Complexity Of Maximum Likelihood Detection Research Articles

Two-Layer LDPC Codes for Low Complexity ML Detection in GSM Systems

Although maximum-likelihood (ML) detection is able to achieve optimal performance in generalized spatial modulation (GSM) systems, its exhaustive search leads to an intractable computational complexity. In this letter, two-layer low-density parity-check (TL-LDPC) codes are proposed to reduce the combinations of transmission vectors in LDPC coded GSM systems. Simulation results show that the complexity of the ML detection in the TL-LDPC-coded GSM systems is much lower than that of the ML detection in conventional LDPC-coded GSM systems with a negligible performance loss.

Low complexity maximum-likelihood detector for DSTTD architecture based on the QRD-M algorithm

This paper presents a new decoder algorithm for the double space–time transmit diversity (DSTTD) system. The decoder is based on the QRD-M algorithm, which performs a breadth-first search of possible solutions tree. The search is simplified by skipping unlikely candidates, and it is stopped when no promising candidates are left. Furthermore, the search is divided into three concurrent iterations, making possible a fast, parallel implementation either in hardware or software. After presenting an analysis of the capacity and diversity of DSTTD, we present performance results showing that the proposed decoder is capable of achieving near maximum likelihood performance. We also show that the proposed algorithm exhibits lower computational complexity than other existing maximum likelihood detectors.

Modified Multiple Feedback QR Aided Successive Interference Cancellation Algorithm for Large MIMO Detection

Multiple-input multiple-output (MIMO) systems have attracted increased interest due to their capability to achieve higher multiplexing and diversity gains. In MIMO systems, reliable symbol detection in one of the major challenges. Maximum likelihood (ML) detection is one such technique which achieves minimum error rate performance for MIMO systems, however due to its exponential complexity ML detection is practically infeasible for large number of antennas. Therefore, in this contribution, we propose a low-complexity modified multiple feedback QR aided successive interference cancellation (MMF-SIC) algorithm which is capable of achieving near optimal performance. The effect of error propagation in SIC can be reduced by using multiple constellation points in decision feedback loops based on the reliability criteria. In MMF-SIC, an enhanced detection diversity is achieved by considering the decision feedback loops in multiple layers of QR aided SIC algorithm. Furthermore, we employ two different ordering schemes in parallel for QR decomposition in MMF-SIC algorithm. Through simulations, it is observed that the MMF-SIC algorithm performs superior over the conventional SIC and other SIC based techniques for detection in MIMO systems, and approach near optimal performance.

Maximum Likelihood Detection With a Closed-Form Solution for the Square QAM Constellation

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.

Combining ML and Compressive Sensing: Detection Schemes for Generalized Space Shift Keying

Generalized space shift keying (GSSK) proposed for large scale MIMO systems promises significant advantages in terms of hardware costs. However, the maximum likelihood (ML) detection for GSSK is computationally intractable. Detection schemes using compressive sensing (CS) offer a favorable performance-complexity tradeoff. In this letter, we propose a novel GSSK detection framework, where CS algorithms are used to reduce the complexity of ML detection. The proposed framework significantly reduces the performance gap between existing CS-based detection schemes and ML detection while retaining the complexity advantage of CS algorithms. Simulation results demonstrate the superiority of proposed scheme over popular CS-based detection schemes.

Near-ML detection for MDL-impaired few-mode fiber transmission.

Few-mode fiber transmission systems are typically impaired by mode-dependent loss (MDL). In an MDL-impaired link, maximum-likelihood (ML) detection yields a significant advantage in system performance compared to linear equalizers, such as zero-forcing and minimum-mean square error equalizers. However, the computational effort of the ML detection increases exponentially with the number of modes and the cardinality of the constellation. We present two methods that allow for near-ML performance without being afflicted with the enormous computational complexity of ML detection: improved reduced-search ML detection and sphere decoding. Both algorithms are tested regarding their performance and computational complexity in simulations of three and six spatial modes with QPSK and 16QAM constellations.

Spatial Modulation Aided Zero-Padded Single Carrier Transmission for Dispersive Channels

In this paper, we consider spatial modulation (SM) operating in a frequency-selective single-carrier (SC) communication scenario and propose zero-padding instead of the cyclic-prefix considered in the existing literature. We show that the zero-padded single-carrier (ZP-SC) SM system offers full multipath diversity under maximum-likelihood (ML) detection, unlike the cyclic-prefix based SM system. Furthermore, we show that the order of ML detection complexity in our proposed ZP-SC SM system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver. Thus, we show that the zero-padding applied in the SC SM system has two advantages over the cyclic prefix: 1) achieves full multipath diversity, and 2) imposes a relatively low ML detection complexity. Furthermore, we extend the partial interference cancellation receiver (PIC-R) proposed by Guo and Xia for the detection of space-time block codes (STBCs) in order to convert the ZP-SC system into a set of narrowband subsystems experiencing flat-fading. We show that full rank STBC transmissions over these subsystems achieves full transmit, receive as well as multipath diversity for the PIC-R. Furthermore, we show that the ZP-SC SM system achieves receive and multipath diversity for the PIC-R at a detection complexity order which is the same as that of the SM system in flat-fading scenario. Our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the ZP-SC SM system is significantly better than that of the SM in cyclic prefix based orthogonal frequency division multiplexing as well as of the SM in the cyclic-prefixed and zero-padded single carrier systems relying on zero-forcing/minimum mean-squared error equalizer based receivers.

