QR Decomposition With M-algorithm Research Articles

A Simplified QRD-<i>M</i> Algorithm in MIMO-OFDM Systems

The Long Term Evolution (LTE) of mobile communication standard was designed by the 3rd generation partnership project (3GPP) to serve the requirements. Nowadays, the combining of the orthogonal frequency division multiplexing (OFDM) and the multiple input multiple output (MIMO) is supported in LTE system. The MIMO-OFDM is considered to improve data rate and channel capacity without additional bandwidth. Because the receivers get all transmission signals from all transmitters at the same time, many detection schemes have been developed for accurate estimation and low complexity. Among the detection schemes, the QR decomposition with M algorithm (QRD-M) achieves optimal error performance with low complexity. Nevertheless, the conventional QRD-M has high complexity for implementation. To overcome the problem, this letter proposes the low complexity QRD-M detection scheme in MIMO-OFDM systems. The proposed scheme has two elements which decide layer value and the limited candidates. The two elements are defined by the number of transmit antennas and the cardinality of modulation set respectively. From simulation results, the proposed scheme has the same error performance with the conventional QRD-M and very lower complexity than the conventional QRD-M.

Improved QRD-M Detection Algorithm for Generalized Spatial Modulation Scheme

Generalized spatial modulation (GSM) is a spectral and energy efficient multiple-input multiple-output (MIMO) transmission scheme. It will lead to imperfect detection performance with relatively high computational complexity by directly applying the original QR-decomposition with M algorithm (QRD-M) to the GSM scheme. In this paper an improved QRD-M algorithm is proposed for GSM signal detection, which achieves near-optimal performance but with relatively low complexity. Based on the QRD, the improved algorithm firstly transforms the maximum likelihood (ML) detection of the GSM signals into searching an inverted tree structure. Then, in the searching process of the M branches, the branches corresponding to the illegitimate transmit antenna combinations (TACs) and related to invalid number of active antennas are cut in order to improve the validity of the resultant branches at each level by taking advantage of characteristics of GSM signals. Simulation results show that the improved QRD-M detection algorithm provides similar performance to maximum likelihood (ML) with the reduced computational complexity compared to the original QRD-M algorithm, and the optimal value of parameter M of the improved QRD-M algorithm for detection of the GSM scheme is equal to modulation order plus one.

Adaptive MIMO Detection Scheme Using Post SNR in Wireless Communication Systems

The QR decomposition with M algorithm (QRD-M) scheme is an advanced and reliable detection scheme. However, the conventional QRD-M scheme has a trade-off between the error performance and the complexity since it fixes the number of the candidates. Therefore, an adaptive detection scheme is proposed to consider this trade-off problem. The proposed scheme uses the channel state information to control the number of candidates per subcarrier automatically. The simulation results show that the proposed scheme can be applied more efficiently than the conventional scheme.

Performance of Overloaded MIMO-OFDM System with Repetition Code

This paper investigates the performance of an overloaded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with a repetition code. It has been demonstrated that diversity with block coding prevents the performance degradation induced by signal multiplexing. However, the computational complexity of a joint decoding scheme increases exponentially with the number of multiplexed signal streams. Thus, this paper proposes the use of a repetition code in the overloaded MIMO-OFDM system. In addition, QR decomposition with M-algorithm (QRM) maximum likelihood decoding (MLD) is applied to the decoding of the repetition code. QRM-MLD significantly reduces the amount of joint decoding complexity. In addition, virtual antennas are employed in order to increase the throughput that is reduced by the repetition code. It is shown that the proposed scheme reduces the complexity by about 1/48 for 6 signal streams with QPSK modulation while the BER degradation is less than 0.ldB at the BER of 10−3.

