Improving the generalized likelihood ratio test for unknown linear Gaussian channels

In this work, we consider the decoding problem for unknown Gaussian linear channels. Important examples of linear channels are the intersymbol interference (ISI) channel and the diversity channel with multiple transmit and receive antennas employing space-time codes (STC). An important class of decoders is based on the generalized likelihood ratio test (GLRT). Our work deals primarily with a decoding algorithm that uniformly improves the error probability of the GLRT decoder for these unknown linear channels. The improvement is attained by increasing the minimal distance associated with the decoder. This improvement is uniform, i.e., for all the possible channel parameters, the error probability is either smaller by a factor (that is exponential in the improved distance), or for some, may remain the same. We also present an algorithm that improves the average (over the channel parameters) error probability of the GLRT decoder. We provide simulation results for both decoders.     

Multilevel coded CPFSK systems for AWGN and fading channels

In this paper, we introduce multilevel coded continuous-phase frequency-shift keying (CPFSK) systems for both additive white Gaussian noise and fading channels based on multilevel coding and multistage decoding techniques. These schemes are designed under the constraint M⩾2P for M-ary CPFSK with modulation index J/P. In order to maintain the phase continuity property after multilevel coding, we use some specific set partitioning rules. We construct examples to show that the proposed systems outperform the corresponding conventional one-level schemes. For the fading case, we consider an ideal fading channel where adjacent fading symbols are assumed to be independent and a correlated fading channel where bit interleavers are needed at each coding level. The computer simulation results show that the proposed systems have bit-error performance and decoder complexity advantages over the corresponding reference codes taken from the literature. It is also shown that there is only a slight degradation on the bit-error performance for correlated fading, compared to the ideal fading case     

Detection of multiple transient signals with unknown arrival times

The problem of optimal detection of signal transients with unknown arrival times contaminated by additive Gaussian noise is considered. The transients are assumed to be time continuous and belong to a parameterized family with the uncertainty about the parameters described by means of an a priori distribution. Under the assumption of a negligible probability that the independent transient observations overlap in time, a likelihood ratio is derived for the problem of detecting an unknown number of transients from the family, each transient with unknown arrival time. The uncertainty about the arrival times is assumed to be equal for all transients and is also described by means of a distribution. Numerical simulations of the performance of detecting a particular transient signal family are presented in the form of receiver operating characteristics (ROCs) for both the optimal detector and the classical generalized likelihood ratio test (GLRT). The results show that the optimal detector yields noticeable performance improvements over the GLRT. Moreover, the results show that the optimal detector may still outperform the GLRT when the true and modeled uncertainties about arrival times no longer agree.     

Performance of parallel and serial concatenated codes on fading channels

The performance of parallel and serial concatenated codes on frequency-nonselective fading channels is considered. The analytical average upper bounds of the code performance over Rician channels with independent fading are derived. Furthermore, the log-likelihood ratios and extrinsic information for maximum a posteriori (MAP) probability and soft-output Viterbi algorithm (SOVA) decoding methods on fading channels are developed. The derived upper bounds are evaluated and compared to the simulated bit-error rates over independent fading channels. The performance of parallel and serial codes with MAP and SOVA iterative decoding methods, with and without channel state information, is evaluated by simulation over independent and correlated fading channels. It is shown that, on correlated fading channels, the serial concatenated codes perform better than parallel concatenated codes. Furthermore, it has been demonstrated that the SOVA decoder has almost the same performance as the MAP decoder if ideal channel state information is used on correlated Rayleigh fading channels.     

A soft decoding scheme for vector quantization over a CDMA channel

The optimal decoding of vector quantization (VQ) over a code-division multiple-access (CDMA) channel is too complicated for systems with a medium-to-large number of users. This paper presents a low-complexity, suboptimal decoder for VQ over a CDMA channel. The proposed decoder is built from a soft-output multiuser detector, a soft bit estimator, and the optimal soft VQ decoding of an individual user. Simulation results obtained over both additive white Gaussian noise and flat Rayleigh fading channels show that with a lower complexity and good performance, the proposed decoding scheme is an attractive alternative to the more complicated optimal decoder.     

