Performance of MFSK signals with postdetection square-law diversity combining in arbitrarily correlated Nakagami-m fading channels

This letter presents an analysis of the error probability for noncoherent orthogonal multiple frequency-shift keying (MFSK) signals with postdetection square-law combining (SLC) when the signals transmitted over additive white Gaussian noise (AWGN) and slow frequency-nonselective arbitrarily correlated Nakagami-m fading channels. New exact expressions in a onefold integral for the probability of error of MFSK signals with postdetection square-law diversity combining operating in AWGN channel as well as in arbitrarily correlated Nakagami-m fading channels are derived. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the L diversity channels are considered. The derived expressions can be easily computed, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.     

Performance limits of M-FSK with Reed-Solomon coding and diversity combining

This paper examines the asymptotic (M/spl rarr//spl infin/) performance of M-ary frequency-shift keying (M-FSK) in multi-channels, or multiple frequency-nonselective, slowly fading channels, with coding, side information, and diversity reception. In particular, Reed-Solomon (RS) coding is considered in conjunction with the ratio-threshold test (RTT), which generates side information regarding the reliability of received symbols. The asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining (MRC), postdetection equal gain combining (EGC), hybrid selection combining (H-SC), and selection combining (SC) is derived for an arbitrary statistical fading model and diversity order. The derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically. In addition, the asymptotic results are evaluated assuming a Nakagami-m fading model, and the effect of fading severity, diversity order, code rate, and side information upon the performance of the various diversity combiners is investigated. The minimum signal-to-noise ratio (SNR) required to achieve arbitrarily reliable or error-free communication, as well as the associated optimal RS code rate, are determined for various cases.     

MFSK和GMSK调制方式在短波跳频通信系统中的应用及性能仿真

本文主要讨论MFSK和GMSK（高斯滤波最小频移键控）控制方式在短波跳频通信系统中的应用，并对其性能进行了数值仿真。对于MFSK调制方式，本文重点讨论了将带反馈链路的选择式频率分集和编码技术应用于短波FH/MFSK系统对性能的改善。并分析当在具有加性高斯噪声的瑞利衰落信道中存在部分频带阻塞时的性能。GMSK具有优良的频谱特性，本文仿真了结合Viterbi算法非相干解调方案时跳频系统的性能。最后对两种调制方式进行了初步比较。     

MFSK和GMSK调制方式在短波跳频通信系统中的应用及性能仿真

本文主要讨论MFSK和GMSK(高斯滤波最小频移键控)调制方式在短波跳频通信系统中的应用,并对其性能进行了数值仿真.对于MFSK调制方式,本文重点讨论了将带反馈链路的选择式频率分集和编码技术应用于短波FH/MFSK系统对性能的改善,并分析当在具有加性高斯噪声的瑞利衰落信道中存在部分频带阻塞时的性能.GMSK具有优良的频谱特性,本文仿真了结合Viterbi算法非相干解调方案时跳频系统的性能.最后对两种调制方式进行了初步比较.     

Coded modulation for noncoherent reception with application to OFDM

Power- and bandwidth-efficient differentially encoded transmission over slowly time-varying fading channels with noncoherent reception and without channel state information is considered. For high bandwidth efficiencies, combined phase and amplitude modulation is used. For increased power efficiency, channel coding and multiple-symbol differential detection are applied, i.e., interleaving and detection are based on blocks of N>2 consecutive symbols. The presented concepts are directly applicable to transmission over flat fading channels. However, concentrating on the situation of frequency-selective channels, we consider their application to multicarrier transmission using orthogonal frequency-division multiplexing (OFDM). When coding across subcarriers, OFDM transforms the actual frequency-selective channel into a slowly time-varying frequency-nonselective fading channel. This paper presents a design for multilevel coding schemes to approach theoretical limits for power- and bandwidth-efficient noncoherent transmission over the equivalent fading channel. It is shown that bit-interleaved coded modulation, which relies on Gray labeling, is competitive only in the case of conventional differential detection with N=2. The theoretic considerations are well approved by simulation results, where turbo codes are applied as component codes     

Error performance of noncoherent MFSK with L-diversity oncorrelated fading channels

