Multiple trellis coded frequency and phase modulation

Multiple trellis coded modulation of constant envelope frequency and phase modulated signal sets (MTCM/FPM) is investigated for performance on the additive white Gaussian noise (AWGN) channel and on the one-sided normal, Rayleigh and Rician fading channels. The Nakagami- m fading model is used as an alternative to the Rician fading model to calculate the error probability upper bound for trellis-coded schemes on the fading channel. The likeliness and the disparity between the upper bounds to the error probability for the two fading models are discussed. The design criteria for the one-sided normal fading channel, modeled by the Nakagami-m distribution, are observed to be the same as those for the Rayleigh-fading channel. For the MTCM/FPM schemes, it is demonstrated that the set partitioning designed to maximize symbol diversity (optimum for fading channels) is optimum for performance on the AWGN channel as well. The MTCM/FPM schemes demonstrate improved performance over MTCM/MPSK schemes and TCM/FPM schemes on the AWGN channel and the fading channel     

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.     

Performance analysis of a convolutional coded DS/CDMA system in Nakagami fading channels

In this paper, we investigate the performance of convolutional coded DS/CDMA with noncoherent M-ary orthogonal modulation operating in a multi-user environment over a slow and frequency nonselective Nakagami-m fading channel with additive white Gaussian noise (AWGN). An expression for the pairwise error probability that can be used to compute the upper bound of coded system is first derived. Performance of the DS/CDMA system with and without the convolutional codes is then presented. We have observed that convolutional codes can compensate for the degradation quite well in multi-user situations over Nakagami fading channels with AWGN. For the case of an extreme fading, however, it has been seen that the convolutional code reaches its limit to improve the overall system performance as the number of users increase. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Trellis Coded Modulation for 4800-9600 bits/s Transmission Over a Fading Mobile Satellite Channel

The combination of trellis coding and MPSK signaling with the addition of asymmetry to the signal set is discussed with regard to its suitabllity as a modulation/coding scheme for the fading mobile satellite channel. For MPSK, introducing nonuniformity (asymmetry) into the spacing between signal points in the constellation buys a further improvement in performance over that achievable with trellis coded symmetric MPSK, all this without increasing the average or peak power, or changing the bandwidth constraints imposed on the system. Whereas previous contributions have considered the performance of trellis coded modulation transmitted over an additive white Gaussian noise (AWGN) channel, the emphasis in this paper is on the performance of trellis coded MPSK in the fading environment. The results will be obtained by using a combination of analysis and simulation. It will be assumed that the effect of the fading on the phase of the received signal is fully compensated for either by tracking it with some form of phase-locked loop or with pilot tone calibration techniques. Thus, our results will only reflect the degradation due to the effect of the fading on the amplitude of the received signal. Also, we shall consider only the case where interleaving/deinterleaving is employed to further combat the fading. This allows for considerable simplification of the analysis and is of great practical interest. Finally, the impact of the availability of channel state information on average bit error probability performance is assessed.     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

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     

Design of trellis coded QAM for flat fading and AWGN channels

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated     

一种改善频谱利用率的新式混合非对称喷泉映射策略

喷泉码的原理是利用传送端产生无限多个编码数据分组,直至接收端正确地接收足够数量的编码数据分组,便可以恢复出原来的未编码信息。这种特性说明,在解出原有未编码的信息过程中,所有编码数据分组具有几乎相等的重要性。本文利用这个特性,提出了一种应用于喷泉码中的新式BPSK/QPSK混合非对称映射策略。此策略可以显著地提高系统的频谱使用率,尤其在信道具有较低信噪比的情况下。本文首先给出了AWGN信道中各种映射方式符号错误率的理论结果,并利用不同的仿真结果,证明了本文提出的BPSK/QPSK混合非对称映射策略在较低信噪比的AWGN信道下,系统性能优于传统的QPSK调制策略。上述结果提供了如下启示:当传输信道为衰落信道或受到多普勒效应影响时,由于它们的瞬时信噪比较低的可能性较高,本文提出的新的混合调制策略在此类环境具有较好的性能。     

Coding Schemes Incorporating Soft-Decision DPSK over HF Rayleigh Fading Channels

A soft-decision 8-DPSK modulation format is introducedin a concatenated coding scheme and the performance of the resultingsystem is evaluated over a slow Rayleigh fading HF ionospheric link inthe presence of Additive White Gaussian noise (AWGN). Well-known UngerboeckTCM techniques are used as inner codes and a Reed–Solomon blockcode as outer code. The coded/modulated signal is differentially encodedbefore transmission to combat random phase changes caused by the channel.Soft-decision demodulator's output is used as an input to a modifiedViterbi decoder that calculates the Euclidean distances of the receivedsignal from an 8-PSK constellation adapted to the signal's amplitudevariations. Block interleaving techniques are necessary to randomise longbursts of errors caused by the fading channel. Simulation results showthat significant coding gains are achieved with a minor bandwidth expansionover uncoded, diversity or other coded systems. Finally, theinteresting effects of interleaving on the performance of the proposedsystems are analysed.     

