Block Diagonal Geometric Mean Decomposition Research Articles

A Hybrid Tomlinson–Harashima Transceiver Design for Multiuser mmWave MIMO Systems

This letter presents a new hybrid transceiver design for multiuser millimeter wave (mmWave) multiple-input–multiple-output downlink systems. To achieve improved sum-rate and error-rate performances, the proposed hybrid system is based on a combination of the Tomlinson–Harashima precoding and the block-diagonal geometric mean decomposition. With some novel observations and design choices, we showed that a closed-form solution can be obtained similarly for the hybrid design. Simulation shows the proposed design performs very close to its fully digital counterpart, and substantially outperforms the existing linear precoder-based hybrid transceivers.

SSLNR 기반의 ZF-THP를 위한 새로운 빔형성 기법

본 논문에서는 협력 빔형성(Coordinated Multi-Point Coordinated Beamforming : CoMP CB) 시나리오에서 인접한 사용자들 때문에 발생되는 간섭(Inter User Interference : IUI)을 제거하기 위해 사용된 Block Diagonal Geometric Mean Decomposition(BD-GMD)기반의 IUI 제거 알고리즘을 Successive Signal to Leakage plus Noise Ratio(SSLNR) 환경에서의 ZF(Zero-Forcing)에 적용하여 누출 전력을 제거한다. 또 IUI 제거 알고리즘을 사용했을 시 문제가 되는 원하는 신호 전력(Desired signal power)의 크기를 크게 보장할 수 없다는 점을 보완하기 위해 적절한 채널 열 순열(Channel ordering)을 수행하여 원하는 신호의 전력을 높인다. IUI 제거 알고리즘 사용과 적절한 채널 열 순열을 통해 기존의 SSLNR-Zero-Forcing Tomlinson Harashima precoding(ZF-THP) 기법보다 더 나은 비트오류확률(Bit Error Rate : BER)성능을 낼 수 있다. In this paper, Inter user interference elimination algorithm based on Block Diagonal Geometric Mean Decomposition(BD-GMD) for eliminating inter user interference apply to Zero-Forcing in the Successive Signal to Leakage plus Noise Ratio(SSLNR) in Coordinated Multi-Point Coordinated Beamforming system(CoMP CB). As a result, the leakage power is eliminated. The inter user interference elimination algorithm, however, cannot guarantee the enough desired signal power therefore we perform the channel ordering to overcome this disadvantage and increase the desired signal power. The simulation results show that the proposed scheme provides the improved Bit Error Rate(BER) performance compared with existing SSLNR-Zero-Forcing-Tomlinson Harashima precoding(SSLNR-ZF-THP).

Novel User Scheduling Schemes Based on Nonlinear Precoding for Multiuser MIMO Systems

This paper proposes a novel greedy user ordering algorithm for the multiuser multiple-input multiple-output (MIMO) systems employing block diagonal geometric mean decomposition method and Tomlinson-Harashima precoding (THP). Theoretical analysis and computer simulations illustrate its low computation complexity relative to the optimal user ordering achieving by brute search over all the possible ordering permutations resulting in extremely high computation complexity. Meanwhile the bit error rate (BER) performance of the proposed algorithm is very close to the optimal user ordering. Moreover, in order to mitigate the impact of users with smaller sub-channel gains to the whole systems BER performance, a joint pre-processing scheme design of adaptive data streams reduction and greedy user ordering (ADSR-GUO) is proposed. By means of choosing different values for the controlling factor, we can obtain different system sum-rate and BER performance to satisfy different quality-of-service (QoS) requirements.

