Reduced Complexity Maximum Likelihood Research Articles

Reduced-Complexity ML Signal Detection for Spatially Multiplexed Signal Transmission Over MIMO Systems With Two Transmit Antennas

In this paper, we address spatially multiplexed (SM) multiple-input-multiple-output (MIMO) systems that are expected to be used in next-generation mobile communication systems that require high-speed data transmission. The data-transmission rate of an SM MIMO system increases in proportion to the number of spatial streams it transmits. However, it is hard to implement large numbers of spatial streams due to the spatial limits of mobile units and the high cost of installing many antennas. In this paper, we focus on the case of two spatial streams and propose a novel signal-detection technique. We first define the bidirectional detectability of a 2-D complex vector, and using the fact that only a small number of vectors, including the maximum-likelihood (ML) solution vector, satisfy the bidirectional detectability, we reduce the search space, thereby enabling efficient ML signal detection at the receiver.

New rate-2 STBC design for 2 TX with reduced-complexity maximum likelihood decoding

We propose a new full-rate space-time block code (STBC) for two transmit antennas which can be designed to achieve maximum diversity or maximum capacity while enjoying optimized coding gain and reduced-complexity maximum-likelihood (ML) decoding. The maximum transmit diversity (MTD) construction provides a diversity order of 2Nr for any number of receive antennas Nr at the cost of channel capacity loss. The maximum channel capacity (MCC) construction preserves the mutual information between the transmit and the received vectors while sacrificing diversity. The system designer can switch between the two constructions through a simple parameter change based on the operating signal-to-noise ratio (SNR), signal constellation size and number of receive antennas. Thanks to their special algebraic structure, both constructions enjoy low-complexity ML decoding proportional to the square of the signal constellation size making them attractive alternatives to existing full-diversity full-rate STBCs in [6], [3] which have high ML decoding complexity proportional to the fourth order of the signal constellation size. Furthermore, we design a differential transmission scheme for our proposed STBC, derive the exact ML differential decoding rule, and compare its performance with competitive schemes. Finally, we investigate transceiver design and performance of our proposed STBC in spatial multiple-access scenarios and over frequency-selective channels.

On Fast-Decodable Space–Time Block Codes

We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2 times 2 and 4times2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2times2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4times2 STBC, and show that it outperforms all previously known codes with certain constellations.

Likelihood Estimation for Reduced-Complexity ML Detectors in a MIMO Spatial-Multiplexing System

This paper proposes a likelihood estimation method for reduced-complexity maximum-likelihood (ML) detectors in a multiple-input multiple-output (MIMO) spatial-multiplexing (SM) system. Reduced-complexity ML detectors, e. g., Sphere Decoder (SD) and QR decomposition (QRD)-M algorithm, are very promising as MIMO detectors because they can estimate the ML or a quasi-ML symbol with very low computational complexity. However, they may lose likelihood information about signal vectors having the opposite bit to the hard decision and bit error rate performance of the reduced-complexity ML detectors are inferior to that of the ML detector when soft-decision decoding is employed. This paper proposes a simple estimation method of the lost likelihood information suitable for the reduced-complexity ML detectors. The proposed likelihood estimation method is applicable to any reduced-complexity ML detectors and produces accurate soft-decision bits. Computer simulation confirms that the proposed method provides excellent decoding performance, keeping the advantage of low computational cost of the reduced-complexity ML detectors.

Exact Reduced-Complexity Maximum Likelihood Reconstruction of Multiple 3-D Objects From Unlabeled Unoriented 2-D Projections and Electron Microscopy of Viruses

In cryo-electron microscopy, the data is comprised of noisy 2-D projection images of the 3-D electron scattering intensity of the object where the orientation of the projections is unknown. Often, the images show randomly selected objects from a mixture of different types of objects. Objects of different type may be unrelated, e.g., different species of virus, or related, e.g., different conformations of the same species of virus. Due to the low SNR and the 2-D nature of the data, it is challenging to determine the type of the object shown in an individual image. A statistical model and maximum likelihood estimator that computes simultaneous 3-D reconstruction and labels using an expectation maximization algorithm exists but requires extensive computation due to the numerical evaluation of 3-D or 5-D integrations of a square matrix of dimension equal to the number of degrees of freedom in the 3-D reconstruction. By exploiting the geometry of rotations in 3-D, the estimation problem can be transformed so that the inner-most numerical integral has a scalar rather than a matrix integrand. This leads to a dramatic reduction in computation, especially as the number of degrees of freedom in the 3-D reconstruction increases. Numerical examples of the 3-D reconstructions are provided based on synthetic and experimental images where the objects are small spherical viruses.