Information theoretic considerations for coded modulation overfading channels

We compute the random coding error exponent for coded modulation transmitted over a flat, memoryless, Rayleigh fading channel. In addition, estimates of code lengths required to achieve a certain error probability are determined and compared to those required for the additive white Gaussian noise channel. Finally, the effect of receiver antenna diversity is also considered as a method to compensate for fading and is shown to have a significant, positive impact on the error exponent. The results we obtain represent an information theoretic view that complements the existing literature on the performance of coded modulation over fading channels with receiver diversity     

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.     

Noncoherent MT-MFSK signals with diversity reception in arbitrarily correlated and unbalanced Nakagami-m fading channels

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.     

An efficient space-frequency coded OFDM system for broadband wireless communications

We propose an efficient space-frequency coded orthogonal frequency-division multiplexing (OFDM) system for high-speed transmission over wireless links. The analytical expression for the pairwise probability of the proposed space-frequency coded OFDM system is derived in slow, space- and frequency-selective fading channels. The design criteria of trellis codes used in the proposed system are then developed and discussed. It is shown that the proposed space-frequency coded OFDM can efficiently achieve the full diversity provided by the fading channel with low trellis complexity, while for traditional space-frequency coded OFDM systems, we need to design space-time trellis codes with high trellis complexity to exploit the maximum achievable diversity order. The capacity properties of space-frequency coded OFDM over multipath fading channels are also studied. Numerical results are provided to demonstrate the significant performance improvement obtained by the proposed space-frequency coded OFDM scheme, as well as the excellent outage capacity properties.     

Performance analysis of a DS/CDMA system with noncoherent M-aryorthogonal modulation in Nakagami fading

The probability of error performance of a direct sequence code-division multiple-access (DS/CDMA) system employing noncoherent M-ary orthogonal signaling in a Nakagami multipath fading channel is analyzed. A RAKE receiver structure with square-law demodulation is used at the receiver. The multiple-access interference are modeled as Gaussian and expressions derived for the exact probability of error. The performance is also evaluated in terms of the number of users that can be supported by the system at a given probability of error. The effect of correlated fading on system performance is also investigated by considering two correlation models, which can be characterized by a single correlation coefficient ρ. In the first model, the correlation coefficient between any two diversity branches is constant. In the second model, it is assumed that the correlation coefficient between any two diversity branches decreases exponentially as the separation between them increases. For both models, it is found that the presence of correlation deteriorates system performance. The use of larger signal alphabets than binary modulation in conjunction with diversity reception provides a considerable performance improvement even in the presence of correlated fading     

Impact of channel-state information on coded transmission overfading channels with diversity reception

We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian     

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     

Soft-decision COVQ for turbo-coded AWGN and Rayleigh fadingchannels

A robust soft-decision channel-optimized vector quantization (COVQ) scheme for turbo coded additive white Gaussian noise (AWGN) and Rayleigh fading channels is proposed, The log likelihood ratio (LLR) generated by the turbo decoder is exploited via the use of a q-bit scalar soft-decision demodulator. The concatenation of the turbo encoder, modulator, AWGN channel or Rayleigh fading channel, turbo decoder, and q-bit soft-decision demodulator is modeled as an expanded discrete memoryless channel (DMC). A COVQ scheme for this expanded discrete channel is designed. Numerical results indicate substantial performance improvements over traditional tandem coding systems, COVQ schemes designed for hard-decision demodulated turbo coded channels (q=1), as well as performance gains over a recent soft decoding COVQ scheme by Ho (see IEEE Commun. Lett., vol.3, p.208-10, 1999)     

带有分集的RS码非相干混合DS-SFH扩频通信系统性能分析

本文针对部分带宽噪声干扰、多址干扰和高斯白噪声等多种干扰以及Ｒｉｃｉａｎ信道衰落存在环境下,编码与非编码的异步非相干ＭＦＳＫ调制混合ＤＳ－ＳＦＨ扩频通信系统性能进行了分析、计算和比较。本文分析的编码为前向纠错编码,包括ＲＳ（Ｎ,Ｋ）码,带有分集的ＲＳ（Ｎ,Ｋ）码。与此同时分析和讨论了分集、Ｒｉｃｉａｎ衰落以及部分带宽噪声干扰、多址干扰等对系统性能的影响,得到一些重要结果。     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.