上限进行了比较,将方案用于传输压缩图像时,可大大提高系统的性能,具有较高的理论意义和衫价值。     

On Trellis Coded Noncoherent Space-Time Modulation

Unitary space-time modulation (USTM) is well-tailored for noncoherent space-time modulation. Trellis coded USTM (TC-USTM) can obtain significant coding gains over uncoded USTM for the noncoherent block fading channel. Conventional TC-USTM schemes expand the signal set of uncoded USTM by a factor of two. In this letter, we propose a new TC-USTM scheme in which the size of USTM set is not limited to be just double for uncoded USTM. However, in TC-USTM schemes, because signals of the same trellis branch are transmitted over the same fading coefficients, one trellis branch can only obtain one temporal diversity. In this letter, we also propose a new trellis coded noncoherent space-time modulation scheme by interleaving space-time signals. The proposed scheme can enlarge temporal diversity at the price of increased complexity and delay. Simulation results demonstrate the excellent error performances of codes found by computer searches for both schemes.     

Probability of error for selection diversity as a function of dwelltime

An expression is derived for the probability of error of an N th-order selection diversity system for the case where the receiver is forced to swell on one channel for several symbols before being allowed to make a decision regarding the best channel. It is found that the time-varying nature of a fading channel causes significant degradation of the probability of error when the dwell time becomes longer than about 10% of the inverse of the fading bandwidth of the channel. The onset of degradation is a function of the signal-to-noise ratio and of the order of diversity. Specific probabilities of error are calculated for differential phase-shift keyed modulation (DPSK). However, the calculations can be done for any other modulation technique     

MQAM Performance over Nakagami channels with diversity

This paper presents the error probability performance for M-ary quadrature amplitude modulation (mqam) signalling with L-branch diversity receiver over Nakagami fading channel. Both maximal ratio combining (mrc) and selection diversity combining (sdc) techniques are considered with reference to predetection diversity architecture, in the case of integer values of fading severity and independent fading. Average symbol error probability is analitycally derived in terms of finite sum of Gauss hypergeometric functions for balanced branches with identical values of the fading severity. In particular, performance analysis of sdc for mqam in Nakagami fading is new since it has not been presented in any previous work. Numerical results are presented allowing to identify those operational conditions in which diversity techniques can aid successfully in counteracting the effects of slow and nonselective short-term fading.     

Cutoff rate of 16-DAPSK over a Rayleigh fading channel

The cutoff rate of 16-DAPSK modulation and differential detection over a Rayleigh fading channel is calculated, which provides the ensemble performance of coded data transmission. Given the code rate, the minimum SNR required for reliable communication is obtained with parameters such as the ring ratio and the diversity number     

Performance Comparison of M-QAM Communications for (S + N) and (S/N) Channel State Estimation Schemes

Channel estimation at the receiver side is essential for adaptive modulation schemes, prohibiting low complexity systems from using variable rate (VR) and/or variable power transmissions. This problem can be solved using variable-rate M-QAM modulation scheme for communications over fading channels in the absence of channel gain estimation at the receiver. It is shown that signal plus noise (S + N) sampling value can serve as a much better criterion compared to signal-to-noise ratio (S/N) for determining modulation order in VR systems. In this way, low complexity transceivers use VR transmissions to improve spectrum efficiency under an error performance constraint. Two kinds of fading channels: Weibull fading and α–μ fading are considered. Spectrum efficiency of (S + N) based systems are compared to that of S/N systems and the advantage of (S + N) scheme over (S/N) scheme is shown. The symbol error rates of two schemes are also studied. As an application, the proposed VR modulation scheme is shown to work with a maximum ratio combining diversity receiver.     

BICM-ID with signal space diversity over cascaded rayleigh fading channels [transactions letters]

Bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) is considered for cascaded Rayleigh fading channels. A tight bound on the asymptotic error probability is derived to determine the optimal rotation matrix for SSD design and to identify the key parameters that influence the system performance. It is shown that, for small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the conventional and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. Illustrative simulation results for various scenarios are in a good agreement with analytical derivations.     

Impact of diversity reception on fading channels with codedmodulation. III. Co-channel interference

For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions     

Performance analysis of coded modulation with generalized selection combining in Rayleigh fading

We consider coded modulation with generalized selection combining (GSC) for bandwidth-efficient-coded modulation over Rayleigh fading channels. Our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance. We provide a number of new results by calculating the cutoff rate, and by deriving analytical upper bounds on symbol-interleaved trellis-coded modulation (TCM) and bit-interleaved-coded modulation (BICM) with GSC. All are verified by simulation. We show that our new bounds on TCM with GSC, which includes maximum ratio combining and selection combining as special cases, are tighter than the previously derived bounds. A new asymptotic analysis on the pairwise error probability, which can be used as a guideline for designing coded modulation over GSC channels, is also given. Finally, we show that BICM with iterative decoding (BICM-ID) can achieve significant coding gain over conventional coded modulation in a multiple-receiving-antenna channel.     

LDPC-based space-time coded OFDM systems over correlated fadingchannels: Performance analysis and receiver design

We consider a space-time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. It is shown that the product of the time-selectivity order and the frequency-selectivity order is a key parameter to characterize the outage capacity of the correlated fading channel. It is also observed that STCs with large effective lengths and ideal built-in interleavers are more effective in exploiting the natural diversity in multiple-antenna correlated fading channels. We then propose a low-density parity-check (LDPC)-code-based STC-OFDM system. Compared with the conventional space-time trellis code (STTC), the LDPC-based STC can significantly improve the system performance by exploiting both the spatial diversity and the selective-fading diversity in wireless channels. Compared with the previously proposed turbo-code-based STC scheme, LDPC-based STC exhibits lower receiver complexity and more flexible scalability. We also consider receiver design for LDPC-based STC-OFDM systems in unknown fast fading channels and propose a novel turbo receiver employing a maximum a posteriori expectation-maximization (MAP-EM) demodulator and a soft LDPC decoder, which can significantly reduce the error floor in fast fading channels with a modest computational complexity. With such a turbo receiver, the proposed LDPC-based STC-OFDM system is a promising solution to highly efficient data transmission over selective-fading mobile wireless channels