Optimum detection and signal selection for partially coherent binary communication

The optimum detectors for coherent and noncoherent reception of binary signals in additive Gaussian noise and the resuiting error probabilities were obtained by Helstrom [1]. In many practical communication systems a reasonable estimate of the phase of the received signal is available as the result of an auxiliary tracking operation of the carrier signal by a coherent tracking device such as a phase-locked loop. It is shown that the optimum detector for this case, which we refer to as partially coherent reception, is a linear combination of the correlation detector and the squared envelope correlation detector, which are optimum for the coherent and noncoherent cases, respectively. The error probabilities are also obtained as a function of the energy-to-noise ratio of the channel and the variance of the error in the phase estimate, which is a function of the signal-to-noise (SNR) in the tracking loop. The signal selection problem is considered in terms of these parameters.     

Noncoherent detection of convolutionally encoded continuous phasemodulation

The authors consider the error probability at large signal-to-noise ratios of rate-1/2 convolutionally encoded CPFSK (continuous-phase frequency-shift keying) with an optimum noncoherent detector on an additive white Gaussian noise channel. The performance is given in terms of a parameter called the minimum squared normalized equivalent Euclidean distance which plays the same role mathematically as the minimum squared normalized Euclidean distance used for coherent detectors. It is shown that by introducing convolutional coding the error performance is significantly improved. The authors propose a decoding algorithm for these convolutionally encoded CPM schemes which is based on a limited tree search algorithm and uses the maximum-likelihood decision rule for noncoherent detection. Computer simulations show that the degradation in error performance compared to the performance of the optimum coherent Viterbi detector is less than 1 dB with a relatively simple noncoherent detector on an additive white Gaussian noise channel for most of the schemes considered     

Locally optimum detection of signals in a generalized observationmodel: the random signal case

Locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal-dependent and multiplicative noise. It is shown that the locally optimum random-signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model. Examples of explicit results for the locally optimum detector test statistics are given for some typical cases. Both asymptotic and finite sample-size performances of the locally optimum detectors are considered and compared with those of other standard detector structures     

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.     

乘性噪声环境下基于符号秩统计量的非参伪码捕获方法

扩频系统常常工作在多径环境中,伴随着加性噪声的同时往往还存在着乘性噪声.该文提出了一种乘性噪声环境下基于符号秩统计量的非参伪码捕获方法,将伪码捕获等价为假设检验问题,利用局部最佳检测算法推导出了乘性噪声环境下基于符号秩的检测统计量,通过简化记分函数进一步给出了局部次佳秩检测器.将局部次佳秩检测器与局部最佳检测器和平方和检测器的性能进行了仿真对比,结果表明该文所提出的捕获方法在乘性噪声环境下检测性能接近于乘性噪声环境下的局部最佳检测器,而较平方和检测器则有较大幅度的提高.     

Autocorrelation-based blind spreading-factor detection for CDMA

Spreading factor (SF) in code-division multiple-access (CDMA) systems depends on the data rate of the user, and is, therefore, unknown a priori for a communication receiver. In this letter, the blind SF-detection problem in an additive white Gaussian noise channel is studied, and a novel one-step autocorrelation-based SF detector is proposed. Three decision rules are derived to find simple and robust SF detectors for practical communication receivers. Performance of the detectors is studied and compared with the optimal detector via Monte Carlo computer simulations. The autocorrelation-based SF detector appears to give performance close to the optimal detector, assuming perfect knowledge of signal-to-noise ratio (SNR). It is also found to be significantly more robust to SNR estimation errors than the optimal detector.     

PN code acquisition using signed-rank-based non-parametric detector in a multiplicative noise model

Multiplicative noise is known to be useful in modelling an environment that is difficult to describe with an additive noise model. In this article, signed-rank-based non-parametric detectors are used for pseudonoise (PN) code acquisition in multiplicative noise. First, a locally optimum (LO) detector based on the signs and ranks of observations is derived, and then the locally suboptimum rank (LSR) detector is proposed by using approximate score functions. The finite sample-size performance of the LSR detector is considered. Numerical results show that the LSR detector asymptotically has almost the same performance as the LO detector for multiplicative noise.     

