Maximum Likelihood Sequence Detection Receiver Research Articles

Near-Optimal Low-Complexity Sequence Detection for Clipped DCO-OFDM

The inherent high peak-to-average power ratio issue of dc-biased optical orthogonal frequency division multiplexing (DCO-OFDM) is sensitive to the limited dynamic region of light emitting diode component and prone to clipping distortion, which deteriorates the performance of visible light communication systems. This letter proposes a maximum likelihood sequence detection (MLSD) method for the clipped DCO-OFDM, whereas the double-sided clipping characteristic is incorporated to improve the performance. Besides that, a near-optimal low-complexity MLSD method is presented to reduce the calculation complexity. Simulations demonstrate that the proposed low-complexity MLSD receiver could approach the performance of ideal case of non-clipped DCO-OFDM.

Maximum Likelihood Sequence Detection Receivers for Nonlinear Optical Channels

The space-time whitened matched filter (ST-WMF) maximum likelihood sequence detection (MLSD) architecture has been recently proposed (Maggio et al., 2014). Its objective is reducing implementation complexity in transmissions over nonlinear dispersive channels. The ST-WMF-MLSD receiver (i) drastically reduces the number of states of the Viterbi decoder (VD) and (ii) offers a smooth trade-off between performance and complexity. In this work the ST-WMF-MLSD receiver is investigated in detail. We show that thespace compressionof the nonlinear channel is an instrumental property of the ST-WMF-MLSD which results in a major reduction of the implementation complexity in intensity modulation and direct detection (IM/DD) fiber optic systems. Moreover, we assess the performance of ST-WMF-MLSD in IM/DD optical systems with chromatic dispersion (CD) and polarization mode dispersion (PMD). Numerical results for a 10 Gb/s, 700 km, and IM/DD fiber-optic link with 50 ps differential group delay (DGD) show that the number of states of the VD in ST-WMF-MLSD can be reduced ~4 times compared to an oversampled MLSD. Finally, we analyze the impact of the imperfect channel estimation on the performance of the ST-WMF-MLSD. Our results show that the performance degradation caused by channel estimation inaccuracies is low and similar to that achieved by existing MLSD schemes (~0.2 dB).

Reduced Complexity MLSD Receivers for Nonlinear Optical Channels

We present a novel maximum likelihood sequence detection (MLSD) receiver structure for nonlinear channels. This scheme is derived by treating the NLC as a multiple input/multiple output system. Then, orthogonal signal components are computed using a special form of space-time whitened matched filter (ST-WMF) obtained by a modified Gram-Schmidt orthogonalization of the Volterra kernels of the NLC. The MLSD receiver consists of the ST-WMF followed by a Viterbi detector (VD) with multidimensional branch metrics. The space orthogonalization and noise whitening achieved by the ST-WMF provide an efficient way to reduce the receiver complexity in the presence of highly dispersive NLC. Complexity reduction is crucial in practical applications such as intensity modulation/direct detection (IM/DD) optical channels. As an example, the number of states of the VD in ST-WMF-MLSD required on a 10 Gb/s, 700 km, IM/DD fiber-optic link is reduced eight times compared with an oversampled MLSD.

State-Complexity Reduction in MLSD Receivers for Optical Communications With Direct Photodetection

We investigate the impact of state-complexity reduction on the performance of maximum likelihood sequence detection (MLSD) receivers for direct-photodetection long-haul optical communication systems affected by uncompensated chromatic dispersion (CD). We directly compare two possible approaches: (i) detection through a simple ldquobrute-forcerdquo state-complexity reduction strategy and (ii) a more structured reduced-state sequence detection (RSSD) strategy. The performance of both state-complexity reduction techniques is evaluated considering two realistic optical transmission schemes, based on on-off keying (OOK) and optical duobinary modulation (ODBM), respectively. The detection algorithms are characterized considering the impact of the timing offset, the quantization scheme, and the amount of uncompensated CD. As one would expect, for a given number of states in MLSD receivers, the schemes based on RSSD exhibit better performance with respect to those based on simple brute-force state-complexity reduction. However, we show that MLSD schemes based on the use of brute-force state-complexity reduction are characterized by a better complexity/performance trade-off for low/medium CD values, whereas RSSD is the best choice for high CD values.

