Polynomial matrix decomposition techniques for frequency selective MIMO channels

For a narrowband, instantaneous mixing multi-input, multi-output (MIMO) communications system, the channel is represented as a scalar matrix. In this scenario, singular value decomposition (SVD) provides a number of independent spatial subchannels which can be used to enhance data rates or to increase diversity. Alternatively, a QR decomposition can be used to reduce the MIMO channel equalization problem to a set of single channel equalization problems. In the case of a frequency selective MIMO system, the multipath channel is represented as a polynomial matrix. Thus conventional matrix decomposition techniques can no longer be applied. The traditional solution to this broadband problem is to reduce it to narrowband form by using a discrete Fourier transform (DFT) to split the broadband channel into N narrow uniformly spaced frequency bands and applying scalar decomposition techniques within each band. This describes an orthogonal frequency division multiplexing (OFDM) based system. However, a novel algorithm has been developed for calculating the eigenvalue decomposition of a para-Hermitian polynomial matrix, known as the sequential best rotation (SBR2) algorithm. SBR2 and its QR based derivatives allow a true polynomial singular value and QR decomposition to be formulated. The application of these algorithms within frequency selective MIMO systems results in a fundamentally new approach to exploiting spatial diversity. Polynomial matrix decomposition and OFDM based solutions are compared for a wide variety of broadband MIMO communication systems. SVD is used to create a robust, high gain communications channel for ultra low signal-to-noise ratio (SNR) environments. Due to the frequency selective nature of the channels produced by polynomial matrix decomposition, additional processing is required at the receiver resulting in two distinct equalization techniques based around turbo and Viterbi equalization. The proposed approach is found to provide identical performance to that of an existing OFDM scheme while supporting a wider range of access schemes. This work is then extended to QR decomposition based communications systems, where the proposed polynomial approach is found to not only provide superior bit-error-rate (BER) performance but significantly reduce the complexity of transmitter design. Finally both techniques are combined to create a nulti-user MIMO system that provides superior BER performance over an OFDM based scheme. Throughout the work the robustness of the proposed scheme to channel state information (CSI) error is considered, resulting in a rigorous demonstration of the capabilities of the polynomial approach

Polynomial matrix QR decomposition and iterative decoding of frequency selective MIMO channels

For a frequency flat multi-input multi-output (MIMO) system the QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we show the PMQRD can do likewise for a frequency selective MIMO system. Two types of transmitter design, based on Horizontal and Vertical Bell Laboratories Layered Space Time (H-BLAST, V-BLAST) encoding have been implemented. Receiver processing utilizes Turbo equalization to exploit multipath delay spread and to facilitate multi-stream data feedback. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for a TDMA system with frequency selective channels

A polynomial QR decomposition based turbo equalization technique for frequency selective MIMO channels.

In the case of a frequency flat multiple-input multiple-output (MIMO) system, QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel equalization problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we extend this work to frequency selective MIMO systems. A transmitter design based on Diagonal Bell Laboratories Layered Space Time (D-BLAST) encoding has been implemented. Turbo equalization is utilized at the receiver to overcome the multipath delay spread and to facilitate multi-stream data feedback. The effect of channel estimation error on system performance has also been considered to demonstrate the robustness of the proposed PMQRD scheme. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for TDMA systems with frequency selective channels

Parallel Searching-Based Sphere Detector for MIMO Downlink OFDM Systems

In this paper, implementation of a detector with parallel partial candidate-search algorithm is described. Two fully independent partial candidate search processes are simultaneously employed for two groups of transmit antennas based on QR decomposition (QRD) and QL decomposition (QLD) of a multiple-input multiple-output (MIMO) channel matrix. By using separate simultaneous candidate searching processes, the proposed implementation of QRD-QLD searching-based sphere detector provides a smaller latency and a lower computational complexity than the original QRD-M detector for similar error-rate performance in wireless communications systems employing four transmit and four receive antennas with 16-QAM or 64-QAM constellation size. It is shown that in coded MIMO orthogonal frequency division multiplexing (MIMO OFDM) systems, the detection latency and computational complexity of a receiver can be substantially reduced by using the proposed QRD-QLD detector implementation. The QRD-QLD-based sphere detector is also implemented using Field Programmable Gate Array (FPGA) and application specific integrated circuit (ASIC), and its hardware design complexity is compared with that of other sphere detectors reported in the literature.Nokia Renesas MobileTexas InstrumentsXilinxNational Science Foundatio

