The generalized spatial modulation (GSM) is a new transmission technique that can realize high-performance multiple-input multiple-output (MIMO) communication systems with a low RF complexity. This paper presents an efficient sphere decoding method used to perform the symbol detection for the generalized spatial modulation (GSM) multiple-input multiple-output (MIMO) systems. In the proposed method, the cost metric is modified so that it does not include the cancellation of the nonexistent interference. The modified cost metric can be computed by formulating a detection tree that has a regular structure representing the transmit antenna combinations as well as the symbol vectors, both of which are detected efficiently by finding the shortest path on the basis of an efficient tree search algorithm. As the tree search algorithm is performed for the regular detection tree to compute the modified but mathematically-equivalent cost metric, the efficiency of the sphere decoding is improved while the bit-error rate performance is not degraded. The simulation results show that the proposed method reduces the complexity significantly when compared with the previous method: for the 6×6 64QAM GSM-MIMO system with two active antennas, the average reduction rate of the complexity is as high as 45.8% in the count of the numerical operations.

The integer least-squares (ILS) problem frequently arises in wireless communication systems. Sphere decoding (SD) is a systematic search scheme for solving ILS problem. The enumeration of candidates is a key part of SD for selecting a lattice point, which will be searched by the algorithm. Herein, the authors present a computationally efficient Schnorr-Euchner enumeration (SEE) algorithm to solve the constrained ILS problems, where the solution is limited into the finite integer lattice. To trace only valid lattice points within the underlying finite lattice, the authors devise an adaptive computation of the enumeration step and counting the valid points enumerated. In contrast to previous SEE methods based on a zig-zag manner, the proposed method completely avoids enumerating invalid points outside the finite lattice, and it further reduces real arithmetic and logical operations.

Efficient detection schemes for an overloaded multiple-input multiple-output (MIMO) system have been investigated recently. The literature shows that trellis coded modulation (TCM) is able to enhance a system's capability to separate signal streams in the detection process of MIMO systems. However, the computational complexity remains high as a maximum likelihood detection (MLD) algorithm is used in the scheme. Thus, a sphere decoding (SD) algorithm with a pseudo distance (PD) is proposed in this paper. The PD maintains the coding gain advantage of the TCM by keeping some potential paths connected unlike conventional SD which truncates them. It is shown that the proposed scheme can reduce the number of distance calculations by about 98% for the transmission of 3 signal streams. In addition, the proposed scheme improves the performance by about 2dB at the bit error rate of 10-2.

The development of high data rate wireless communications systems using Multiple Input — Multiple Output (MIMO) antenna techniques requires detectors with reduced complexity and good Bit Error Rate (BER) performance. In this paper, we present the Semi-fixed Complexity Sphere Decoder (SCSD), which executes the process of detection in MIMO systems with a significantly lower computation cost than the high-performance/reduced-complexity detectors: Sphere Decoder (SD), K-best, Fixed Complexity Sphere Decoder (FSD) and Adaptive Set Partitioning (ASP). Simulation results show that when the Signal-to-Noise Ratio (SNR) is less than 15dB, the SCSD reduces the complexity by up to 90% with respect to SD, up to 60% with respect to K-best or ASP and by up to 90% with respect to FSD. In the proposed algorithm, the BER performance does not show significant degradation and therefore, can be considered as a complexity reduction scheme suitable for implementing in MIMO detectors.

This letter presents a technique to reduce the complexity of the soft-output multiple-input multiple-output symbol detection based on Dijkstra's algorithm. By observing that the greedy behavior of Dijkstra's algorithm can entail unnecessary tree-visits for the symbol detection, this letter proposes a technique to evict non-promising candidates early from the search space. The early eviction technique utilizes layer information to determine if a candidate is promising, which is simple but effective. When the SNR is 30dB for 6×6 64-QAM systems, the average number of tree-visits in the proposed method is reduced by 72.1% in comparison to that in the conventional Dijkstra's algorithm-based symbol detection without the early eviction.

An efficient pruning method is proposed for the infinity-norm sphere decoding based on Schnorr-Euchner enumeration in multiple-input multiple-output spatial multiplexing systems. The proposed method is based on the characteristics of the infinity norm, and utilizes the information of the layer at which the infinity-norm value is selected in order to decide unnecessary sub-trees that can be pruned without affecting error-rate performance. Compared to conventional pruning, the proposed pruning decreases the average number of tree-visits by up to 37.16% in 44 16-QAM systems and 33.75% in 66 64-QAM systems.

A modified Schnorr-Euchner sphere decoding (SE-SD) algorithm to search for the receive minimum distance is presented. In the proposed algorithm, the visit to negative symmetric vectors of already spanned vectors is avoided by using a biased spanning, and the redundant processes to visit the all-zero vector are also eliminated. A numerical experiment shows that the modified SE-SD algorithm is much more efficient than the conventional algorithm in terms of average computational complexity.

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.

This letter deals with computationally efficient maximum-likelihood (ML) detection for the quasi-orthogonal space-time block code (QOSTBC) with four transmit antennas. The proposed ML detector uses a permutation based real-valued equivalent channel matrix representation. As a result, the complexity of ML detection problem is moderated from O(2|A|2) to O(4|A|), where |A| is modulation order. Numerical results show that the proposed ML detector provides ML performance and achieves greatly high computational savings.

This letter presents a new vertical Bell Labs layered space-time (V-BLAST) transmission scheme for developing low-complexity tree searching in the QRD-M algorithm. In the new V-BLAST system, we assign modulation scheme in ascending order from top to bottom tree branches. The modulation set to be assigned is decided by two criteria: minimum performance loss and maximum complexity reduction. We also propose an open-loop power allocation algorithm to surmount the performance loss. Numerical results show that the proposed V-BLAST transmission approach can significantly reduce the computational loads of the QRD-M algorithm with a slight performance degradation.

This paper proposes a co-channel interference cancellation method for multiple-input multiple-output (MIMO) wireless communication systems. Maximum-likelihood multi-user detection (ML-MUD), which is one of the co-channel interference cancellation methods at a receiver side, has excellent bit error rate (BER) performance. However, computational complexity of the ML-MUD is prohibitive, because the ML-MUD must search for the most probable symbol vector from all candidates of the transmitted signals. We apply sphere decoding (SD) to the ML-MUD in order to reduce the computational complexity of the ML-MUD, and moreover we propose a modified version of the SD suitable for the ML-MUD. The proposed method extracts desired signal components from a received signal vector and a channel matrix decomposed the upper triangular form, and then performs the SD to the low dimensional model in order to detect the transmitted signals of the desired user. Computer simulation confirms that the proposed method can suppress the undesired signals and detect the desired signals, offering significant reduction of the computational complexity of the conventional method.

We propose a sub-optimal but computationally efficient Modified Fano Detection algorithm (MFD) for V-BLAST systems. This algorithm utilizes the QR decomposition of the channel matrix and the sequential detection scheme based on tree searching to find the optimal symbol sequence. For more reliable signal detection, the decoder is designed to move backward for the specified value at the end of the tree. This results in significant reduction of the complexity while the performance of MFD is comparable to that of ML detector.