On the universality of the LZ-based decoding algorithm

A universal decoder for a family of channels is a decoder that can be designed without prior knowledge of the particular channel in the family over which transmission takes place, and it yet attains the same random-coding error exponent as the optimal decoder tuned to the channel in use. We study Ziv's (1985) decoding algorithm, which is based on Lempel-Ziv (1978) incremental string parsing, and demonstrate that while it was originally proposed as a universal decoder for the family of finite-state channels with deterministic (but unknown) transitions, it is in fact universal for the broader class of all finite-state channels. We also demonstrate that the generalized likelihood decoder may not be universal even for finite families for which a universal decoder always exists     

On the Outage Capacity of a Practical Decoder Accounting for Channel Estimation Inaccuracies

The optimal decoder achieving the outage capacity under imperfect channel estimation is investigated. First, by searching into the family of nearest neighbor decoders, which can be easily implemented on most practical coded modulation systems, we derive a decoding metric that minimizes the average of the transmission error probability over all channel estimation errors. Next, we specialize our general expression to obtain the corresponding decoding metric for fading MIMO channels. According to the notion of Estimation-induced outage (EIO) capacity introduced in our previous work and assuming a block Rayleigh-fading channel, we characterize the maximal achievable information rates using Gaussian codebooks associated to the proposed decoder. These achievable rates are compared to the rates achieved by the classical mismatched maximumlikelihood (ML) decoder and the ultimate limits given by the EIO capacity. Numerical results show that the derived metric provides significant gains, in terms of achievable EIO rates and bit error rate (BER), in a bit interleaved coded modulation (BICM) framework, without introducing any additional decoding complexity. However, the achievable rates of such metric are still far from the EIO capacity.     

A new low SNR,correlated fading-suited space-time block code based on zero-padding and unitary transforms

In recent years, extensive studies have been done to design space-time codes appropriate for communications over fading channels in multiple input-multiple output (MIMO) systems. Most of these designs have been based upon the assumption that the channel fading coefficients are uncorrelated hence independent jointly Gaussian random variables. Naturally the best strategy in such situations that the elements of the channel matrix are independent is to employ diversity techniques to combat the adverse effects of these fading media and thus the most famous space-time codes, i.e. orthogonal and trellis codes have been designed with an eye to realizing the maximum attainable diversity order in a MIMO system. In this paper, we will remove this practically difficult to meet condition and shall introduce a new linear space-time block code based on zero-padding and unitary transforms that due to having some inherent redundancy as well as diversity is better-suited to correlated fading channels. We will discuss the properties of the proposed code, derive its maximum likelihood (ML) decoder and provide simulation results which show its superiority over the highly used orthogonal space-time block codes in a wide range of signal to noise ratios in correlated fading channels.     

未知噪声信息多径衰落信道的软判决度量生成

信道解码中的软判决技术需要利用信道噪声方差信息来产生软判决度量,而通常情况下,这一信息是未知和时变的。本文首先简要分析了信道噪声方差对软判决度量的影响,进而提出一种新的在多径衰落信道中估计时变噪声方差的方法,并利用该方法的估计结果为信道解码器生成软判决度量。将该算法应用于中国地面数字电视广播传输系统外接收机的仿真结果表明：与已有的信道噪声方差估计算法相比,本文算法具有收敛速度快、估计结果准确的优点,生成的软判决度量逼近于多径衰落信道的最优软判决度量。     

Gaussian codes and weighted nearest neighbor decoding in fading multiple-antenna channels

We investigate the fading multiple-antenna channel. The decoder is assumed to possess imperfect channel fading information. A modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information (GMI), the achievable rate, is obtained. We show that under certain conditions the achievable rate is equivalent to that of a fading multiple-antenna Gaussian channel where fading is known to the receiver and is equal to the channel estimation, and where noise is due to both the channel noise and the channel estimation error. We show that for our communication scheme, the minimum mean square error (MMSE) channel estimator is optimal in the sense that it achieves the highest value of GMI, and hence the highest communication rate. Additionally, a training based multiple-input multiple-output (MIMO) scheme in a block-fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal-to-noise ratio (SNR).     