Noncoherent diversity reception of M-ary frequency-shift keying (MFSK) signals becomes increasingly important due to its widespread use in wireless communications. Its error performance analysis, however, is not available in the literature except for the simple case using binary modulation. We address the problem directly based on the decision variables, ending up with closed-form solutions to both conditional and average error probabilities for a general noncoherent MFSK diversity system operating on Rayleigh, Rician, and Nakagami fading channels. The solutions involve some higher order derivatives, and efficient recursive algorithms have been derived for their calculation. The solutions are very general permitting arbitrary diversity order, symbol size, channel parameters, and antenna-array covariance matrix. Numerical examples are also presented for illustration     

Coherent detection of biorthogonal signals over Rayleigh fadingchannels

A practical coherent detection scheme for biorthogonal signals over Rayleigh fading channels is proposed. The proposed scheme improves the bit error rate (BER) performance compared to the noncoherent detection schemes for biorthogonal signals. It also outperforms the coherent and noncoherent detection schemes for orthogonal signals with comparable bandwidth efficiency. The BER performance for a Rayleigh fading channel with two path diversity combining is obtained by computer simulation. The results show that the required average signal-to-noise ratio per bit γ_b can be reduced by as much as 1.4 dB when we use this system in the CDMA cellular reverse link     

A new method for phase synchronization and automatic gain controlof linearly modulated signals on frequency-flat fading channels

An optimal phase synchronization and automatic gain control (AGC) scheme for coherent reception of linearly modulated signals on frequency-flat mobile fading channels is presented. The channel model and receiver performance are described. It is shown that using the technique allows the irreducible error floors (due to random FM) known from the noncoherent methods to be practically eliminated. Depending on the fastness of the fading, large power gains over the noncoherent methods are achieved. Unfavorable analog signal processing and/or the high bandwidth inefficiency of the FDM-pilot coherent methods are also avoided     

Two-Dimensional DPCM Image Transmission Over Fading Channels

A combined source-channel coding approach is described for the encoding, transmission, and remote reconstruction of image data. The transmission medium considered is that of a fading dispersive communications channel. Both the Rician fading and Rayleigh fading channel models are considered. The image source encoder employs two-dimensional (2-D) differential pulse code modulation (DPCM). This is a relatively efficient encoding scheme in the absence of channel errors. In the presence of fading, however, the performance degrades rapidly. By providing error control protection to those encoded bits which contribute most significantly to image reconstruction, it is possible to minimize this degradation without sacrificing transmission bandwidth. Several modulation techniques are employed in evaluation of system performance including noncoherent multiple frequency shift-keyed (MFSK) modulation. Analytical results are provided for assumed 2-D autoregressive image models, while simulation results are described for real-world images.     

An efficient modulation/coding scheme for MFSK systems on bandwidthconstrained channels

The performance of a bandwidth-efficient multiple-tone modulation scheme for M-ary frequency-shift keying (MFSK) is presented. The use of balanced incomplete block (BIB) designs is proposed to form the signaling frames. On each symbol interval the modulator selects a group of elements from a BIB design and divides its energy into the orthogonal waveforms corresponding to these elements. The multiple-tone FSK scheme based on these block designs is shown to increase greatly the bandwidth efficiency of a conventional M-ary FSK system. An implicit diversity is incorporated in the modulation scheme. Thus, a performance improvement comparable to that obtained by using time or frequency diversity is shown on a Rayleigh fading channel and also on an interference channel with partial-band Gaussian noise. The multiple-tone scheme based on this design is compared to a multiple-tone scheme based on Hadamard matrices suggested by J.F. Pieper et al. (1978). It is shown that similar performance is achieved on a fading channel, while an advantage close to 4 dB is obtained for the proposed scheme on an AWGN (additive white Gaussian noise) channel     

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.     

Differential modulation diversity

In this paper, differential modulation diversity (DMD) is introduced. This diversity scheme is based on diagonal signal constellations which have been previously proposed for differential space-time modulation (DSTM). DMD can exploit both space and time diversity and DSTM, which is a pure space-diversity scheme, results as a special case. Low-complexity noncoherent receivers originally designed for DSTM are adapted to DMD and the power efficiency of DMD for Ricean fading with spatial correlation and imperfect interleaving is investigated. Based on analytical expressions for the pairwise error probability it is shown that space diversity increases the effective fading bandwidth, which has a negative influence on performance. Time diversity does not have this disadvantage and is preferable especially for fast fading channels. If space and time diversity are combined, a robust receiver results that yields high performance for a wide range of fading velocities.     