MLSD Bounds and Receiver Designs for Clipped OFDM Channels

We derive tight closed-form approximations of symbol and bit error probability on maximum-likelihood sequence detection (MLSD) of Nyquist-rate and oversampled OFDM systems over the AWGN, flat and frequency-selective quasi-static Rayleigh fading channels. Contrary to common knowledge, we show that on a frequency-selective channel, clipping at the transmitter leads to achievable frequency-diversity and performance gain over unclipped systems with MLSD. We derive closed-form expressions of the diversity and the performance gain over the no-clipping case, as well as the optimal clipping ratio for a given system. We show that such diversity and performance gain are a result of both clipping and channel frequency-selectivity, and they do not occur on the AWGN and flat fading channels.We also present a new near-optimum detection algorithm that achieves the MLSD performance bound with a few iterations for the clipped OFDM systems with both high and low clipping levels on the AWGN and flat Rayleigh fading channels. For the frequency selective channel, we present a receiver design that utilizes the advantage of clipping to some extent. We consider rectangular QAM signaling in this paper.

Optimal Joint Detection/Estimation in Fading Channels With Polynomial Complexity

The problem of sequence detection in frequency-nonselective/time-selective fading channels, when channel state information (CSI) is not available at the transmitter and receiver, is considered in this paper. The traditional belief is that exact maximum-likelihood sequence detection (MLSD) of an uncoded sequence over this channel has exponential complexity in the channel coherence time. Thus, for slowly varying channels, i.e., channels having coherence time on the order of the sequence length, the complexity appears to be exponential in the sequence length. In the first part of this work, it is shown that exact MLSD can be computed with only polynomial worst case complexity in the sequence length regardless of the operating signal-to-noise ratio (SNR) for equal-energy signal constellations. By establishing a relationship between the aforementioned complexity and the rank of the correlation matrix of the fading process, an understanding of how complexity of the optimal MLSD receiver varies as the channel dynamics change is provided. In the second part of this paper, the problem of decoding turbo-like codes in frequency-nonselective/time-selective fading channels without receiver CSI is examined. Using arguments similar to the ones used for the MLSD case, it is shown that the exact symbol-by-symbol soft-decision metrics (SbSSDMs) implied by the min-sum algorithm can be evaluated with polynomial worst case complexity in the sequence length regardless of SNR for equal-energy signal constellations. Finally, by simplifying some key steps in the polynomial-complexity algorithm, a family of fast, approximate algorithms is derived, which yield near-optimal performance

Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD

This paper thoroughly investigates the maximum-likelihood sequence detection (MLSD) receiver for the optical ON-OFF keying (OOK) channel in the presence of both polarization mode dispersion and group velocity dispersion (GVD). A reliable method is provided for computing the relevant performance for any possible value of the system parameters, with no constraint on the sampling rate. With one sample per bit time, a practically exact expression of the statistics of the received samples is found, and therefore the performance of a synchronous MLSD receiver is evaluated and compared with that of other electronic techniques such as combined feedforward and decision-feedback equalizers (FFE and DFE). It is also shown that the ultimate performance of electronic processing can be obtained by sampling the received signal at twice the bit rate. An approximate accurate closed-form expression of the receiver metrics is also identified, allowing for the implementation of a practically optimal MLSD receiver