Soft Decoding Assisted SNR Estimation Under Block Fading Channels for Orthogonal Modulations

The performance of the coded orthogonal modulation (OM) system under slow fading channels heavily depends on the estimation of the signal-to-noise ratio (SNR), including the fading amplitude and the noise spectral density. However, a relatively long packet of pilot symbols is often required to guarantee the accuracy of the SNR estimation, which makes it impractical in some situations. To address this problem, this paper proposes an iterative SNR estimation algorithm using the soft decoding information based on the expectation-maximization algorithm. In the proposed method, a joint iterative loop between the SNR estimator and decoder is performed, where the extrinsic information generated by the soft decoder is employed to enhance the estimation accuracy and the SNR estimated by the estimator is used to generate the soft information to the decoder. Also, no pilot symbols are needed to estimate the SNR in the proposed estimator. The Cramer–Rao lower bound (CRLB) of fully data-aided (FDA) estimation is derived to works as the final benchmark. The performance of the proposed algorithm is evaluated in terms of the normalized mean square errors (NMSEs) and the bit error rates (BERs) under block fading channels. Simulation results indicate that the NMSE of the proposed estimator reaches the CRLB of the FDA estimator and outperforms that of the approximate ML (ML-A) estimator proposed by Hassan et al. by 4.1 dB. The BER performance of coded OM system with the proposed estimation algorithm is close to the ideal case where the channel fading and the noise spectral density are known at the receiver.     

Sequence estimation over the slow nonselective Rayleigh fadingchannel with diversity reception and its application to Viterbi decoding

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented     

A systematic approach to carrier recovery and detection ofdigitally phase modulated signals of fading channels

The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified     

A GLRT-based spread-spectrum receiver for joint channel estimationand interference suppression

The author considers the problem of demodulating a direct-sequence (DS) spread-spectrum signal in the presence of narrowband interference and multipath. A receiver is considered that is based on the generalized likelihood-ratio test (GLRT), in which the interferer is modeled as an Nth-order circular Gaussian autoregressive (AR) process and the multipath channel is represented by a tapped-delay line. The maximum-likelihood joint estimator for the channel coefficients and interferer AR parameters is then derived. Analytical expressions for bit-error rate are presented for GLRT receiver, under the assumption of perfect estimates of the channel and interferer parameters. The performance of the GLRT receiver is compared to that of a DS receiver using a transversal equalizer. It is shown that the GLRT receiver consistently outperforms the equalizer-based receiver by 2-3 dB. The performance of an adaptive GLRT receiver is evaluated where the recursive least-squares algorithm is used to jointly estimate the interferer and channel parameters     

Universal decoding for memoryless Gaussian channels with adeterministic interference

A universal decoding procedure is proposed for memoryless Gaussian channels with deterministic interfering signals from a certain class. The proposed decoder is universal in the sense that it is independent of the channel parameters and the unknown interfering signal, and, at the same time, attains the same random coding error exponent as the optimal maximum likelihood (ML) decoder, which utilizes full knowledge of the channel parameters and the interfering signal. The proposed decoding rule can be regarded as a continuous-alphabet version of the universal maximum mutual information decoder     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

Performance Analysis of Land Mobile Satellite Communication Systems with Equal-Gain Combining over Shadowed-Rice Fading Channels

An accurate model for performance analysis of land mobile satellite (LMS) channels is the Shadowed-Rice (SR) fading model. Recently, an approximate SR model has been proposed by the author for LMS channels. Compared with the existing models, the proposed model is analytically tractable and makes it possible to approximate very accurately the probability density function (PDF) of the SR random variable (RV) by a finite weighted sum of Rice PDFs. In this paper and based on the proposed model, the statistics of the sum of independent SR RVs is studied. While this problem is well understood for common fading models such as the Rayleigh, Rice, and Nakagami, a minor attention has been devoted to the SR case. In this paper and by using the well-known Beaulieu series approach, the PDF and the Cumulative distribution function (CDF) of the sum of independent SR RVs are derived in the form of infinite convergent series. In this regard, analytical, closed-form expressions are derived for the coefficients of the Beaulieu series. To give an application of the presented results, the performance of LMS communication system employing equal-gain combining (EGC) diversity techniques over SR fading channel is investigated and novel closed-form expression is derived for the outage probability of the system.     

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.     

A sequential Monte Carlo blind receiver for OFDM systems infrequency-selective fading channels

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations