Noncoherent maximum-likelihood block detection of orthogonalNFSK-LDPSK signals

This paper investigates the noncoherent block detection of orthogonal N frequency-shift keying (FSK)-L differential phase shift keying (DPSK) signals transmitted over the additive white Gaussian noise channel, based on the principle of maximum-likelihood (ML) sequence estimation. By virtue of a union bound argument, asymptotic upper bounds for the bit error probability of the developed ML block receiver are derived and verified by simulation. It is analytically shown that the noncoherent NFSK-LDPSK ML block receiver performs comparably with the ideal coherent NFSK-L phase shift keying (PSK) receiver for L = 2 and 4, as the observation block length is large enough. Furthermore, substantial performance improvement can be achieved by the ML block detection of the NFSK-LDPSK signal with L > 2 by increasing the observation block length     

Iterative and recursive estimators for hidden Markoverrors-in-variables models

In this paper we propose maximum-likelihood (ML) estimation of errors in variables models with finite-state Markovian disturbances. Such models have applications in econometrics, speech processing, communication systems, and neurobiological signal processing. We derive the maximum likelihood (ML) model estimates using the expectation maximization (EM) algorithm. Then two recursive or “on-line” estimation schemes are derived for estimating such models. The first on-line algorithm is based on the EM algorithm and uses stochastic approximations to maximize the Kullback-Leibler (KL) information measure. The second on-line algorithm we propose is a gradient-based scheme and uses stochastic approximations to maximize the log likelihood     

Frequency estimation in the presence of Doppler spread: performanceanalysis

We are concerned with the estimation of the frequency of a complex sinusoid that has been corrupted by complex-valued multiplicative and additive noise. This problem is important in many applications including array processing in the case of spatially distributed sources and synchronization in the context of time-selective channels. The multiplicative noise smears the spectral line due to the sinusoid. This smearing, which is often called Doppler spreading, may significantly degrade the estimation accuracy. The goal of this paper is to analytically assess this degradation. The finite-sample Cramer-Rao bounds (CRBs) are derived, and closed-form expressions are given for the large-sample CRB. The latter gives insights into the effective coherent and noncoherent SNRs for frequency estimation. We then analyze the accuracy of frequency estimators that are based on the angles of the sample covariances. Simulations results are presented to illustrate the theoretical results     

相干快跳频系统中基于最大似然合并的多音干扰抑制算法研究

频率子集相干快跳频系统(S-CFFH)是一种新颖的快跳频方案,可在FFH系统中实现有效信道估计。本文推导了S-CFFH/BPSK系统在多音干扰(MTJ)和瑞利衰落信道中最大似然(ML)合并的理论误码率,给出了理想估计信道时的误码率闭合表达式,也给出了非理想估计信道时在特殊情况下的误码率闭合表达式,并通过仿真验证了理论推导的正确性。仿真结果表明S-CFFH/BPSK系统中的ML合并与最大比合并(MRC)相比有显著的干扰抑制增益,并且有效降低了干扰方的干扰效率;与非相干FFH/BFSK系统的ML合并相比,随着信干比的增大,S-CFFH/BPSK系统的ML合并展示出显著的性能增益。      

Interception of frequency-hopped spread-spectrum signals

A frequency-hopped spread-spectrum signal is modeled as a sinusoid that has one of N random frequencies. Coherent and noncoherent interception receiver structures based on Neyman-Pearson detection theory are determined. Under the assumption that there is a single hop per detection period, the optimum receiver structure is shown to consist of a bank of matched filters called the average likelihood (AL) receiver. A suboptimum structure called the maximum likelihood (ML) receiver is also analyzed. It is shown that AL and ML receivers have essentially the same performance. Simple formulas that relate the probability of detection, P_D, to the probability of false alarm, P_F, and the signal-to-noise ratio (SNR) for large N are derived. Receiver structures are also derived and analyzed for the case where the signal hops a number of times in one detection interval. This may correspond to the detection of a multihop signal in one symbol interval or to detection based on integration over a number of symbol intervals. The relationships of P_D to P_F, for both coherent and noncoherent multiple-hop receivers, are examined     

Partially coherent digital matched filters

The structure and performance of digital matched filters (DMFs) with partial phase estimation, i.e., partial coherent (PC) DMFs, are considered in this paper. The case of a PC-DMF with one-bit digitization and matched to a binary phase modulated signal is investigated. The filter structure is derived as an approximation to Viterbi's optimum PC analog detector structure and is shown to be a generalization of Turin's noncoherent (NC) DMF structure. The performance of the PC-DMF is investigated in detail for three types of interference, namely, the Gaussian noise, the noncoherent constant amplitude interference (NCAI), and the coherent constant amplitude interference (CCAI). The results are compared with those of the two coherence limiting cases, i.e., the NC-DMF and the coherent DMF case.     

