A reduced state variant of maximum likelihood sequence detection attaining optimum performance for high signal-to-noise ratios

In the detection ofm-level pulse-amplitude modulation (PAM) signals transmitted over a noisy linearnu-symbol memory channel, maximum likelihood sequence detection (MLSD) is asymptotically optimum in the sense that the exponent of the probability of symbol error in the limit of small noise is the largest that can be achieved by any detector. A reduced state detection (RSD) is developed with the aim of mitigating the computational complexity of MLSD while attaining the same error exponent as MLSD. In RSD, for each baud, the recent received signal levels delineate a certain list of the most probable of them^{nu}possible states. Retention of only the paths threading through these most probable states is the key to success of RSD. Suppose it is required that the number of states retained at any time not exceedpsi. Whenpsiis less than the number of states required for RSD, it is shown how to modify RSD so that no more thanpsistates are retained and how to assess the degradation of the error exponent.     

Iterative detectors for trellis-code multiple-access

Trellis-code multiple-access (TCMA) is a narrow-band multiple-access scheme based on trellis-coded modulation. There is no bandwidth expansion, so K users occupy the same bandwidth as one single user. The load of the system, in number of bits per channel use, is therefore much higher than the load in, for example, conventional code-division multiple-access systems. Interleavers are introduced as a new feature to separate the users. This implies that the maximum-likelihood sequence detector (MLSD) is now too complex to implement. Iterative detectors are therefore suggested as an alternative to the joint MLSD. The conventional interference cancellation (IC), detector has lower complexity than the MLSD, but its performance is shown to be far from acceptable. Even after a novel improvement of the IC detector, the performance is unsatisfactory. Instead of using IC, another iterative detector is suggested. This detector updates the branch metric for every iteration, and avoids the standard Gaussian approximation. Simulations show that the performance of this detector can be close to single-user performance, even when the interleaver and the phase offset are the only user-specific features in the TCMA system.     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

A Class of Soft Decision Error Detectors for the Gaussian Channel

The main idea of this concise paper is to use symbol reliability information for improving the performance of error detectors. A class of soft decision error detectors (SDED's) is presented, where low weight error patterns are selectively corrected. The reliability numbers govern which error pattern to correct. Asymptotic performance and bounds are derived for the Gaussian channel. It is shown that singleerror correcting SDED's without thresholds have an exponentially lower repeat request probability than the hard decision error detector, but the same exponent in the probability of undetected errors. Detectors with thresholds are also considered. In this case it is possible to contruct an error detector with both better probability of undetected errors and better probability of repeat request than for the hard decision error detector (HDED). Bounds and computer simulations are presented and SDED's are compared to HDED's.     

On differentially encoded star 16QAM with differential detectionand diversity

Star 16QAM is a modulation method that transmits 4 bits per symbol and has the advantage that it may be differentially encoded and detected. It is very robust to fast multiplicative Rayleigh fading and is suitable for mobile telephone systems and personal communication networks. The main contribution of this paper is the derivation and bit error probability simulation of the maximum likelihood differential detector using phase differences and amplitude ratios from L diversity branches for bit decisions. As a comparison, much simpler previously known post detection combining techniques are generalized for star 16QAM and optimized. The bit error probability is simulated for both diversity detectors on a multiplicative Rayleigh fading channel with additive white Gaussian noise. It is found that the bit error probability of the ML detector may also be obtained by the simple combining detector. This is also true for the error floor due to the maximum Doppler frequency. The diversity gain is almost 8 dB, measured in signal to noise ratio per diversity branch, at a bit error probability of 1 percent. The diversity detector can sustain an almost 3 times larger Doppler frequency again at a bit error probability of 1 percent. We also show that star 16QAM offers, at most, 3 subchannels with different bit error probabilities     

