A new zero-forcing block diagonalization (ZF-BD) scheme that enables both a more simplified ZF-BD and further increase in sum rate of MU-MIMO channels is proposed in this paper. The proposed scheme provides the improvement in BER performance for equivalent SU-MIMO channels. The proposed scheme consists of two components. First, a permuted channel matrix (PCM), which is given by moving the submatrix related to a target user to the bottom of a downlink MIMO channel matrix, is newly defined to obtain a precoding matrix for ZF-BD. Executing QR decomposition alone for a given PCM provides null space for the target user. Second, a partial MSQRD (PMSQRD) algorithm, which adopts MSQRD only for a target user to provide improvement in bit rate and BER performance for the user, is proposed. Some numerical simulations are performed, and the results show improvement in sum rate performance of the total system. In addition, appropriate bit allocation improves the bit error rate (BER) performance in each equivalent SU-MIMO channel. A successive interference cancellation is applied to achieve further improvement in BER performance of user terminals.

In this letter, a two-stage QR decomposition scheme based on Givens rotation with novel modified real-value decomposition (RVD) is presented. With the modified RVD applied to the result from complex Givens rotation at first stage, the number of non-zero terms needed to be eliminated by real Givens rotation at second stage decreases greatly and the computational complexity is thereby reduced significantly compared to the decomposition scheme with the conventional RVD. Besides, the proposed scheme is suitable for the hardware design of QR decomposition. Evaluation shows that the proposed QR decomposition scheme is superior to the related works in terms of computational complexity.

In this letter, a low latency, high throughput and hardware efficient sorted MMSE QR decomposition (MMSE-SQRD) for multiple-input multiple-output (MIMO) systems is presented. In contrast to the method of extending the complex matrix to real model and thereafter applying real-valued QR decomposition (QRD), we develop a highly parallel decomposition scheme based on coordinate rotation digital computer (CORDIC) which performs the QRD in complex domain directly and then converting the complex result to its real counterpart. The proposed scheme can greatly improve the processing parallelism and curtail the nullification and sorting procedures. Besides, we also design the corresponding pipelined hardware architecture of the MMSE-SQRD based on highly parallel Givens rotation structure with CORDIC algorithm for 4×4 MIMO detectors. The proposed MMSE-SQRD is implemented in SMIC 55nm CMOS technology achieving up to 50M QRD/s throughput and a latency of 59 clock cycles with only 218 kilo-gates (KG). Compared to the previous works, the proposed design achieves the highest normalized throughput efficiency and lowest processing latency.

In this letter, a post-detection signal to noise ratio (SNR) is considered for transmit antenna selection, when a sorted QR decomposition (SQRD) algorithm is used for signal detection in spatial multiplexing (SM) ultra-wideband (UWB) multiple input multiple output systems. The post-detection SNR expression is obtained using a QR factorization algorithm based on a sorted Gram-Schmidt process. The employed antenna selection criterion is to utilize the largest minimum post-detection SNR value. It is shown via simulations that the antenna selection significantly enhances the BER performance of the SQRD-based SM UWB systems on a log-normal multipath fading channel.

Maximum likelihood block signal detection employing QR decomposition and M-algorithm (QRM-MLBD) can significantly improve the bit error rate (BER) performance of single-carrier (SC) transmission while significantly reducing the computational complexity compared to maximum likelihood detection (MLD). However, its computational complexity is still high. In this paper, we propose the computationally efficient 2-step QRM-MLBD. Compared to conventional QRM-MLBD, the number of symbol candidates can be reduced by using preliminary decision made by minimum mean square error based frequency-domain equalization (MMSE-FDE). The BER performance achievable by 2-step QRM-MLBD is evaluated by computer simulation. It is shown that it can significantly reduce the computational complexity while achieving almost the same BER performance as the conventional QRM-MLBD.

This letter presents a criterion for selecting a transmit antenna subset when ZF detectors followed by Rake combiners are employed for spatial multiplexing (SM) ultra-wideband (UWB) multiple input multiple output (MIMO) systems. The presented criterion is based on the largest minimum post-processing signal to interference plus noise ratio of the multiplexed streams, which is obtained on the basis of QR decomposition. Simulation results show that the proposed antenna selection algorithm considerably improves the BER performance of the SM UWB MIMO systems when the number of multipath diversity branches is not so large and thus offers diversity advantages on a log-normal multipath fading channel.