A Family of Hybrid Space-Time Codes for MIMO Wireless Communications

Hybrid MIMO space-time codes combine the benefits of spatial multiplexing with diversity gain to achieve both high spectral efficiency and link reliability. In this paper, we present a family of hybrid codes, known as LD STBC-VBLAST codes, along with a receiver architecture suitable for low-complexity hardware implementation. We show that, under Rayleigh fading, the performance of LD STBC-VBLAST codes is superior to other recently proposed hybrid codes. We also present a technique to derive, from a given propagation scenario, spatially correlated MIMO channel models adequate for space-time coding performance analysis. Using this technique, we evaluate the performance of LD STBC-VBLAST codes under several correlated channels.ITESO, A.C.ITSONCINVESTAV-IPNPROME

A Novel VLSI Architecture of Fixed-complexity Sphere Decoder

Fixed-complexity Sphere Decoder (FSD) is a recently proposed technique for Multiple-Input Multiple-Output (MIMO) detection. It has several outstanding features such as constant throughput and large potential parallelism, which makes it suitable for efficient VLSI implementation. However, to our best knowledge, no VLSI implementation of FSD has been reported in the literature, although some FPGA prototypes of FSD with pipeline architecture have been developed. These solutions achieve very high throughput but at very high cost of hardware resources, making them impractical in real applications. In this paper, we present a novel four-nodes-per-cycle parallel architecture of FSD, with a breadth-first processing that allows for short critical path. The implementation achieves a throughput of 213.3 Mbps at 400 MHz clock frequency, at a cost of 0.18 mm2 Silicon area on 0.13{\mu}m CMOS technology. The proposed solution is much more economical compared with the existing FPGA implementations, and very suitable for practicl applications because of its balanced performance and hardware-complexity; moreover it has the flexibility to be expanded into an eight-nodes-per-cycle version in order to double the throughput.Comment: 8 pages, this paper has been accepted by the conference DSD 201

Efficient VLSI Implementation of Soft-input Soft-output Fixed-complexity Sphere Decoder

Fixed-complexity sphere decoder (FSD) is one of the most promising techniques for the implementation of multipleinput multiple-output (MIMO) detection, with relevant advantages in terms of constant throughput and high flexibility of parallel architecture. The reported works on FSD are mainly based on software level simulations and a few details have been provided on hardware implementation. The authors present the study based on a four-nodes-per-cycle parallel FSD architecture with several examples of VLSI implementation in 4 × 4 systems with both 16-quadrature amplitude modulation (QAM) and 64-QAM modulation and both real and complex signal models. The implementation aspects and details of the architecture are analysed in order to provide a variety of performance-complexity trade-offs. The authors also provide a parallel implementation of loglikelihood- ratio (LLR) generator with optimised algorithm to enhance the proposed FSD architecture to be a soft-input softoutput (SISO) MIMO detector. To the authors best knowledge, this is the first complete VLSI implementation of an FSD based SISO MIMO detector. The implementation results show that the proposed SISO FSD architecture is highly efficient and flexible, making it very suitable for real application

QRD-QLD searching based sphere detection for emerging MIMO downlink OFDM receivers

In this paper, a detection algorithm with parallel partial candidate-search algorithm is presented. Two fully independent partial search processes are simultaneously employed for two groups of transmit antennas based on QR and QL decompositions of the channel matrix. Proposed QRDQLD detection algorithm is compared with well-known QRD-M scheme adopted for several emerging wireless standards. Latency of the QRD-QLD candidate search is about twice as small for similar error-rate performance and for identical hardware resources. Total detection latency of QRD-QLD algorithm that also includes computation of soft information for outer decoder is also substantially smaller.Nokia CorporationNational Science Foundatio

Complexity Analysis of MMSE Detector Architectures for MIMO OFDM Systems

In this paper, a field programmable gate array (FPGA) implementation of a linear minimum mean square error (LMMSE) detector is considered for MIMO-OFDM systems. Two square root free algorithms based on QR decomposition (QRD) are introduced for the implementation of LMMSE detector. Both algorithms are based on QRD via Givens rotations, namely coordinate rotation digital computer (CORDIC) and squared Givens rotation (SGR) algorithms. Linear and triangular shaped array architectures are considered to exploit the parallelism in the computations. An FPGA hardware implementation is presented and computational complexity of each implementation is evaluated and compared.ElekrobitNokiaTexas InstrumentsNational Technology Agency of FinlandTeke