Breadth-first maximum likelihood sequence detection: basics

The problem of performing breadth-first maximum likelihood sequence detection (MLSD) under given structural and complexity constraints is solved and results in a family of optimal detectors. Given a trellis with S states, these are partitioned into C classes where B paths into each class are selected recursively in each symbol interval. The derived result is to retain only those paths which are closest to the received signal in the Euclidean (Hamming) distance sense. Each member in the SA(B, C) family of sequence detectors (SA denotes search algorithm) performs complexity constrained MLSD for the additive white Gaussian noise (AWGN) (BSC) channel. The unconstrained solution is the Viterbi algorithm (VA). Analysis tools are developed for each member of the SA(B, C) class and the asymptotic (SNR) probability of losing the correct path is associated with a new Euclidean distance measure for the AWGN case, the vector Euclidean distance (VED). The traditional Euclidean distance is a scalar special case of this, termed the scalar Euclidean distance (SED). The generality of this VED is pointed out. Some general complexity reductions exemplify those associated with the VA approach     

Performance evaluation of differential and discriminator detection of continuous phase modulation

Recently, bandwidth efficient constant-amplitude digital modulation schemes have also been shown to be power efficient when coherent detection is used. Partial-response continuous phase modulation (CPM) schemes are within this class. In some applications noncoherent detection is preferred. The performance of CPM systems is analyzed for differential and discriminator detection. An additive white Gaussian channel is assumed. The detectors make symbol-by-symbol decisions. The considered schemes are M-ary with an arbitrary modulation index and pulse shaping over several symbol intervals. The performance is analyzed by means of error probability expressions. The IF filter for the detectors is optimized within a special class of filters to give good performance. The differential detector is also analyzed on a Rayleigh fading channel. The fading is assumed to be slow. The IF filter is also optimized on this channel. Simulated error probabilities for discriminator detection with a Viterbi detector are also presented both for the Gaussian and the Rayleigh fading channel. The discriminator detector making symbol-by-symbol decisions is simulated on the Rayleigh fading channel. It is shown that partial-response CPM schemes with good performance can also be obtained with noncoherent detectors.     

Aspects on single symbol signaling on the frequency flat Rayleighfading channel

The optimal single symbol detector on the Rayleigh fading channel computes a functional quadratic form in the time continuous received signal. A drawback is that closed-form solutions of integral equations based on the channel statistics are required. This makes simplified discrete receivers attractive. A class of suboptimal receivers that transforms the received random process to a set of discrete observables is derived. The set of observables constitutes a random vector in a finite dimensional receiver signal space. Given this vector, the maximum likelihood detector computes a quadratic form in the received vector. The discretization implies a loss of information, therefore such a detector is not, in general, optimal given the received time continuous signal. The purpose is, however, to achieve close to optimal performance when the number of observables becomes large. This class of detectors is analyzed using exact error probability calculations, which reveal several interesting properties. The length of the observation interval and the number of discrete observables have significant influences on the error probability when the time variations of the fading process are rapid compared with the symbol duration. By increasing the number of observables, the error floor is lowered, and the implicit diversity order is increased. This implicit diversity arises as soon as more than one observable per symbol interval is used and is a consequence of the information bearing signal being a random process. Matched filter receivers use few discrete observables per symbol interval, and thus suffer from high error floors and low implicit diversity orders on fast fading channels. The error probability is highly dependent on the shapes and durations of the modulator waveforms. For instance, pulses of long duration give lower error probabilities than shorter pulses, and for a certain type of orthogonal waveforms there is no error floor     

Efficient sequence detection for intersymbol interference channelswith run-length constraints

This paper addresses the data detection problem of intersymbol interference (ISI) channels with a specific modulation code-constraint known as the (d, k) run-length-limited (RLL) constraint, a popular modulation code-constraint for data storage channels as well as certain communication channels. A computationally efficient sequence detection algorithm is proposed which yields a performance close to that of the maximum likelihood sequence detector when applied to such ISI channels. The proposed detector is derived as a high signal-to-noise ratio approximation to the delay-constrained optimum detector, one which minimizes the symbol error probability given a fixed decision-delay constraint. The proposed algorithm is essentially a fixed-delay tree search (FDTS) algorithm with systematic ambiguity checking and is closely related to existing finite-depth tree search algorithms. It is observed that long critical error events common in uncoded ISI channels are eliminated by the RLL constraint. Based on this observation, we show that for some important RLL constrained channels, the proposed FDTS algorithm yields the same minimum Euclidean distance between distinguishable channel output sequences as the unconstrained maximum likelihood sequence detector     

Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.     