Reduced-Complexity Near-Maximum-Likelihood Detection for Decision Feedback Assisted Space-Time Equalization

A novel decision-feedback (DF) aided reduced complexity maximum likelihood (ML) space-time equalizer (STE) designed for a single-carrier system is introduced. Two different methods of incorporating DF into the recursive tree search based receiver structure are proposed for allowing detection at a moderate computational cost. Additionally, a further complexity reduction scheme is proposed, which exploits the specific characteristics of both the wide-band channel and the proposed DF-STE. In comparison to the DF-STE not benefiting from this complexity reduction, the proposed detector is capable of reducing the complexity by several orders of magnitude. More quantitatively, for the specific rank-deficient system considered, which detected the signal transmitted from four transmit antennas with the aid of two receive antennas, the complexity might be reduced by a factor of 100 at low Signal-to-noise ratios (SNRs) without noticeable performance degradation. By contrast, at higher SNRs a complexity reduction of a factor of 10 might be achieved, depending on the tolerable performance degradation.

Complexity Reduced Maximum Likelihood Detection for SDM-OFDM System

This paper proposes two complexity reduced Maximum Likelihood Detection (MLD) methods for Space Division Multiplexing-OFDM (SDM-OFDM) system to exploit the spatial diversity so as to achieve the improved transmission quality. The proposed methods enable to outperform the other suboptimal detection methods and achieve near MLD performance with a significant reduction in calculation complexity. The various computer simulation results confirm that the proposed methods could realize the above targets and might be promising solution in practical systems.

Reduced complexity maximum likelihood decoding of linear block codes

Reduced complexity maximum likelihood decoding of linear block codes

Recursive Channel Estimation Based on Finite Parameter Model Using Reduced-Complexity Maximum Likelihood Equalizer for OFDM over Doubly-Selective Channels

To take intercarrier interference (ICI) attributed to time variations of the channel into consideration, the time- and frequency-selective (doubly-selective) channel is parameterized by a finite parameter model. By capitalizing on the finite parameter model to approximate the doubly-selective channel, a Kalman filter is developed for channel estimation. The ICI suppressing, reduced-complexity Viterbi-type Maximum Likelihood (RML) equalizer is incorporated into the Kalman filter for recursive channel tracking and equalization to improve the system performance. An enhancement in the channel tracking ability is validated by theoretical analysis, and a significant improvement in BER performance using the channel estimates obtained by the recursive channel estimation method is verified by Monte-Carlo simulations.

Combined ML and MMSE Multiuser Detection for STBC-OFDM Systems

Performance of the minimum mean square error (MMSE) detection is far below that of the maximum likelihood (ML) detection in a multiuser environment and decreases significantly as the number of co-channel users increases. In this paper, we propose a combined MMSE and ML multiuser detection scheme for space-time block coded (STBC) orthogonal frequency division multiplexing (STBC-OFDM) which has improved performance but with low complexity. In particular, we propose a reduced complexity ML post-detection (ML-PDP) scheme which can correct erroneously estimated bits from the outputs of MMSE multiuser detection. The proposed ML-PDP scheme performs sequential search to detect a predefined number of bits with higher probability of error and then uses ML detection to correct them. Upon controlling the number of corrected bits it is possible to balance the system performance with complexity associated with the ML-PDP. We show that significant improvement can be achieved at the cost of only small additional complexity compared with the MMSE multiuser detection.

Reduced-complexity ML decoding of rate 6/8 and rate 1 linear complex space-time codes for up to eight transmit antennas with phase feedback

It is shown that single symbol maximum-likelihood (ML) decoding for chosen rate 6/8 linear complex space-time codes for up to eight transmit antennas is possible in the presence of a phase feedback. The performance of the code is the same as that of an ideal code, for which the sufficient statistic of the channel is its Frobenius norm. For rate 1 codes for up to eight antennas, a two-phase feedback enables a symbol to see the interference from only one symbol instead of three, thereby reducing the complexity of ML decoding. Quantization of the feedback is also considered.