Analytic behavior of the LMS adaptive line enhancer for sinusoidscorrupted by multiplicative and additive noise

The least mean squares adaptive line enhancer (LMS ALE) has been widely used for the enhancement of coherent sinusoids in additive wideband noise. This paper studies the behavior of the LMS ALE when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise. The multiplicative noise decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Closed-form expressions are derived for the optimum (Wiener filter) ALE output SNR as a function of the residual coherent sine wave power, the noncoherent sine wave power spectrum, and the background additive white noise. When the coherent to noncoherent sine wave power ratio is sufficiently small, it is shown that a nonlinear (e.g., square law) transformation of the ALE input results in a larger optimum ALE output SNR     

Comparison of known signal detection schemes under a weaklydependent noise model

The authors consider the discrete-time signal detection problem under the presence of additive noise exhibiting weak dependence. They first propose a weakly dependent noise model, in which the additive noise is modelled as a moving average process. They derive the locally optimum, memoryless, and one-memory detector test statistics under the model. The asymptotic performance of the one-memory detector is compared with that of the locally optimum and memoryless detectors. Specific examples for the asymptotic performance comparison of these detectors are considered. The authors also investigate the finite sample-size performance of several detectors through Monte-Carlo simulation. It is observed that the one-memory detector can achieve almost optimum performance at the expense of only one memory unit under the weakly dependent noise model, and is rather insensitive to slight model change     

Adaptive nonparametric locally optimum Bayes detection in additive non-Gaussian noise

A nonparametric generalization of the locally optimum Bayes (LOB) parametric theory of signal detection in additive non-Gaussian noise with independent sampling is presented. From a locally asymptotically normal (LAN) expansion of the log-likelihood ratio the nonparametric detector structure, in both coherent and incoherent modes, is determined. Moreover, its statistics under both hypotheses are obtained. The nonparametric LAN log-likelihood ratio is then reduced to a least informative (i.e., having minimum variance under the hypothesis, H/sub 0/) local parametric submodel, which is referred to as adaptive. In the adaptive submodel, certain nonlinearities are replaced by their efficient estimates. This is accomplished such that no information is lost when the noise first-order density is no longer parametrically defined. Adaptive nonparametric LOB detectors are thus shown to be asymptotically optimum (AO), canonical in signal waveform, distribution free in noise statistics, and identical in form (in the symmetric cases) to their parametric counterparts. A numerical example is provided when the underlying density is Middleton's (see ibid., vol.45, p.1129-49, May 1999)Class-A noise, which demonstrates that even with a relatively small sample size (O(10/sup 2/)) adaptive LOB nonparametric detectors perform nearly as well as the classical LOB detectors.     

乘性噪声环境下基于局部最佳检测器的伪码捕获方法

扩频系统常常工作在多径环境中,伴随着加性噪声的同时往往还存在着乘性噪声。该文提出了一种乘性噪声环境下伪码捕获方法,将伪码捕获等价为假设检验问题,利用局部最佳检测算法推导出乘性噪声环境下的伪码捕获检测统计量,文中给出了基于局部最佳检测算法的捕获结构,并与传统的平方和检测器进行了性能仿真对比,结果表明该文所提出的捕获方法在乘性噪声环境下检测性能较平方和检测器有较大幅度的提高,而在无乘性噪声的环境下检测性能只较传统的平方和检测器检测性能稍有降低。     

Pattern-dependent noise prediction in signal-dependent noise

Maximum and near-maximum likelihood sequence detectors in signal-dependent noise are discussed. It is shown that the linear prediction viewpoint allows a very simple derivation of the branch metric expression that has previously been shown as optimum for signal-dependent Markov noise. The resulting detector architecture is viewed as a noise predictive maximum likelihood detector that operates on an expanded trellis and relies on computation of branch-specific, pattern-dependent noise predictor taps and predictor error variances. Comparison is made on the performance of various low-complexity structures using the positional-jitter/width-variation model for transition noise. It is shown that when medium noise dominates, a reasonably low complexity detector that incorporates pattern-dependent noise prediction achieves a significant signal-to-noise ratio gain relative to the extended class 4 partial response maximum likelihood detector. Soft-output detectors as well as the use of soft decision feedback are discussed in the context of signal-dependent noise     

Improved energy detector for random signals in gaussian noise

New and improved energy detector for random signals in Gaussian noise is proposed by replacing the squaring operation of the signal amplitude in the conventional energy detector with an arbitrary positive power operation. Numerical results show that the best power operation depends on the probability of false alarm, the probability of detection, the average signal-to-noise ratio or the sample size. By choosing the optimum power operation according to different system settings, new energy detectors with better detection performances can be derived. These results give useful guidance on how to improve the performances of current wireless systems using the energy detector. It also confirms that the conventional energy detector based on the generalized likelihood ratio test using the generalized likelihood function is not optimum in terms of the detection performance.     

