Conventional Maximum Likelihood Sequence Estimation Research Articles

Decision region partition aided MLSE for O-band 65-Gbaud PAM-4 system over 40-km transmission with a severe bandwidth constraint.

Maximum likelihood sequence estimation (MLSE) is an optimal solution to realize sequence detection in the digital signal processing (DSP) of short reach O-band intensity modulation/direct detection (IM/DD) systems with bandwidth limitation. However, traditional MLSE requires relatively high computational complexity for short reach optical interconnect. Although the computational complexity of single-symbol sequence detection is quite low, the capability of combating with the inter symbol interference (ISI) is inadequate. To combine the low computational complexity of single-symbol sequence detection with the high reliability of multi-symbol sequence detection in MLSE, decision region partition aided MLSE (DRP-MLSE) is proposed and verified with 60-Gbaud and 65-Gbaud PAM-4 IM/DD systems over 40-km single-mode fiber (SMF) transmission. The experimental results show that the DRP-MLSE can realize similar performance of conventional MLSE with negligible penalty and significantly lower computational complexity.

Reduced-state MLSE for an IM/DD system using PAM modulation.

The performance of a high-speed intensity-modulation (IM)/direct-detection (DD) transmission system could be limited by the bandwidth of optical transceivers. One popular way to cope with this performance limitation is to utilize the maximum likelihood sequence estimation (MLSE) at the receiver. However, a practical problem of MLSE is its high implementation complexity. Even though the channel impulse response can be truncated by using a two-tap filter before applying the MLSE, it still faces an implementation problem when used for multi-level modulation formats. In this paper, we propose and demonstrate a reduced-state MLSE for band-limited IM/DD transmission systems using M-ary pulse amplitude modulation (PAM-M) formats. We use a conventional Viterbi algorithm to search a reduced-state trellis, which is constructed by using the coarse pre-decision of the signal equalized by a feed-forward equalizer. Thus, the proposed MLSE reduces the implementation complexity significantly. We evaluate the performance of the proposed reduced-state MLSE over 100∼140-Gb/s PAM-4/6/8 transmission systems implemented by using a 1.3-µm directly modulated laser. The results show that the proposed MLSE achieves almost the same performance as the conventional MLSE but reduces the implementation complexity by a factor of 4∼10 when the complexity is assessed by the number of multiplications and additions.

Decoding of 10-G Optics-Based 50-Gb/s PAM-4 Signal Using Simplified MLSE

A simplified maximum likelihood sequence estimation (MLSE) based on Viterbi algorithm has been proposed. Experimental results show that compared with the conventional MLSE, the proposed algorithm saves the multiplication by 25% with no sensitivity penalty when the memory length of MLSE is 2 both in the 25 Gb/s nonreturn to zero and 50 Gb/s four-level pulse-amplitude modulation (PAM-4) transmission systems. In order to further reduce the number of multiplications in the 50 Gb/s PAM-4 transmission system, we use 75 taps of feed-forward equalization to equalize the received PAM-4 signal into duo-binary PAM-4 (DB-PAM-4) signal and then use MLSE with the memory length of 1 to decode, which improves the sensitivity performance by 1.8 dB and reduces the computing complexity by ∼98% compared with conventional MLSE (L = 4) method. As a result, a 10-km C-band transmission of 50 Gb/s PAM-4 signal is achieved using optical transceivers with a combined 3-dB bandwidth of ∼8 GHz, and only 107 multiplications are required by using our proposed simplified algorithm for equalization.

High Speed Band-Limited 850-nm VCSEL Link Based on Time-Domain Interference Elimination

Short-distance optical interconnection among servers in data centers has attracted the attentions of a multitude of researchers. The method to make the optical link with high transmission capacity and low cost becomes increasingly crucial. Considering these requirements, we propose a new equalization method for time-domain interference elimination in this letter, employed in a band-limited 850-nm vertical cavity surface-emitting laser (VCSEL) link. The method is named simplified maximum likelihood sequence estimation (MLSE), which reduces about 87.8% computational complexity in digital signal processing compared with the conventional MLSE. Based on the proposed simplified-MLSE and combined with the feed-forward equalizer (FFE), a 60-Gb/s non-return-to-zero (NRZ)-modulated VCSEL link could transmit via 56-m OM4 multimode fiber (MMF), and the bit error rate (BER) is still lower than the 7% hard-decision forward error correction (FEC) threshold. The 3-dB bandwidth of the employed 850-nm VCSEL in this transmission system is only 18 GHz, fulfilling the principle of cost-efficient optical interconnects and showing the enormous potential of our proposal in data centers.