Adaptive MLSD receiver employing noise correlation

A per-survivor processing (PSP) maximum likelihood sequence detection (MLSD) receiver is developed for a fast time-varying frequency-selective Rayleigh fading channel with coloured additive noise, which follows an autoregressive (AR) model with unknown parameters. The correlation between noise samples is exploited to considerably enhance the performance of the communications. The maximum likelihood criterion is employed based on unknown noise parameters. This criterion has some desired properties, e.g. it has a unique joint minimum at the true values of the channel and the noise parameters. The new PSP–MLSD algorithm detects the input data and jointly estimates the noise and the channel parameters all together. The proposed structure can be viewed as a traditional PSP–MLSD receiver combined with an adaptive whitening filter. In a coloured noise environment, this scheme offers a faster tracking property, more accurate estimation of the channel and a substantially lower error probability compared with the traditional PSP–MLSD structure. The signal-to-noise ratio (SNR) improvement achieved by the proposed receiver, which can be called the noise whitening gain (NWG), is almost equal to the ratio of the energy of the additive noise to the energy of the unpredictable noise component. The square of the NWG gives also an accurate approximation for the bit error rate (BER) improvement ratio obtained by using the proposed algorithm compared with the traditional one.

Sequence detection in nonlinear channels: a convenient alternative to analog predistortion

A new maximum-likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed. The receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion. Contrary to other solutions in the literature, in the proposed technique there is no need for a bank of matched filters, and the receiver front end reduces to a single lowpass filter. For a given peak power level, a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels, such as those based on predistortion, if a moderate spectral expansion is allowed. To analyze the receiver performance, the concept of distance spectrum is employed, since the minimum distance alone cannot account for a reliable performance evaluation. Both analysis and simulation are carried out for realistic narrowband nonlinear channels, possibly employing reduced-state sequence detection. Appreciable gain margins are confirmed to be possible in these realistic cases.

Synchronized per survivor MLSD receiver using a differential Kalman filter

A synchronized per survivor processing (PSP) maximum likelihood sequence detection (MLSD) receiver is presented for a fast frequency-selective Rayleigh fading channel and large carrier frequency offset. It is shown that, by incorporating the synchronization parameters (the timing error, carrier frequency and phase offsets) into the channel-impulse response (CIR) and modifying the resulting state-space model by a differential approach, the time-varying carrier frequency offset can be effectively tracked using a simple least mean square (LMS) estimator. New criteria are proposed based on the smoothness of the estimated channel derivatives. New criteria are proposed based on this fact that, for smoothly time-varying CIR and frequency offset, the magnitude of the CIR time derivative compared with the magnitude of CIR should be very small. It is illustrated that the new criteria and the conventional mean square error (MSE) are complementary.

Performance of Volterra and MLSD receivers for nonlinear band-limited satellite systems

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers.

Adaptive state allocation algorithm in MLSD receiver for multipath fading channels: structure and strategy

This paper presents the adaptive state allocation (ASA) algorithm, a new scheme based on maximum likelihood sequence detection (MLSD) of signals transmitted over Rayleigh fading channels. Although MLSD is an optimal scheme, its computational complexity limits many applications. The ASA algorithm is a detection method whose performance is close to that of MLSD, but with greatly reduced computational complexity. Adaptive state partitioning in the trellis diagram is used in this algorithm by measuring the short-term received signal power. Also, an adaptive threshold for selecting only a few states of the trellis is employed in this algorithm based on the Chernoff distance between the probability density functions (PDFs) of correct and incorrect branch metrics. The ASA-DF, a special case of ASA using decision feedback, shows a very good tradeoff between the performance and computational complexity for selective fading channels. Using ASA with diversity reception not only improves the performance, but also decreases the computational complexity in comparison with the computational complexity of using MLSD with diversity reception.

Performance of multiple pulse position modulation on multipath channels

The effect of multipath dispersion on multiple pulse position modulation (MPPM) and its variants PPM and overlapping PPM are examined. Upper bounds for the error probability of each modulation scheme in the presence of intersymbol interference are presented, considering both an unequalised receiver and the optimal maximum-likelihood sequence detection receiver. Numerical results show that all the PPM-based schemes are approximately equally sensitive to multipath dispersion, and significantly more sensitive to multipath dispersion than on-off keying when maximum-likelihood sequence detection is used.