A Simplified Maximum Likelihood Detector for OFDM-SDM Systems in Wireless LAN

This paper presents a reduced-complexity maximum likelihood detection (MLD) scheme for orthogonal frequency division multiplexing with space division multiplexing (OFDM-SDM) systems. Original MLD is known to be an optimal scheme for detecting the spatially multiplexed signals. However, MLD suffers from an exponentially computational complexity because it involves an exhaustive search for the optimal result. In this paper, we propose a novel detection scheme, which drastically reduce the complexity of MLD while keeping performance losses small. The proposed scheme decouples the spatially multiplexed signals in two stages. In stage one, the estimated symbols obtained from zero-forcing (ZF) are used to limit the candidate symbol vectors. In stage two, to form a final estimate of the transmitted symbol vector, the Euclidean or original defined likelihood metric is examined over all symbol vectors obtained from stage 1. Both the bit error rate (BER) and packet error rate (PER) performances are evaluated over a temporally and spatially uncorrelated frequency selective channel through the computer simulations. For a four-transmit and four-receive OFDM-SDM system transmitting data at 144 Mbit/s and 216 Mbit/ss i.e., employing 16 Quadrature Amplitude Modulation (16QAM) and 64QAM subcarrier modulation over 16.6 MHz bandwidth channel, the degradation in required SNR from MLD for PER = 1% are about 0.6 dB and 1.5 dB, respectively. However, the complexity of MLD is reduced to 0.51000% and 0.01562%.

A Reduced-Complexity Maximum-Likelihood Method for Multiuser Detection

Multiuser or joint detection has recently been receiving significant research interest because of its potential for the significant increase in system capacity and performance. Among the conventional multiuser detection schemes such as the minimum mean-squared error and successive interference cancellation-based ones, maximum-likelihood multiuser detection has the best system performance. However, the complexity of maximum-likelihood detection (MLD) increases exponentially in the number of users and constellation size. In this paper, a low-complexity MLD scheme based on the use of a sensitive-bits algorithm is proposed. It is demonstrated that the proposed method can greatly reduce the computational complexity with a minimal penalty in performance compared with the exhaustive optimal MLD scheme.

A New Algorithm for Optimum Multiuser Detection in Synchronous CDMA Systems

Optimum multiuser detection for Code Division Multiple Access (CDMA) systems requires the solution of an NP-hard combinatorial optimization problem. It is well known that the computational complexity of the optimum multiuser detector is exponential with the number of active users in the system. In order to reduce the complexity of the optimum multiuser detection, we propose a Reduced Complexity Maximum Likelihood (RCML) algorithm that includes a set of novel certain boundary rules and characteristics. We investigate the performance and complexity tradeoffs for the RCML algorithm by conducting a set of simulations; Maximum Likelihood (ML) detection as a reference for performance comparisons, and relaxation based Semidefinite Programming (SDPB) algorithm as a reference for complexity comparisons. We show that the RCML algorithm is a promising algorithm for its computational savings over relaxation based algorithms in lightly-to-moderately loaded CDMA systems, and for its optimality in highly loaded CDMA systems.

Reduced complexity maximum likelihood sequence estimation for multitrack high-density magnetic recording channels

In this paper we investigate the problem of designing reduced complexity detectors for multitrack high-density magnetic recording systems. The detectors derived in this work operate on superstate sets and carry several survivors for each set. We show that such a reduced state increased survivor approach provides near optimal performance to the maximum likelihood method, namely the Viterbi Algorithm (VA), but operate at a fractional complexity of the VA.

Reduced-complexity detection and phase synchronization of CPM signals

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes, expressed in terms of the number of matched filters and states of a Viterbi algorithm, is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes do not require an increased number of matched filters, and are perfectly suitable to be used in conjunction with these receivers. Based on the phase-locked loop (PLL) equivalent linear model, a method for optimizing the parameters of digital second-order PLL's is presented. Numerical examples, based on theoretical analysis and computer simulation, are provided for two specific formats in the CPM class: tamed frequency modulation (TFM) and a quaternary raised-cosine (RC) modulation.