Chromatic Dispersion Compensation Using Full-Field Maximum-Likelihood Sequence Estimation

We investigate full-field detection-based maximum- likelihood sequence estimation (MLSE) for chromatic dispersion compensation in 10 Gbit/s OOK optical communication systems. Important design criteria are identified to optimize the system performance. It is confirmed that approximately 50% improvement in transmission reach can be achieved compared to conventional direct-detection MLSE at both 4 and 16 states. It is also shown that full-field MLSE is more robust to the noise and the associated noise amplifications in full-field reconstruction, and consequently exhibits better tolerance to nonoptimized system parameters than full-field feedforward equalizer. Experiments over 124 km spans of field-installed single-mode fiber without optical dispersion compensation using full-field MLSE verify the theoretically predicted performance benefits.

Fibre nonlinearity mitigation of OOK signals with MLSE utilising MZ filter for diverse VSB filtering

Fibre nonlinearity mitigation of non-return-to-zero on-off keying (NRZ-OOK) signals with diverse-vestigial-sideband (DVSB) filtering maximum likelihood sequence estimation (MLSE) is demonstrated by experiments and simulations, in which DVSB filtering is realised with a Mach-Zehnder (MZ) filter. In a 10.709-Gbit/s NRZ-OOK system, experimental results show that, at a fixed optical signal-to-noise ratio, the Q -factor is improved significantly with DVSB-MLSE compared to that with conventional MLSE. Simulations reveal that the performance of DVSB-MLSE can be further improved by optimising the parameters of DVSB filters for different launch powers.

Long-Haul Optically Uncompensated IMDD Transmission With MLSE Using the M-Method

Recent experimental evidence with off-line processing has shown that intensity-modulation direct-dectection receivers using maximum-likelihood sequence estimation (MLSE) can successfully operate over a very long distance without any optical dispersion compensation. One hurdle towards the actual exploitation of the technology is the required complexity of the processor, which grows exponentially with distance. In this letter, we investigate the use of a complexity-reduction algorithm originally proposed for nonoptical communications, called the M-method. We show by simulation that over 400 and 700 km of G.652 fiber, at 10.7 Gb/s, the M-method allows us to operate with virtually no excess penalty with respect to conventional MLSE, while keeping track of only 32 and 128 trellis states, respectively, out of optimum full-fledged trellises requiring 512 and 8192 states, respectively. We investigate the robustness of the algorithm versus limited analog-digital resolution and confirm its effectiveness by testing it over experimental data at 10 Gb/s over 1040 km.

Adaptive Arrays for Broadband Communications in the Presence of Unknown Co-Channel Interference

We present an adaptive detection (AD) for broadband communication in the presence of co-channel interference (CCI). In the case of imperfect channel estimation, a robust AD (RAD) is proposed to maintain the good performance. We also show that both AD and RAD can be further improved by using an iterative scheme, referred to as iterative AD (IAD) and iterative RAD (IRAD), respectively. Numerical examples show that all the proposed methods outperform the conventional maximum likelihood sequence estimator (MLSE) significantly, and that they are also computationally more efficient.

Single antenna interference cancellation for synchronised GSM networks using a widely linear receiver

A novel cochannel single antenna interference cancellation (SAIC) receiver is proposed for synchronised Group Special Mobile (GSM) systems. The receiver uses a two-stage strategy, where in the first stage cochannel interference is cancelled by a widely linear filter, while inter-symbol interference due to the GSM frequency-selective Rayleigh-fading environment is removed by a second-stage equaliser. Analytical results for the optimal widely linear filter coefficients are derived. Simulation results show excellent performance with large gains over the conventional receiver under interference limited channel conditions. It is shown that the conventional maximum likelihood sequence estimator or maximum a posteriori probability receiver is optimal when cochannel interference it not the dominant impairment, and it is proposed that the SAIC algorithm is disabled when the estimated carrier-to-interference (C/I) ratio is above a certain threshold.