MRC performance for binary signals in Nakagami fading with generalbranch correlation

Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation     

Exact analysis of postdetection combining for DPSK and NFSK systemsover arbitrarily correlated Nakagami channels

Postdetection combining is a popular means to improve the bit error performance of DPSK and noncoherent FSK (NFSK) systems over fading channels. Nevertheless, the error performance of such systems in an arbitrarily correlated Nakagami environment is not available in the literature. The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output. We directly determine the error probability from the characteristic function of decision variables, resulting in closed-form solutions involving matrix differentiation. The performance calculation is further simplified by developing a recursive technique. The theory is illustrated by analyzing two feasible antenna arrays used in base stations for diversity reception, ending up with some findings of interest to system design     

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.     

Performance of fast frequency-hopped MFSK receivers with linear andself-normalization combining in a Rician fading channel withpartial-band interference

An error probability analysis is performed for both self-normalized and conventional M-ary orthogonal frequency-shift-keying (MFSK) noncoherent receivers using fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a Rician fading channel with partial-band interference. The self-normalization receiver uses a nonlinear combination procedure to minimize performance degradation due to partial-band interference. The performance of the conventional receiver is significantly degraded by worst-case partial-band interference regardless of the modulation order or number of hops per data symbol used, while the self-normalization receiver can provide a significant immunity to worst-case partial-band interference for many channel conditions when diversity is used, provided the signal-to-thermal-noise ratio is large enough to minimize degradation due to nonlinear combining losses. The improvement afforded by higher modulation orders is dependent on channel conditions     

Joint noncoherent demodulation and decoding for the block fading channel: a practical framework for approaching Shannon capacity

The paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels, guided by explicit comparisons with information-theoretic benchmarks. Noncoherent reception is interpreted as joint data and channel estimation, assuming that the channel is time varying and a priori unknown. We consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection. For an information rate of about 1/2 bit per channel use, the proposed scheme, using a quaternary phase-shift keying (QPSK) alphabet, provides performance within 1.6-1.7 dB of Shannon capacity for the block fading channel, and is about 2.5-3 dB superior to standard differential demodulation in conjunction with an outer channel code. We also provide capacity computations for noncoherent communication using standard phase-shift keying (PSK) and quadrature amplitude modulation (QAM) alphabets; comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal-to-noise ratio. These results imply that QPSK suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations, but that QAM is superior to PSK for higher information or fading rates, motivating further research into efficient noncoherent coded modulation with QAM alphabets.     

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.     

Hybrid DS/SFH-SSMA with predetection diversity and coding overindoor radio multipath Rician-fading channels

The authors investigate the bit-error-rate (BER) performance of hybrid direct-sequence/slow-frequency-hopped spread-spectrum multiple-access (DS/SFH-SSMA) systems operating over a multipath Rician-fading channel (which models indoor radio propagation in factories). They consider both phase-shift-keying (PSK) modulation with coherent demodulation and differential phase-shift-keying (DPSK) modulation with noncoherent demodulation. Predetection multipath diversity (maximal ratio combining for coherent reception and equal gain combining for noncoherent reception) and simple interleaved channel coding are employed for improving the BER performance. The BER of both coherent and noncoherent hybrid systems is obtained using a Gaussian interference approximation     

Analytical study of FFH systems with square-law diversity combiningin the presence of multitone interference

An analytical study of the performance of fast frequency-hopped (FFH), M-ary orthogonal frequency-shift keyed noncoherent modulation with linear combining of square-law envelopes in the presence of multitone interference is presented. The multiple equal-power interference tones are assumed to correspond to some of the possible FFH/M-ary orthogonal signaling tones. It is also assumed that the channel fading characteristics of the signal and interference tones are independent. We evaluate the effect of the channel fading on the system's performance as a function of various parameters, such as the number of hops per symbol, the signal power to multitone interference power ratio, and the number of interference tones. Our numerical results indicate that by use of square-law time diversity combining, a large number of hops per symbol make the bit-error probability of the system more sensitive to the fading of multitone interference. Finally, the analysis has been proven valid by simulation