Estimating the number of signals (NIS) is an important goal in array signal processing, such as direction-of-arrival (DOA) estimation. A common approach for solving this problem is to use an eigenvalue of the array covariance matrix and information criterion, such as the Akaike information criterion (AIC) and minimum description length (MDL). However they suffer serious degradation, when the incoming signals are coherent. To estimate the NIS of the coherent signals impinging on a uniform linear array (ULA), a method for estimating the number of signals without eigendecomposition (MENSE) is proposed. The accuracy of the NIS estimation performance of MENSE is superior to the other algorithms equipped with preprocessing such as the spatial smoothing preprocessing (SSP) and forward/backward spatial smoothing techniques (FBSS) to decorrelate the coherency of signals. Instead of using SSP or FBSS preprocessing, MENSE uses the Hankel correlation matrices. The Hankel correlation matrices can not only decorrelate the coherency of signals but also suppress the influence of noise. However, in severe conditions like low signal-to-noise ratio (SNR) or a closely spaced signals impinging on a ULA, the NIS estimation metric of MENSE has some bias which causes estimation error. In this paper, we pay attention to the multiplicity defined by the ratio of the geometric mean to the arithmetic mean. Accordingly, we propose a new estimation metric that has less bias than that in MENSE. The Computer simulation results show that the proposed method is superior to MENSE in the above severe conditions.

In this letter, we propose a novel signal detection method, reduced complexity QRM-MLD, which achieves almost identical error performance to that of the conventional QRM-MLD while significantly reducing the computational complexity.

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.

This letter proposes an efficient transmit power allocation using partial channel information feedback for the closed-loop sorted QR decomposition (SQRD) based V-BLAST systems. For the feedback information, the positive real-valued diagonal elements of R are forwarded to the transmitter. With the proposed transmit power allocation that is numerically derived by the Lagrange optimization method, the bit error rate performance of the system can be remarkably improved compare to the conventional open-loop SQRD based V-BLAST systems without increasing the receiver complexity.

At present, when using space-time processing techniques with multiple antennas for mobile radio communication, real-time weight adaptation is necessary. Due to the progress of integrated circuit technology, dedicated processor implementation with ASIC or FPGA can be employed to implement various wireless applications. This paper presents a resource and performance evaluation of the QRD-RLS systolic array processor based on fixed-point CORDIC algorithm with FPGA. In this paper, to save hardware resources, we propose the shared architecture of a complex CORDIC processor. The required precision of internal calculation, the circuit area for the number of antenna elements and wordlength, and the processing speed will be evaluated. The resource estimation provides a possible processor configuration with a current FPGA on the market. Computer simulations assuming a fading channel will show a fast convergence property with a finite number of training symbols. The proposed architecture has also been implemented and its operation was verified by beamforming evaluation through a radio propagation experiment.

In this paper, we investigate a detection ordering scheme of OSIC (Ordered Successive Interference Cancellation) systems suitable for power controlled MIMO transmission. Most studies about power controlled systems have mainly focused on strategies for transmitter, while the ordering scheme optimized at open-loop system has not been modified. In a conventional ordering scheme, the ordering process is done according to the largeness and smallness relation of each sub-stream's SNR. Unlike the conventional scheme, we derive an optimized detection ordering scheme that uses proximity to the optimal SNR. Because of error propagation, our proximity based algorithm is not valid for open-loop MIMO system in many cases. An optimization problem analysis and simulation results show that the system using the proposed ordering scheme outperforms the system using the conventional ordering scheme. Furthermore, due to the nature of QR decomposition, the proposed scheme shows not only lower implementation complexity but also better BER performance compared with the conventional scheme based on pseudo-inverse.