On the least-squares performance of a novel efficient center estimation method for clustering-based MLSE equalization

Recently, a novel maximum-likelihood sequence estimation (MLSE) equalizer was reported that avoids the explicit estimation of the channel impulse response. Instead, it is based on the fact that the (noise-free) channel outputs, needed by the Viterbi algorithm, coincide with the points around which the received (noisy) samples are clustered and can thus be estimated directly with the aid of a supervised clustering method. Moreover, this is achieved in a computationally efficient manner that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. The resulting computational savings over the conventional MLSE equalization scheme are significant even in the case of relatively short channels where MLSE equalization is practically applicable. It was demonstrated, via simulations, that the performance of this algorithm is close to that using a least-squares (LS) channel estimator, although its computational complexity is even lower than that of the least-mean squares (LMS)-trained MLSE equalizer. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the LS method. It is proved that, when using LS with the training sequence employed by CE, the two methods lead to the same solution. However, when LS is trained with random data, it outperforms CE, with the performance difference being proportional to the channel length. A modified CE method, called MCE, is thus developed, that attains the performance of LS with perfectly random data, while still being much simpler computationally than classical LS estimation. Through the results of this paper, CE is confirmed as a methodology that combines high performance, simplicity, and low computational cost, as required in a practical equalization task. An alternative, algebraic viewpoint on the CE method is also provided.

Nonparametric trellis equalization in the presence of non-gaussian interference

We consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference (CCI). Conventional maximum-likelihood sequence estimation (MLSE) and maximum a posteriori probability (MAP) trellis equalizers treat the sum of noise and interference as additive white Gaussian noise, while CCI is generally a colored non-Gaussian process. We propose a novel nonparametric approach based on the estimation of the probability density function of the noise-plus-interference. Given the availability of a limited volume of data, the density is estimated by kernel-smoothing techniques. The use of a whitening filter in the presence of temporally colored disturbance is also addressed. Simulation results are provided for the global system for mobile communications (GSM), showing a significant performance improvement with respect to the equalizer based on the Gaussian assumption. Major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available.

An MLSE receiver using channel classification for Rayleigh fading channels

We propose a channel classification method that identifies the delay path profile of Rayleigh fading channels, which can be used in conjunction with conventional maximum-likelihood sequence estimation (MLSE) receivers. The proposed method determines the appropriate number of delay taps for the MLSE trellis, based on a decision variable obtained from multiple traffic bursts. By formulating the decision variable using the F-distribution, we derive exact expressions for misclassification probability. A new MLSE receiver structure that utilizes the channel classification method is described, and bit error rate (BER) simulation results are presented to demonstrate the performance improvement. The particular application which is discussed is the IS-136 TDMA standard.

Adaptive MLSE receiver over rapidly fading channels

This paper develops an adaptive maximum likelihood sequence estimator (MLSE) for rapidly fading channels corrupted by additive white Gaussian noise. This estimator is based on an explicit incorporation of the time-varying characteristics in channel modelling. When the multipath is caused by a few strong reflectors, the channel is shown to be poly-periodically time varying. The channel impulse response is then approximated by a linear combination of a finite set of complex exponential functions whose frequencies are termed Doppler frequencies. This modelling is well motivated in aeronautical radio communications and cellular telephony. During the training period, a cyclic statistics-based approach is developed to estimate the Doppler frequencies. An eigenvector approach as well as a maximum likelihood method are proposed to estimate the coefficients of linear expansion. After this initialization, the channel parameters are updated using a modified version of the LMS algorithm. Computer simulations are carried out to evaluate the proposed receiver performance. The new approach exhibits a large saving in computational complexity and offers superior performance over conventional adaptive MLSE in rapidly fading environment.