Spectrally efficient noncoherent communication

This paper considers noncoherent communication over a frequency-nonselective channel in which the time-varying channel gain is unknown a priori, but is approximately constant over a coherence interval. Unless the coherence interval is large, coherent communication, which requires explicit channel estimation and tracking prior to detection, incurs training overhead which may be excessive, especially for multiple-antenna communication. In contrast, noncoherent detection may be viewed as a generalized likelihood ratio test (GLRT) which jointly estimates the channel and the data, and hence does not require separate training. The main results in this paper are as follows. (1) We develop a "signal space" criterion for signal and code design for noncoherent communication, in terms of the distances of signal points from the decision boundaries. (2) The noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude/phase constellations. These are significantly more efficient than conventional differential phase-shift keying (PSK), especially at high signal-to-noise ratio (SNR). Also, known results on the high-SNR performance of multiple-symbol demodulation of differential PSK are easily inferred from the noncoherent metric. (3) The GLRT interpretation is used to obtain near-optimal low-complexity implementations of noncoherent block demodulation. In particular, this gives an implementation of multiple symbol demodulation of differential PSK, which is of linear complexity (in the block length) and whose degradation from the exact, exponential complexity, implementation can be made as small as desired     

Noncoherent space-time equalization

In this paper, noncoherent equalization is combined with multiple receive antennas. The resulting noncoherent space-time equalization (NSTE) schemes are analyzed and compared with the corresponding coherent receivers. In particular, noncoherent linear equalization (NLE), noncoherent decision-feedback equalization (NDFE), and noncoherent sequence estimation (NSE) are considered. For NLE and NDFE novel approximations for the signal-to-distortion ratio (SDR) are derived and verified by simulations. It is shown that NSTE can suppress interfering users and exploit diversity as efficiently as coherent STE. However, NSTE is more robust against channel phase variations than the combination of coherent STE and synchronization. Robust noncoherent recursive least squares (NC-RLS) algorithms, which compare favorably with the conventional RLS algorithm with additional carrier synchronization loop, are proposed for fast filter adaptation.     

Performance Analysis of Optimum and Suboptimum Selection Diversity Schemes on Rayleigh Fading Channels With Imperfect Channel Estimates

In this paper, we present a comparative analysis on the effects of channel estimation errors on the performance of optimum and suboptimum selection diversity (SD) receivers on Rayleigh-fading channels. By modeling the estimation errors as independent complex Gaussian random variables, we derive simple closed-form expressions for the average probability of error for both optimum and suboptimum SD schemes with noisy channel estimates. With dual diversity and imperfect estimates, we establish a connection between optimum SD and maximal-ratio combining (MRC), and between suboptimum SD and equal-gain combining diversity schemes. Interestingly, we show that the optimum SD receiver structure and the resulting performance for differential binary coherent phase-shift keying (DBPSK) signaling can be obtained, in a straightforward way, as a special case of the performance of the optimum SD scheme with binary PSK signaling and channel estimation errors. For a fixed average power and bit duration, in conjunction with pilot-assisted minimum mean-square error channel estimation, we show that the optimum coherent SD scheme coincides with that of the optimum noncoherent SD scheme with binary frequency-shift keying (BFSK) signaling, whereas the coherent MRC scheme coincides with the optimum noncoherent receiver (i.e., the square-law combiner) for BFSK. The optimum number of diversity channels, under an energy-sharing mode of operation, is also studied. Finally, we formulate the problem of optimal pilot placement, consider channel estimation with a practical pilot-symbol-assisted modulation technique, and present some numerical results illustrating the comparative performances of various SD receivers     

Threshold region performance of maximum likelihood direction of arrival estimators

This paper presents a performance analysis of the maximum likelihood (ML) estimator for finding the directions of arrival (DOAs) with a sensor array. The asymptotic properties of this estimator are well known. In this paper, the performance under conditions of low signal-to-noise ratio (SNR) and a small number of array snapshots is investigated. It is well known that the ML estimator exhibits a threshold effect, i.e., a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard techniques such as the Crame/spl acute/r-Rao bound and asymptotic analysis. In this paper, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Both the deterministic ML and stochastic ML estimators are treated for the single-source and multisource estimation problems. These approximations alleviate the need for time-consuming computer simulations when evaluating the threshold region performance. For the special case of a single stochastic source signal and a single snapshot, it is shown that the ML estimator is not statistically efficient as SNR/spl rarr//spl infin/ due to the effect of outliers.     

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 Data Transition Tracking Loops for Symbol Synchronization in Digital Communications Receivers

Starting with the maximum a posteriori (MAP) estimation approach, this paper derives the optimum (in the MAP estimation sense) means for performing symbol timing recovery in the absence of carrier phase information (i.e., prior to carrier phase recovery). Specifically, we examine the necessary modification of a well-known form of coherent symbol synchronizer, namely, the data transition tracking loop (DTTL) to allow its operation in the absence of carrier phase information, i.e., as a so-called noncoherent symbol sync loop. By employing such a noncoherent scheme, one can eliminate the need for iteration between the carrier and symbol sync functions, as typically takes place in receivers that more commonly perform carrier tracking and acquisition prior to symbol timing. The performance of both the linear and nonlinear versions of this noncoherent DTTL is obtained by a combination of analysis and simulation, and compared with that of the corresponding coherent DDTLs.     

