In very-large multiple-input multiple-output (MIMO) systems, the base station (BS) is equipped with very large number of antennas as compared to previously considered systems. There are various advantages of increasing the number of antennas, and some schemes require handling large matrices for joint processing (pre-coding) at the BS. The dirty paper coding (DPC) is an optimal pre-coding scheme and has a very high complexity. However, with increasing number of BS antennas, linear pre-coding performance tends to that of the optimal DPC. Although linear pre-coding is less complex than DPC, there is a need to compute pseudo inverses of large matrices. In this paper we present a low complexity approximation of down-link Zero Forcing (ZF) linear pre-coding for very-large multi-user MIMO systems. Approximation using a Neumann series expansion is opted for inversion of matrices over traditional exact computations, by making use of special properties of the matrices, thereby reducing the cost of hardware. With this approximation of linear pre-coding, we can significantly reduce the computational complexity for large enough systems, i.e., where we have enough BS antenna elements. For the investigated case of 8 users, we obtain 90% of the full ZF sum rate, with lower computational complexity, when the number of BS antennas per user is about 20 or more.

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Approximative matrix inverse computations for very-large MIMO and applications to linear pre-coding systems

Matrix inversion and triangularization problems are common to a wide variety of communication systems, signal processing applications and solution of a set of linear equations. Matrix inversion is a computationally intensive process and its hardware implementation based on fixed-point (FP) arithmetic is a challenging problem. This paper proposes a fully parallel VLSI architecture under fixed-precision for the inverse computation of a real square matrix using QR decomposition with modified Gram-Schmidt (MGS) orthogonalization. The MGS algorithm is stable and accurate to the integral multiples of machine precision under fixed-precision for a well-conditioned non-singular matrix. For typical matrices (4 times 4) found in MIMO communication systems, the proposed architecture was able to achieve a clock rate of 277 MHz with a latency of 18 time units and area of 72K gates using 0.18-mum CMOS technology. For a generic square matrix of order n, the latency required is 5n - 2 which is better than all previously known architectures. With the use of LUTs and log-domain computations, the total area has been reduced compared to architectures based on linear-domain computations

VLSI Architecture for Matrix Inversion using Modified Gram-Schmidt based QR Decomposition

This paper presents a VLSI architecture of QR decomposition for 4×4 MIMO-OFDM systems. A real-value decomposed MIMO system model is handled and thus the channel matrix to be processed is extended to the size of 8×8. Instead of direct factorization, a QR decomposition scheme by cascading one complex-value and one real-value Givens rotation stages is proposed, which can save 44% hardware complexity. Besides, the requirement of skewed inputs in the conventional QR-decomposition systolic array is eliminated and 36% of delay elements are removed. The real-value Givens rotation stage is also constructed in a form of a stacked triangular systolic array to match with the throughput of the complex-value one. Hardware sharing is considered to enhance the utilization. The proposed design is implemented in 0.18-μm CMOS technology with 152K gates. From measurement, the maximum operating frequency is 100 MHz. It generates QR decomposition results every four clock cycles and accomplishes continuous projection every clock cycle to support MIMO detection up to 2.4 Gb/s. The measured power consumption is 318.6 mW and 219.6 mW for QR decomposition and projection, respectively, at the highest operating frequency. From the comparison, our proposed design achieves the highest throughput with high efficiency.

Efficient Implementation of QR Decomposition for Gigabit MIMO-OFDM Systems

In very-large multiple-input multiple-output (MIMO) systems, the BS (base station) is equipped with very large number of antennas as compared to previously considered systems. There are various advantages of increasing the number of antennas, and some schemes would require handling large matrices for joint processing (pre-coding) at the base station. The dirty paper coding (DPC) is an optimal pre-coding scheme and has a very high complexity. However with increasing number of BS antennas linear pre-coding performance tends to that of the optimal DPC. Although linear pre-coding is less complex than DPC, there is a need to compute pseudo inverses of large matrices. In this paper we present a low complexity approximation of down-link Zero Forcing linear pre-coding for very-large multi-user MIMO systems. Approximation using a Neumann series expansion is opted for inversion of matrices over traditional exact computations, by making use of special properties of the matrices, thereby reducing the cost of hardware. With this approximation of linear pre-coding, we can significantly reduce the computational complexity for large enough systems, i.e., where we have enough BS antenna elements. For the investigated case of 8 users, we obtain 90% of the full ZF sum rate, with lower computational complexity, when the number of BS antennas per user is about 20 or more. (Less)

/pdf/approximative-matrix-inverse-computations-for-very-large-11jc7svqyb.pdf

Approximative Matrix Inverse Computations for Very-large MIMO and Applications to Linear Pre-coding Systems

The QR decomposition (QRD) is an important prerequisite for many different detection algorithms in multiple-input multiple-output (MIMO) wireless communication systems. This paper presents an optimized fixed-point VLSI implementation of the modified Gram-Schmidt (MGS) QRD algorithm that incorporates regularization and additional sorting of the MIMO channel matrix. Integrated in 0.18 mum CMOS technology, the proposed VLSI architecture processes up to 1.56 million complex-valued 4times4-dimensional matrices per second. The implementation results of this work are extensively compared to the Givens rotation (GR)-based QRD implementation of Luethi et al., ISCAS 2007. In order to ensure a fair comparison, both QRD circuits have been integrated in the same IC manufacturing technology, with equal functionality, and the same numeric precision. The comparison of the implementation results clearly showed superiority of the GR-based VLSI solution in terms of area, processing cycles, and throughput.

/pdf/gram-schmidt-based-qr-decomposition-for-mimo-detection-vlsi-2kjxsd1swq.pdf

Gram-Schmidt-based QR decomposition for MIMO detection: VLSI implementation and comparison

Matrix triangularization and orthogonalization are prerequisites to solving least square problems and find applications in a wide variety of communication systems and signal processing applications such as MIMO systems and matrix inversion. QR decomposition using modified Gram-Schmidt (MGS) orthogonalization is one of the numerically stable techniques used in this regard. This paper presents a fixed point implementation of QR decomposition based on MGS algorithm using a novel LUT based approach. The proposed architecture is based on log-domain arithmetic operations. The error performance of various fixed-point arithmetic operations has been discussed and optimum LUT sizes are presented based on simulation results for various fractional-precisions. The proposed architecture also paves way for an efficient parallel VLSI implementation of QR decomposition using MGS

Chitranjan Kumar Singh

Papers

VLSI Architecture for Matrix Inversion using Modified Gram-Schmidt based QR Decomposition

A Fixed-Point Implementation for QR Decomposition