Cluster-based blind nonlinear-channel estimation

A cluster-based maximum-likelihood sequence estimator (MLSE) for nonlinear channels was described, which consists of a clustering network and an MLSE implemented by the Viterbi algorithm. The cluster-based MLSE can be used for digital communication through nonlinear finite-length channels because channel mapping estimation is used instead of channel estimation in the conventional MLSE. The clustering network of the cluster-based MLSE, which estimates the channel mapping between the signal input vectors and the noiseless channel outputs, is a supervised network and requires a training sequence. We propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence. The blind channel mapping estimator has a clustering block and a mapping block. The clustering block estimates the channel outputs, which represent the channel mapping, subject to an unknown permutation operation because no training sequence is utilized. That permutation operation is resolved by the mapping block, and therefore, the channel mapping is obtained. Introducing the blind channel mapping estimator into the cluster-based MLSE, a blind cluster-based MLSE for nonlinear channels can be done. Computer simulations of the blind channel mapping estimator and the blind MLSE for nonlinear channels are presented.

Adaptive combined DFE/MLSE techniques for ISI channels

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay.

Performance of sequence estimation scheme of narrowband digital FM signals with limiter-discriminator detection

A communication scheme using binary FM with noncoherent limiter-discriminator detection has been well known. Up to now, the improvement of bit error rate at the receiver side has been carried out through the bandwidth optimization of the IF filter, the decision feedback equalization (DFE), or simple two-state maximum likelihood sequence estimator (MLSE). This channel is inherently the intersymbol interference (ISI) channel due to the premodulation baseband filtering as well as the narrowband IF filtering. So the sequence estimation scheme using the Viterbi algorithm can be applied successfully, although the channel is not additive white Gaussian and maximum likelihood in the strict sense. In this paper, through computer simulations, we examine the actual BER improvement of the sequence estimation scheme with multiple-state trellis especially for MSK and GMSK signals. We mainly consider static AWGN and frequency nonselective Rician fading channels. Consequently, by adjusting the IF filter bandwidth, very large estimation gains are obtained compared to the conventional DFE or MLSE detector for AWGN and Rician fading channels. This scheme does not produce large demodulation delay and is implemented only by adding the signal processing part to the final stage of the receiver. This scheme seems to be very useful for any applications including satellite mobile channels. >

Joint data and channel estimation for TDMA mobile channels

One of the main problems in the proposed Northern American digital cellular system (IS-54) is the poor performance of the receiver for fast fading channels. The authors propose to use a novel joint data and channel estimation technique to improve performance. The basic idea of this method was described by N. Seshadri (1990) in the context of blind equalization. Simulation results indicate that this approach solves the problems of decision delay and divergence caused by error decision feedback in conventional maximum likelihood sequence estimation (MLSE). The specified IS-54 requirement of 19 dB at a BER of 3% and a speed of 100 km/h can be met with a margin of 8 dB. This result is 4.5 dB better than the conventional maximum likelihood receiver. >

Maximum likelihood sequence estimation from the lattice viewpoint

Considers the problem of data detection in multilevel lattice-type modulation systems in the presence of intersymbol interference and additive white Gaussian noise. The conventional maximum likelihood sequence estimator using the Viterbi algorithm has a time complexity of O(m/sup /spl nu/+1/) operations per symbol and a space complexity of O(/spl delta/m/sup /spl nu//) storage elements, where m is the size of input alphabet, /spl nu/ is the length of channel memory, and /spl delta/ is the truncation depth. By revising the truncation scheme and viewing the channel as a linear transform, the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point. From this lattice viewpoint, the lattice sequence estimator for PAM systems is developed, which has the following desired properties: 1) its expected time-complexity grows as /spl delta//sup 2/ as SNR/spl rarr//spl infin/; 2) its space complexity grow as /spl delta/; and 3) its error performance is effectively optimal for sufficiently large m. A tight upper bound on the symbol error probability of the new estimator is derived, and is confirmed by the simulation results of an example channel. It turns out that the estimator is effectively optimal for m/spl ges/4 and the loss in signal-to-noise ratio is less than 0.5 dB even for m=2. Finally, limitations of the proposed estimator are also discussed. >