Continuous Phase Modulation of F-QPSK-B Signals

A continuous phase modulation (CPM) implementation alternative of a recently standardized class of Feher-patented quadrature phase-shift keying (F-QPSK-B) modulation is proposed. Based on the fact that the F-QPSK-B signal has a quasi-constant envelope and continuous phase characteristics, it is shown that it can indeed be generated by the CPM scheme. For example, an F-QPSK-B signal can be fully generated using an existing FM-based transmitter with a modulation index of 0.5. Furthermore, a premodulation filter and an alternating change monitor differential encoder for the continuous-phase-modulated F-QPSK-B signal to be fully compatible with the I/Q modulated F-QPSK-B signal are proposed, allowing direct symbol-by-symbol coherent detection without the use of any special decoding schemes inherent in all CPM schemes. It is shown that the power spectral density and eye diagram of the continuous-phase-modulated F-QPSK-B signal are practically the same as those of the I/Q modulated F-QPSK-B signal. By utilizing CPM characteristics, an optimum maximum-likelihood (ML) coherent receiver for the F-QPSK-B signal is proposed. It is shown that the bit-error-rate performances of the optimum ML coherent detection, symbol-by-symbol coherent detection, and noncoherent detection of the continuous-phase-modulated F-QPSK-B signal are almost the same as those of the I/Q modulated F-QPSK-B signal     

Noncoherent data transition tracking loops for symbol synchronization in digital communication receivers

Starting with the maximum a posteriori (MAP)estimation approach, this paper derives the optimum (in the MAP estimation sense) means for performing symbol-timing recovery in the absence of carrier-phase information (i.e., prior to carrier-phase recovery). Specifically, we examine the necessary modification of a well-known form of coherent symbol synchronizer,namely, the data transition tracking loop (DTTL), to allow its operation in the absence of carrier-phase information, i.e., as a so-called noncoherent symbol sync loop. By employing such a noncoherent scheme, one can eliminate the need for iteration between the carrier and symbol sync functions,as typically takes place in receivers that more commonly perform carrier tracking and acquisition prior to symbol timing. The performance of both the linear and nonlinear versions of this noncoherent DTTL is obtained by a combination of analysis and simulation, and compared with that of the corresponding coherent DTTLs.     

Unified analysis of switched diversity systems in independent andcorrelated fading channels

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed     

Analysis of a simple successive interference cancellation scheme ina DS/CDMA system

Compensating for near/far effects is critical for satisfactory performance of DS/CDMA systems. So far, practical systems have used power control to overcome fading and near/far effects. Another approach, which has a fundamental potential in not only eliminating near/far effects but also in substantially raising the capacity, is multiuser detection and interference cancellation. Various optimal and suboptimal schemes have been investigated. Most of these schemes, however, get too complex even for relatively simple systems and rely on good channel estimates. For interference cancellation, estimation of channel parameters (viz. received amplitude and phase) is important. We analyze a simple successive interference cancellation scheme for coherent BPSK modulation, where the parameter estimation is done using the output of a linear correlator. We then extend the analysis for a noncoherent modulation scheme, namely M-ary orthogonal modulation. For the noncoherent case, the needed information on both the amplitude and phase is obtained from the correlator output. The performance of the IC scheme along with multipath diversity combining is studied     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

Semiblind channel estimation for CDMA systems with parallel data and pilot signals

Semiblind channel estimation combines the methods of channel estimation based on a pilot signal and blind channel estimation based on a data-only conveying signal. Maximum-likelihood (ML)-based semiblind estimators with Gaussian assumptions can provide improvement in performance, compared with channel-estimation schemes using the pilot signal only. This improvement can be even larger when the pilot and the data signals are sent simultaneously, as is the case in the third-generation wideband code-division multiple-access standards. However, the Gaussian ML approach results in very large complexity. Previously proposed semiblind methods with low complexity have been derived for serial pilot and data transmission, and are not suitable for the parallel transmission case. In this paper, algorithms for semiblind channel estimation for the parallel data and training signal case are developed. Approximations which reduce the computational complexity of the Gaussian ML method significantly are proposed. Solutions with iterations with very low attendant complexity are provided. The mean squared error analysis of the proposed method is obtained and compared with that of a method with no approximations. The approximations are justified through simulations, and the performance improvement over estimation schemes using the pilot signal solely is verified.     

Further results on noncoherent block-coded MPSK [transactions papers]

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed recently. In this paper, we present further research results on NBC-MPSK. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear complexity multistage decoder for NBC-MPSK is proposed. Then we investigate a tree-search ML decoding algorithm for NBCMPSK. The derived algorithm is shown to have low complexity and excellent error performance. In this paper, we also utilize the idea of the NBC-MPSK to design noncoherent space-time block codes, called noncoherent space-time block-coded MPSK (NSTBC-MPSK). For two transmit antennas, we propose a signal set with set partitioning and derive the minimum noncohent distance of NSTBC-MPSK with this signal set. For the decoding of NSTBC-MPSK, we modify the ML decoding algorithm of NBC-MPSK and propose an iterative hard-decision decoding algorithm. Compared with training codes and unitary space-time modulation, NBC-MPSK and NSTBC-MPSK have larger minimum noncoherent distance and thus better error performance for the noncoherent ML decoder.