Pooi Yuen Kam

Bit error probabilities MDPSK over the nonselective Rayleigh fading channel with diversity reception

Data transmission using M-ary differential phase shift keying (MDPSK) over the nonselective Rayleigh fading channel with diversity reception is considered. While previous studies on error probability mostly assume no fading fluctuation, the author considers, exclusively, the case in which the fading process fluctuates from one symbol interval to the next. Exact bit error probability results for 2, 4, and 8 DPSK as well as tight upper bounds are derived. Some applications of the results are discussed. >

Maximum Likelihood Carrier Phase Recovery for Linear Suppressed-Carrier Digital Data Modulations

The problem of ML estimation of the Phase of a general data-modulated carrier is considered. The shortcomings of current iterative approaches to the problem are pointed out, and the correct conceptual approach is proposed. The true ML estimator is then obtained and found to be nonimplementable. However, by specializing to limits of high and low SNR, the general ML estimator is shown to reduce to implementable DA and NDA ML estimators, respectively. The DA receivers performance in terms of phase tracking and symbol error probability can be analyzed, and even the effects of past decision errors on current system performance can be assessed. For circular signal constellations, the DA receiver has a simple and totally linear structure which is easy to implement. The NDA ML estimator is shown to be equivalent to the common carrier loops. Our emphasis here on explicit computation of the ML phase estimate from the past received signal leads to detection strategies which do not require a carrier loop and a VCO for coherent detection.

Optimal detection of digital data over the nonselective Rayleigh fading channel with diversity reception

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference. >

Decision-Aided Carrier Phase Estimation for Coherent Optical Communications

We analytically studied the block length effect (BLE) of decision-aided maximum likelihood (DA ML) carrier phase estimation in coherent optical phase-modulated systems. The results agree well with the trends found using extensive Monte Carlo simulations. In order to eliminate the BLE and accurately recover the carrier phase, an adaptive decision-aided (DA) receiver is proposed that does not require knowledge of the statistical characteristics of the carrier phase, or any parameter to be preset. The simulation results show that using the adaptive DA receiver, the maximum tolerance ratio of the linewidth per laser to symbol rate (¿vT) at a bit error rate (BER) = 10-4 has been increased to 2.5 × 10-4, 4.1 × 10-5, and 9.5 × 10-6, respectively, for quadrature-, 8- and 16-phase-shift keying formats. The ratio (¿vT) of the adaptive DA receiver in 16 quadrature amplitude modulation (QAM) is decreased to 2 × 10-5 due to the constellation penalty from 2.5 × 10-5 by using DA ML with optimum memory length, though it consistently performs well without optimizing any parameters as in DA ML. The phase error variance of the adaptive DA receiver is also analytically investigated. In addition, an analog-to-digital converter with bit resolution higher than 4 bits is shown to be sufficient to implement our adaptive DA receiver.

Maximum-Likelihood Digital Data Sequence Estimation Over the Gaussian Channel with Unknown Carrier Phase

We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.

Decision-aided maximum likelihood detection in coherent optical phase-shift-keying system

A novel decision-aided maximum likelihood (DA ML) technique is proposed to estimate the carrier phase in coherent optical phase-shift-keying system. The DA ML scheme is a totally linear computational algorithm which is feasible for on-line processing in the real systems. The simulation results show that the DA ML receiver can outperform the conventional Mth power scheme, especially when the nonlinear phase noise is dominant.

Laser Linewidth Tolerance of Decision-Aided Maximum Likelihood Phase Estimation in Coherent Optical

This letter extends the decision-aided (DA) maximum likelihood (ML) phase estimation in an M -ary phase-shift keying (PSK) system to quadrature amplitude modulation (QAM) signals. The block length effect is simulated for both M-ary PSK and QAM systems, and also investigated in M -ary PSK systems through analysis. Our results show that the tolerance of DA ML to laser linewidth for square 16-QAM can be increased by >10 times compared to the block Mth power scheme.

M

We consider about a multiple relay system operating under amplify-and-forward (AF) protocol and non-coherent modulation and demodulation. When the relays are under long-term power constraints, a near-maximum likelihood (ML) receiver and a diversity combining receiver are proposed. Both the near- ML receiver and the diversity combining receiver are expressed in simple closed forms and only rely on the second order statistics of the fading coefficients. Moreover, both of the proposed detectors outperform a non-cooperative system which only has a direct link with non-coherent ML detection in a Rayleigh fading environment. However, when the relay output is under a short-term power constraint, the ML detector derived here for the non-coherent AF relay performs the same as the non-cooperative system.

-ary PSK and QAM Systems

Using the convexity property of the exponential function, we obtain a family of exponential lower bounds on the Gaussian Q-function using the Jensens inequality. The tightness of the bounds can be improved by increasing the number of exponential terms. The coefficients of the exponentials are constants, allowing easy averaging over the fading distribution using the moment generating function method. This method is also applied to the symbol error probability of M-ary phase shift keying and M-ary differential phase shift keying over additive white Gaussian noise and fading channels. The tightness of the bounds is demonstrated.

Non-Coherent Detection for Amplify-and-Forward Relay Systems in a Rayleigh Fading Environment

The bit-error rate (BER) expressions of 16- phase-shift keying (PSK) and 16- quadrature amplitude modulation (QAM) are analytically obtained in the presence of a phase error. By averaging over the statistics of the phase error, the performance penalty can be analytically examined as a function of the phase error variance. The phase error variances leading to a 1-dB signal-to-noise ratio per bit penalty at BER=10(-4) have been found to be 8.7 x 10(-2) rad(2), 1.2 x 10(-2) rad(2), 2.4 x 10(-3) rad(2), 6.0 x 10(-4) rad(2) and 2.3 x 10(-3) rad(2) for binary, quadrature, 8-, and 16-PSK and 16QAM, respectively. With the knowledge of the allowable phase error variance, the corresponding laser linewidth tolerance can be predicted. We extend the phase error variance analysis of decision-aided maximum likelihood carrier phase estimation in M-ary PSK to 16QAM, and successfully predict the laser linewidth tolerance in different modulation formats, which agrees well with the Monte Carlo simulations. Finally, approximate BER expressions for different modulation formats are introduced to allow a quick estimation of the BER performance as a function of the phase error variance. Further, the BER approximations give a lower bound on the laser linewidth requirements in M-ary PSK and 16QAM. It is shown that as far as laser linewidth tolerance is concerned, 16QAM outperforms 16PSK which has the same spectral efficiency (SE), and has nearly the same performance as 8PSK which has lower SE. Thus, 16-QAM is a promising modulation format for high SE coherent optical communications.