Further Studies of Soft Decision Error Detectors for the Gaussian Channel

This correspondence is an extension of the work in [1] and [2]. We present two new classes of error detectors which utilize symbol reliability information (i.e., soft decision error detectors). First, a simple class of selectively single error correcting error detectors is discussed where the syndrome information is used and where just one single reliability number is compared to a threshold value. These error detectors are simpler than those in [1] and [2], but less powerful. Second, a class of soft decision error detectors with low probability of undetected errors is considered. The reliability information is used to reduce the probability of undetected errors without increasing the repeat request probability (compared to the hard decision error detector). Exponential properties for large signal-to-noise ratios and bounds are calculated for both classes of error detectors. Computer simulations are also presented.     

Error probability analysis for continuous phase modulation withViterbi detection on a Gaussian channel with multiple signalinterference

The effects are studied on the symbol error probability of the Viterbi detector for continuous phase modulations with constant amplitude, when the desired signal is received in multiple interfering signals and white Gaussian noise. The detection is assumed to be coherent and, furthermore, perfect timing in the detector is also assumed. An upper bound on the symbol error probability is derived for the Viterbi detector. The bound is based on the union bound technique, and it is shown to be tight for small error probability levels. It is found that the smoothed binary and all quaternary modulations sustain much larger interference power in adjacent channel interference than minimum-shift keying (MSK) does and, thus, the adjacent channels can be spaced closer in frequency for these modulations, In particular, the smoothed quaternary modulations seem to be significantly more efficient than MSK. In cochannel interference the difference in error performance between the schemes is relatively small     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for knownM-ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.     

UWB multi-pulse position modulation for high data-rate wireless application

1 Introduction UWB technology is considered to be a good candidate for future short-range high-data rate wireless communications [1, 2], and modulation plays an important role in UWB wireless communication systems. There are several modulation schemes possible for UWB, such as pulse position modulation (PPM), pulse amplitude modulation (PAM), On-Off keying (OOK), binary phase-shift keying (BPSK), and so on. Reference [3] provides the analysis result of the different modulation methods…     

酉空时调制系统中最大似然多符号差分检测的性能分析

在酉空时调制系统中,针对连续衰落信道下最大似然多符号差分检测给出了一种误符号率截断联合界的数值计算方法.采用Gauss-Chebyrshev求积公式对成对错误概率进行数值计算,并利用提取主要错误事件技术对误符号率的联合界进行了化简.数值与仿真结果表明,采用该方法计算出的截断联合界可以在低信噪比下提供误符号率的一个上界,在较高信噪比下获得它的良好估计.在性能分析基础上进一步提出了一种近似最大似然度量,分析与仿真说明,采用该度量的多符号差分检测算法的性能非常接近最大似然检测.     

Penalties of Sample-and-Sum and Weighted Partial Decision Detectors in Gaussian Noise

The deterioration in performance, measured in the probability of error sense, of sample-and-sum and weighted partial decision detectors are analyzed for arbitrary signal-to-noise ratios. These suboptimal detectors have more modest computational requirements than the optimal digital matched filter making them amenable to simple digital implementations. The effects on the penalties of the signaling waveform employed, the number of samples processed, and the signal-to-noise ratio are considered in detail. Included are the penalties for the optimum weighted partial decision detector. The optimum weighted partial decision detector is the optimum detector, in the minimum probability of error sense, for hard-limited samples. The penalty of the optimum weighted partial decision detector relative to the digital matched filter detector represents the fundamental loss in signal detectability due to hard-limiting in a sampled system.     

Improving error probability of the prefiltered Viterbi equalizer

The article deals with the design of suboptimal data detectors for binary transmission over frequency selective channels. A detector consisting of a prefilter followed by a Viterbi processor with a number of states lower than that needed for maximum likelihood sequence estimation is considered. Often the parameters of the receiver are optimized according to the minimum mean square error criterion. Here a stochastic approximation algorithm that optimizes the parameters of the receiver according to a measure of the error probability is introduced. Simulation results show that the proposed design gives substantial benefits at moderate to high signal to noise ratio     

Optimum Pilot Symbol Assisted Modulation

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.