基于量子Grover算法的VBLAST系统信号检测

In the VBLAST system, linear detection has low computational complexity, but its detection performance is poor. Conversely, Maximum Likelihood (ML) detection achieves optimal detection performance, but its computational complexity grows exponentially with the number of transmit antennas and the signal modulation order. This is a typical NP problem. To reduce the computational complexity of ML detection in the VBLAST system, while at the same time retaining optimal detection performance, an improved ML detection method is proposed in this paper. Both the quantum Grover and Grover-Long algorithms are used in the ML detection algorithm for the VBLAST system, and the complexity and performance of the algorithm are simulated. The simulation results show that not only is the computational complexity of Grover algorithm detection square accelerated, but also that the detection performance of the algorithm is close to that of ML detection. Moreover, this is the first time that a quantum algorithm is used to solve an engineering problem.

Soft Log Likelihood Ratio Replacement for Low-Complexity Maximum-Likelihood Detection

For multiple-input multiple-output systems, spatial multiplexing techniques can provide significant throughput gain. However, this promised gain can be attained by using maximum-likelihood detection (MLD) which requires huge computational complexity, and thus several low-complexity schemes are proposed to reduce the search space of the MLD. In this letter, we consider the log likelihood ratio (LLR) computation in low complexity MLD for soft channel decoding. We design a weighted combining method for a reliable LLR computation, compensating for the performance loss incurred by insufficient candidates of low-complexity MLD. The proposed LLR generation algorithm effectively reduces the computational complexity while maintaining the system performance of spatial multiplexing systems.

High user capacity collaborative code-division multiple access

In this study, the authors propose a novel collaborative multi-user transmission and detection scheme for the uplink of code-division multiple access (CDMA) that exploits the differences between users' fading channel signatures to increase the user capacity well beyond the spreading length in multiple access interference (MAI) limited environment. The authors show that it is possible to achieve this increase at a low complexity and high bit error rate (BER) performance in flat fading channels, which is a major research challenge for overloaded CDMA systems. In this approach, instead of using one sequence per user as in conventional CDMA, the authors group a small number of users to share the same spreading sequence and enable group spreading and despreading operations. The proposed collaborative multi-user receiver consists of two stages: group multi-user detection (MUD) stage to suppress the MAI between the groups and a low complexity maximum-likelihood detection stage to recover jointly the co-spread users' data using minimum Euclidean distance measure and users' channel gain coefficients. The scheme is investigated analytically and by extensive simulations and comparisons with conventional CDMA, overloaded CDMA using group pseudo-decorrelation (G-PD) and layered space–time (LAST) MUD. It is shown that the total number of full-rate users supported by the scheme is substantially higher than the available sequences. Moreover, it achieves much lower complexity and significantly improved BER for the same user capacity compared with G-PD. It is also shown that, with antenna diversity reception, collaborative CDMA considerably outperforms LAST scheme, particularly when more transmit antennas per group than available receive antennas are employed.

A new reduced complexity ML detection scheme for MIMO systems

For multiple-input multiple-output (MIMO) systems, the optimum maximum likelihood (ML) detection requires tremendous complexity as the number of antennas or modulation level increases. This paper proposes a new algorithm which attains the ML performance with significantly reduced complexity. Based on the minimum mean square error (MMSE) criterion, the proposed scheme reduces the search space by excluding unreliable candidate symbols in data streams. Utilizing the probability metric which evaluates the reliability with the normalized likelihood functions of each symbol candidate, near optimal ML detection is made possible. Also we derive the performance analysis which supports the validity of our proposed method. A threshold parameter is introduced to balance a tradeoff between complexity and performance. Besides, we propose an efficient way of generating the log likelihood ratio (LLR) values which can be used for coded systems. Simulation results show that the proposed scheme achieves almost the same performance as the ML detection at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> with 28% and 15% of real multiplications compared to the conventional QR decomposition with M-algorithm (QRD-M) in 4-QAM and 16- QAM, respectively. Also we confirm that the proposed scheme achieves the near-optimal performance for all ranges of code rates with much reduced complexity. For instance, our scheme exhibits 74% and 46% multiplication reduction in 4-QAM and 16-QAM, respectively, compared to the sphere decoding based soft-output scheme with rate-1/2 convolutional code.

Throughput Improvement with Discrete Pilot Signal Assignment and Iterative Channel Identification for MQRD-PCM/OFDM

In MIMO systems, the channel identification is important to distinguish transmitted signals from multiple transmit antennas. One of the most typical channel identification schemes is to employ a code division multiplexing (CDM) based scheme in which a unique spreading code is assigned to distinguish both BS and MS antenna elements. However, by increasing the number of base stations and transmit antenna elements, large spreading codes and pilot symbols are required to distinguish the received power from all the connectable BS, as well as to identify all the CSI for the combination of transmitter and receiver antenna elements. Furthermore, the complexity of maximum likelihood detection (MLD) for implementation of MIMO is a considerable work. To reduce these problems, in this paper, we propose the parallel detection algorithm using multiple QR decompositions with permuted channel matrix (MQRD-PCM) with discrete pilot signal assignment and iterative channel identification for MIMO/OFDM.

