Maximum Likelihood Detection Rule Research Articles

Maximum Likelihood Detection in a Four-Dimensional Stokes-Space Receiver

The maximum likelihood detection rule for a four-dimensional direct-detection optical front-end is derived. The four dimensions are two intensities and two differential phases. Three different signal processing algorithms, composed of symbol-by-symbol, sequence and successive detection, are discussed. To remedy dealing with special functions in the detection rules, an approximation for high signal-to-noise ratios (SNRs) is provided. Simulation results show that, despite the simpler structure of the successive algorithm, the resulting performance loss, in comparison with the other two algorithms, is negligible. For example, for an 8-ring/8-ary phase constellation, the complexity of detection reduces by a factor of 8, while the performance, in terms of the symbol error rate, degrades by 0.5 dB. It is shown that the high-SNR approximation is very accurate, even at low SNRs. The achievable rates for different constellations are computed and compared by the Monte Carlo method. For example, for a 4-ring/8-ary phase constellation, the achievable rate is 10 bits per channel use at an SNR of 25 dB, while by using an 8-ring/8-ary phase constellation and an error correcting code of rate 5/6, this rate is achieved at an SNR of 20 dB.

Performance Analysis of Maximum Likelihood Detection for Decode and Forward MIMO Relay Channels in Rayleigh Fading

Maximum-likelihood (ML) detectors for single-input-single-output (SISO) relay systems are well known. In this paper, closed form expressions for the bit error rate (BER) for multiple-input-multiple-output (MIMO) relay systems employing ML based decode and forward (DF) cooperative diversity are obtained. The DF operation at the relay intelligently employs the multiple antennas available at the relay for receive diversity on the source-relay link and space-time coding (STC) on the relay-destination link resulting in an extension of the ML detection rule for SISO systems to MIMO systems as well. For the piecewise linear (PL) approximation to the ML detector, exact expressions for the BER are obtained for single-relay systems with both the source and relay supporting multiple antennas. For a multirelay system, each relay having multiple antennas, approximate expressions for the BER are obtained. This is done by finding the statistics of conditionally Gaussian (CG) random variables, that appear in the decision variable. Through numerical results obtained from the BER expressions, it is shown that using multiple antennas at the source as well as the relay leads to significant improvement in BER performance.

ML performance analysis of the decode-and-forward protocol in cooperative diversity networks

We analyze the maximum-likelihood (ML) performance of the decode-and-forward protocol in a cooperative diversity network which consists of a source, a relay, and a destination with a direct path signal, but which is not equipped with cyclicredundancy- check (CRC) codes. In this system, due to a symbol error at the relay, the ML receiver at the destination needs to consider all the possible symbol detection scenarios at the relay as well as at the destination. Therefore, the ML detection metric is given by a linear combination of exponential functions, which prevents the use of the classical minimum Euclidean distance rule. Adopting the max-log approximation, we approximate the ML detection rule which makes the ML performance analysis tractable. In order to facilitate the derivation of decision regions, we simplify the ML detection rule in the two-dimensional real space such that two metric values of two adjacent constellation points are sequentially compared. Then we obtain decision regions in a form without union and intersection. Finally, based on the decision regions, we derive a very accurate closedform BER approximation for M-pulse amplitude modulation (PAM) and M-quadrature amplitude modulation (QAM). The obtained BER expression can serve as the error performance upper-bound of the decode-and-forward protocol in cooperative diversity networks.

Adaptive group detection for DS/CDMA systems over frequency‐selective fading channels

AbstractIn this paper we consider the problem of group detection for asynchronous Direct‐Sequence Code Division Multiple Access (DS/CDMA) systems operating over frequency‐selective fading channels. A two‐stage near‐far resistant detection structure is proposed. The first stage is a linear filter, aimed at suppressing the effect of the unwanted user signals, while the second stage is a non‐linear block, implementing a maximum likelihood detection rule on the set of desired user signals. As to the linear stage, we consider both the Zero‐Forcing (ZF) and the Minimum Mean Square Error (MMSE) approaches; in particular, based on the amount of prior knowledge on the interference parameters which is available to the receiver and on the affordable computational complexity, we come up with several receiving structures, which trade system performance for complexity and needed channel state information. We also present adaptive implementations of these receivers, wherein only the parameters from the users to be decoded are assumed to be known. The case that the channel fading coefficients of the users to be decoded are not known a priori is also considered. In particular, based on the transmission of pilot signals, we adopt a least‐squares criterion in order to obtain estimates of these coefficients. The result is thus a fully adaptive structure, which can be implemented with no prior information on the interfering signals and on the channel state. As to the performance assessment, the new receivers are shown to be near‐far resistant, and simulation results confirm their superiority with respect to previously derived detection structures. Copyright © 2003 AEI.

Two-stage ML-based group detection for direct-sequence CDMA systems

In this paper a two-stage maximum-likelihood (ML) detection structure for group detection in DS/CDMA systems is presented. The first stage of the receiver is a linear filter, aimed at suppressing the effect of the unwanted (i.e., out-of-group) users' signals, while the second stage is a non-linear block, implementing a ML detection rule on the set of desired users signals. As to the linear stage, we consider both the decorrelating and the minimum mean square error approaches. Interestingly, the proposed detection structure turns out to be a generalization of Varanasi's group detector, to which it reduces when the system is synchronous, the signatures are linearly independent and the first stage of the receiver is a decorrelator. The issue of blind adaptive receiver implementation is also considered, and implementations of the proposed receiver based on the LMS algorithm, the RLS algorithm and subspace-tracking algorithms are presented. These adaptive receivers do not rely on any knowledge on the out-of-group users' signals, and are thus particularly suited for rejection of out-of-cell interference in the base station. Simulation results confirm that the proposed structure achieves very satisfactory performance in comparison with previously derived receivers, as well as that the proposed blind adaptive algorithms achieve satisfactory performance.

Interference estimation with applications to blind multiple-access communication over fading channels

We consider the detection of nonorthogonal multipulse signals on multiple-access fading channels. The generalized maximum-likelihood rule is employed to decode users whose complex fading gains are unknown. We develop geometrical interpretations for the resulting detectors and their corresponding asymptotic efficiencies. The generalized maximum-likelihood detection rule is then applied to find a matched subspace detector for the frequency-selective fading channel, under the assumption of a short coherence time (or long coherence time without the computational power to track the fading parameters). We propose blind implementations of these detectors for nonorthogonal multipulse signaling on both frequency-nonselective and frequency-selective multiple-access fading channels. These blind detectors extend the results of Wang and Poor (see ibid., vol.44, p.677-89, 1998) to multipulse modulation and fast frequency selective fading. For comparison, the minimum mean-squared error decision rules for these channels are derived and blind implementations of their corresponding detectors are developed.