Direct-Detection Optical Communication Receivers

A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for randomly filtered doubly stochastic Poisson processes observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector-valued Markov process that modulates the intensity of the doubly stochastic Poisson process are obtained. Quasi-optimum estimators and detectors are specified in general terms and specialized for several important applications. These include a demodulator for subcarrier angle modulation, a detector structure for binary signaling with known intensities, and a detector structure for binary signaling in the turbulent atmosphere.     

Novel noncoherent detection for multi‐hop amplify‐and‐forward relaying systems

Because of the multiplication of fading gains and noise, the actual distributions of the received signals in multi‐hop amplify‐and‐forward relaying systems are no longer Gaussian. In this work, they are fitted with the t location‐scale distribution and the logistic distribution. Using these distributions, two novel noncoherent detectors are proposed based on the maximum likelihood method. Numerical results show that both new detectors outperform the conventional energy detector. The performance gain increases when the signal‐to‐noise ratio increases or when the hop number decreases. Importantly, the bit error rate of the conventional energy detector reaches an error floor while the bit error rates of the new detectors do not. Copyright © 2015 John Wiley & Sons, Ltd.     

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     

Coherent MAP detection of DQPSK bits

Both IS-136 and PDC digital cellular systems employ forward error correction (FEC) encoding followed by a form of DQPSK modulation. In this letter, we derive the maximum a posteriori (MAP) bit detector for DQPSK modulation in non-ISI channels for a coherent receiver with one or more antennas. The MAP detector forms a bit log-likelihood ratio, which provides the optimal “soft information” for MLSE or MAP convolutional decoding. MAP detection requires exponentiation and logarithm operations, as well as knowledge of the noise covariance. To avoid these operations, two approximate forms are developed, which do not require the noise covariance value under certain assumptions. Both approximate approaches, when used with soft FEC decoding, are within 0.5 dB of the optimal approach     

A statistical-mechanics approach to large-system analysis of CDMAmultiuser detectors

We present a theory, based on statistical mechanics, to evaluate analytically the performance of uncoded, fully synchronous, randomly spread code-division multiple-access (CDMA) multiuser detectors with additive white Gaussian noise (AWGN) channel, under perfect power control, and in the large-system limit. Application of the replica method, a tool developed in the literature of statistical mechanics, allows us to derive analytical expressions for the bit-error rate, as well as the multiuser efficiency, of the individually optimum (IO) and jointly optimum (JO) multiuser detectors over the whole range of noise levels. The information-theoretic capacity of the randomly spread CDMA channel and the performance of decorrelating and linear minimum mean-square error (MMSE) detectors are also derived in the same replica formulation, thereby demonstrating validity of the statistical-mechanical approach     

Linear multiuser detectors for synchronous code-divisionmultiple-access channels

Under the assumptions of symbol-synchronous transmissions and white Gaussian noise, the authors analyze the detection mechanism at the receiver, comparing different detectors by their bit error rates in the low-background-noise region and by their worst-case behavior in a near-far environment where the received energies of the users are not necessarily similar. Optimum multiuser detection achieves important performance gains over conventional single-user detection at the expense of computational complexity that grows exponentially with the number of users. It is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection. Attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations, and on the optimum linear detector. It is shown that the generalized inverse detectors exhibit the same degree of near-far resistance as the optimum multiuser detectors. The optimum linear detector is obtained     

Continuous Phase Chirp (CPC) Signals for Binary Data Communication--Part II: Noncoherent Detection

Previous work has shown that coherent multiple bit observation of binary continuous phase chirp (CPC) signals gives improved error rate performance compared to the conventional bit-by-bit detection scheme. This paper determines bounds on the error rate improvement made possible by multiple bit observation for optimum and suboptimum [average matched filter (AMF)] noncoherent detection of binary CPC signals in additive white Gaussian noise (AWGN). For the same observation interval, it is shown that noncoherent CPC receivers provide higher signal-to-noise (SNR) gain than coherent receivers compared to the respective optimum single bit schemes. In particular, the three-bit noncoherent AMF receiver is shown to yield 3 dB SNR gain over a wide range of signal parameters.