Efficient maximum likelihood detector for MIMO systems with small number of streams

The problem of maximum likelihood detection (MLD) of overlayed data symbols, which occurs in MIMO communications and interference mitigation applications, is addressed. A simple algorithm is presented that reduces the complexity of MLD by a factor of the constellation size compared to the complexity assumed in other publications. Although the complexity remains exponential in the number of transmit antennas, this reduction in complexity makes implementation of full-set MLD for MIMO systems with two-three streams feasible. The main difference compared to suboptimal schemes such as QRD-M and sphere decoding is that the result is exactly equivalent to full-set MLD. An efficient implementation is also presented.

Tree Search Detection Based on LLR Using M Algorithm in MC-CDMA Systems

In this paper, we propose a new multiuser detection scheme using Maximum Likelihood (ML) criterion and the M algorithm for Multi Carrier (MC)-Code Division Multiple Access (CDMA) systems in the down-link channel. We first describe an implementation of ML detection separating In- and Quadrature-phase components and using well-known linear filters. In the proposed algorithm, we produce hypothesis symbol vectors in a tree structure by partly changing the sub-optimum hard decisions based on the linear filter output. At each stage, we adopt the best M likely paths with respect to the true log likelihood or distance function as survivors. We determine the symbol vector which minimizes the distance function at the final stage. Although the complexity of ML detector is exponentially increasing as a function of the number of users, the proposed scheme requires by far less complexity. We demonstrate that the proposed scheme achieves equivalent Bit Error Rate (BER) performance with lower complexity in comparison with ML detector by computer simulations. Moreover we compare the proposed detection scheme with QRD-M algorithm which is based on QR decomposition combined with M algorithm.

Orthotope sphere decoding and parallelotope decoding—reduced complexity optimum detection algorithms for MIMO channels

The complexity of maximum likelihood detection (MLD) in multiple input multiple output (MIMO) systems with N transmit antennas typically grows exponentially with N. This makes MLD too complex to implement, particularly if higher order modulation schemes such as quadrature amplitude modulation are employed. Recently, generalised sphere decoding (GSD) was proposed, which provides the same performance as MLD, but complexity is only a polynomial function of N for small values of N. This is achieved by only considering lattice points that lie within a hypersphere centred at the received signal. Determining which lattice points lie within the sphere requires a complex distance calculation, so this paper investigates an different approach, called parallelotope decoding (PD) or alternatively the Kannan strategy. This method fits a parallelotope around the sphere, and simplifies the distance calculation. It turns out that PD performs poorly under certain channel conditions, so a novel hybrid scheme called orthotope sphere decoding is also proposed. This decoder is a hybrid of PD and GSD and is usually the most cost effective of the four optimal algorithms under discussion. Simulation results are presented to compare the performance and complexity of the optimal detectors described in the paper and the sub-optimal V-BLAST algorithm.

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.

BER Performance of a Hierarchical APSK UEP System over Nakagami-m fading

Bit error rate (BER) performance studies of amplitude phase shift keying (APSK) have not looked at the unequal error protection (UEP) facility provided by such a modulation scheme. In this paper hierarchical 16-APSK is studied using a bit allocation mechanism that allows for UEP for two classes of multimedia traffic. Theoretical BER expressions are derived for two UEP bit streams using the nearest neighbourhood method in additive white Gaussian noise (AWGN) and Nakagami-m fading channels. Simulation results are then used to validate the accuracy of the theoretical expressions. A low complexity maximum likelihood (ML) detection for hierarchical 16-APSK is also proposed and simulation results show that the proposed low complexity ML detector achieves the same BER performance as the optimum ML detector.

Instantaneous Bit Error Rate Based ASM Scheme for MPSK Spatial Modulation

In this paper, we propose an instantaneous bit error rate (IBER) based adaptive spatial modulation (ASM) scheme for the M-ary phase shift keying (MPSK) constellation (ASM-MPSK). In the proposed ASM-MPSK system, the combination of MPSK modulation order and number of transmit antennas is chosen based on the one that yields the smallest IBER while keeping the average transmission bit rate (TBR) constant. Furthermore, a low complexity maximum likelihood (ML) detection scheme for MPSK SM is employed which significantly reduces the complexity of the proposed system compared with other adaptive modulation schemes that use the high complexity ML detector for detection. Additionally, in this paper, we also analyse the computational complexity for the proposed ASM-MPSK. The simulation results indicate that the proposed scheme provides a significant improvement in terms of the error performance compared to conventional MPSK SM systems under a particular TBR; for TBR = 5 bits/s/Hz, a performance gain of approximately 4 dB had been achieved at a BER of 1 × 10−6.