Complexity Reduced MIMO Interleaved SC-FDMA Receiver with Iterative Detection

In this paper, we propose the receiver structure for Multiple Input Multiple Output (MIMO) Interleaved Single Carrier-Frequency Division Multiple Access (SC-FDMA) where the Frequency Domain Equalization (FDE) is firstly done for obtaining the tentative decision results and secondly using them the Inter-Symbol Interference (ISI) is cancelled by ISI canceller and then the Maximum Likelihood Detection (MLD) is used for separating the spatially multiplexed signals. Furthermore the output from MLD is fed back to ISI canceller repeatedly. In order to reduce the complexity, we replace the MLD by QR Decomposition with M-Algorithm (QRD-M) or Sphere Decoding (SD). Moreover, we add the soft output function to SD using Repeated Tree Search (RTS) algorithm to generate soft replica for ISI cancellation. We also refer to the Single Tree Search (STS) algorithm to further reduce the complexity of RTS. By examining the BER characteristics and the complexity reduction through computer simulations, we have verified the effectiveness of proposed receiver structure.

Depth-First QRD-M Detection Algorithm for MIMO Systems

Maximum likelihood (ML) detection algorithm for multiple input multiple output (MIMO) systems provided the best bit error rate (BER) performance with heavy calculating complexity. The use of QR decomposition with M-algorithm (QRD-M) had been proposed to provide near-ML detection performance and lower calculating complexity. However, its complexity still grew exponentially with increasing dimension of the transmitted signal. To reduce the problem, an improved detection scheme was proposed here. After constructing the tree detecting model of MIMO systems, the ML search of one layer was done, the branch metrics were calculated and sorted, which gave an ordered set of the layer, then depth-first search were used to search the left layers with termination methods. The proposed algorithm provides near QRD-M detection performance.

Linear and Nonlinear Time Domain Block Equalizers on MIMO Frequency Selective Channels

Single-Carrier (SC) transmission with the same bandwidth as Multi-Carrier (MC) transmission (such as OFDM) may have far shorter symbol duration and is considered to be more robust against time selective fading. In this paper, we proposed the novel equalization and signal separation schemes in time domain for short block length transmission, i.e., Block Linear Equalization (BLE) and Block Nonlinear Equalization (BNLE) on MIMO frequency selective fading channels. The proposed BLE uses the MMSE based inverse matrix in time domain and the BNLE utilizes the QRD-M (QR Decomposition with M algorithm) with appropriate receiver complexity. We compared the computational complexity among the conventional SC-FDE (Frequency Domain Equalization) scheme and the proposed equalizers. We also used the Low-Density Parity Check (LDPC) decoder concatenated to the proposed BLE and BNLE.

Adaptive Parallel and Iterative QRDM Detection Algorithms for MIMO Multiplexing Systems

QR-decomposition with M-algorithm (QRDM) achieves quasi-ML performance in multiple-input multiple-output (MIMO) multiplexing systems. Nevertheless, QRDM performs avoidable computations because of i...

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.

Iterative Modified QRD-M Based on CRC Codes for OFDM MIMO Multiplexing

To improve the channel estimation accuracy of multiple-input multiple-output (MIMO) multiplexing, we previously proposed iterative QR-decomposition with M-algorithm (QRD-M) with decision directed channel estimation. In this paper, to keep the computational complexity low while further improving the transmission performance, we will modify previously proposed iterative QRD-M by incorporating cyclic redundancy check (CRC) coding. In the proposed method, transmitted signals are ranked according to their results of CRC decoding and the received signal-to-interference plus noise power ratio (SINR). In the modified M-algorithm, since the results of Turbo decoding and CRC decoding are used to generate the surviving symbol replica, the accuracy of signal detection in the following steps can be improved. Furthermore, based on the results of CRC decoding, iterative process can be terminated before reaching the maximum allowable number of iterations. Computer simulation results show that the loss in the required average received signal energy per bit-to-noise power spectrum density ratio E b /N o for average packet error rate (PER) = 10 -2 is only about 0.4 dB from maximum likelihood detection (Full MLD) with ideal channel estimation.