In multiple-input multiple-output (MIMO) wireless relay networks, simultaneously using multiple relay nodes can improve the capacity of source-to-destination communications. Recent information theories have shown that passing the same message across multiple relay nodes can improve the capacity of source-to-destination communications. We have previously proposed three relay schemes that use jointly QR decomposition and the phase control matrix; computer simulations have confirmed the superiority of these schemes over conventional ones such as amplify-and-forward and zero-forcing schemes. In this paper, we analyze the capacity and achievable gains (distributed array gain, intra-node array gain and spatial multiplexing gain) of the previously proposed relay schemes (QR-P-QR, QR-P-ZF, and ZF-P-QR) and thus provide an insight into what contributes to their superiority over conventional schemes. The analyses show that the location of the relay nodes used has a significant impact on capacity. On the basis of this observation, we further propose a method that enables each relay node to individually select its relay scheme according to its channel conditions so as to maximize the capacity. A computer simulation confirms the capacity improvement achieved by the proposed selection method.

A method for searching minimum Euclidean distances of respective substreams for different modulation orders of M-ary quadrature amplitude modulation signals in multiple-input and multiple-output systems is described. A channel matrix is cyclically-sorted sequentially and QR-decomposed. Using upper triangular matrices obtained by QR decomposition, minimum Euclidean distances are searched over trellis diagrams consisting of symbol-difference lattice points by computationally efficient multiple trellis-search algorithms. The simulation results demonstrate that per-substream minimum Euclidean distances can be detected with a high correct-estimation probability by path-re-searching controls over different modulation orders.

This paper proposes likelihood function generation of complexity-reduced Maximum Likelihood Detection with QR Decomposition and M-algorithm (QRM-MLD) suitable for soft-decision Turbo decoding and investigates the throughput performance using QRM-MLD with the proposed likelihood function in multipath Rayleigh fading channels for Orthogonal Frequency and Code Division Multiplexing (OFCDM) multiple-input multiple-output (MIMO) multiplexing. Simulation results show that by using the proposed likelihood function generation scheme for soft-decision Turbo decoding following QRM-MLD in 4-by-4 MIMO multiplexing, the required average received signal energy per bit-to-noise power spectrum density ratio (Eb/N0) at the average block error rate (BLER) of 10-2 at a 1-Gbps data rate is significantly reduced compared to that using hard-decision decoding in OFCDM access with 16 QAM modulation, the coding rate of 8/9, and 8-code multiplexing with a spreading factor of 8 assuming a 100-MHz bandwidth. Furthermore, we show that by employing QRM-MLD associated with soft-decision Turbo decoding for 4-by-4 MIMO multiplexing, the throughput values of 500 Mbps and 1 Gbps are achieved at the average received Eb/N0 of approximately 4.5 and 9.3 dB by QPSK with the coding rate of R = 8/9 and 16QAM with R = 8/9, respectively, for OFCDM access assuming a 100-MHz bandwidth in a twelve-path Rayleigh fading channel.

This paper presents the outline of the systolic array recursive least-squares (RLS) processor prototyped primarily with the aim of broadband mobile communication applications. To execute the RLS algorithm effectively, this processor uses an orthogonal triangularization technique known in matrix algebra as QR decomposition for parallel pipelined processing. The processor board comprises 19 application-specific integrated circuit chips, each with approximately one million gates. Thirty-two bit fixed-point signal processing takes place in the processor, with which one cycle of internal cell signal processing requires approximately 500 nsec, and boundary cell signal processing requires approximately 80 nsec. The processor board can estimate up to 10 parameters. It takes approximately 35 µs to estimate 10 parameters using 41 known symbols. To evaluate signal processing performance of the prototyped systolic array processor board, processing time required to estimate a certain number of parameters using the prototyped board was comapred with using a digital signal processing (DSP) board. The DSP board performed a standard form of the RLS algorithm. Additionally, we conducted minimum mean-squared error adaptive array in-lab experiments using a complex baseband fading/array response simulator. In terms of parameter estimation accuracy, the processor is found to produce virtually the same results as a conventional software engine using floating-point operations.

The sidelobe canceler in radar systems is a highly computational demanding problem. It can be efficiently tackled by resorting to the QR decomposition mapped onto a systolic array processor. The paper reports several mapping strategies by using massive parallel computers available on the market. MIMD as well as SIMD machines have been used, specifically MEIKO Computing Surface, nCUBE2, Connection Machine CM-200, and MasPar MP-1. The achieved data throughput values have been measured for a number of operational situations of practical interest.