Analysis of adaptive proportional fair scheduling method on BD-GMD scheme for MIMO systems

The Proportional Fair Scheduling (PFS) algorithm is always exploited in multiple input multiple output systems to make a balance between maximising the system throughput and guaranteeing the data rate fairness among different users. Besides the traditional PFS, many modified PFS algorithms have also been proposed to further improve user fairness. Among these, an adaptive PFS algorithm attracts our attention. It defines a new priority number which is multiplying traditional PFS priority number by a factor. And this very factor is the ratio of instantaneous request rate over average request rate. What is different is that while the average transmission rate in traditional PFS has a fixed definition and updating strategy, the average request rate in the adaptive method may not. In this paper, we analyse the adaptive PFS algorithm under different definition and updating strategies on block-diagonal geometric mean decomposition scheme and investigate their performance.

Block Diagonal GMD for Zero-Padded MIMO Frequency Selective Channels

In the class of systems with linear precoder and decision feedback equalizers (DFE) for zero-padded (ZP) multiple-input multiple-output (MIMO) frequency selective channels, existing optimal transceiver designs present two drawbacks. First, the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as the bandwidth (BW) efficiency increases. In this paper, we propose using block diagonal geometric mean decomposition (BD-GMD) to design the transceiver. Two new BD-GMD transceivers are proposed: the ZF-BD-GMD system, where the receiver is a zero-forcing DFE (ZF-DFE), and the MMSE-BD-GMD system, where the receiver is a minimum- mean-square-error DFE (MMSE-DFE). The BD-GMD systems introduced here have the following four properties: a) They use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation. b) For any block size, the BD-GMD systems are optimal within the family of systems using block diagonal unitary precoders and DFEs. As block size gets larger, the BD-GMD systems produce uncoded bit error rate (BER) performance similar to the optimal systems using unitary precoders and DFEs. c) For the two ZF transceivers (ZF-Optimal and ZF-BD-GMD) and the two MMSE transceivers (MMSE-Optimal and MMSE-BD-GMD), the average BER degrades as the BW efficiency increases. d) In the case of single-input single-output (SISO) channels, the BD-GMD systems have the same performance as those of the lazy precoder transceivers. These properties make the proposed BD-GMD systems more favorable designs in practical implementation than the optimal systems.

A Novel Dynamic Proportional Fair Scheduling Based on Block Diagonal Geometric Mean Decomposition

The combined Block Diagonalization and Geometric Mean Decomposition (BD-GMD) is a precoding scheme that is asymptotically optimal for downlink Multi-User Multiple-Input-Multiple-Output(MU-MIMO)systems. BD-GMD eliminate the interference between different user channels in MU-MIMO system under ideal condition, which leads to an improvement of the quality of users’ channel and brings a promotion of system throughput. In a downlink MU-MIMO system, there are a large number of users, the base station need to select a subset of users to serve for the reason that the number of simultaneously supportable users with BD-GMD is limited by the number of transmitting and receiving antennas. In the past, we paid our attention mostly on how to maximize the total throughput. However, the fairness is ignored may lead to “starvation”, which means that some subscribers are not able to get service in unacceptable long time. We introduce proportional fair scheduling schemes (PFS) into the system to guarantee the fairness, and also propose new schemes. The proposed algorithms update the adaptive parameters indicating past channel quality in each time slot. According to current and past channel information, we can make better multi-user scheduling and improve the system performance while maintaining the users’ fairness.

A User Scheduling with Minimum-Rate Requirement for Maximum Sum-Rate in MIMO-BC

This letter considers a sum-rate maximization problem with user scheduling wherein each user has a minimum-rate requirement in multiple-input-multiple-output broadcast channel. The multiuser strategy used in the user scheduling is a joint transceiver scheme with block diagonal geometric mean decomposition. Since optimum solution to the user scheduling problem generally requires exhaustive search, we propose a suboptimum user scheduling algorithm with each user's minimum-rate requirement as the main constraint. In order to satisfy maximum sum-rate and minimum-rate constraints simultaneously, we additionally consider power allocation for scheduled users. Simulation results show that the proposed user scheduling algorithm, together with the user power allocation, achieves sum-rate close to the exhaustive search, while also guarantees minimum-rate requirement of each user.

Advanced Joint Transceiver Design for Block-Diagonal Geometric-Mean-Decomposition-Based Multiuser MIMO Systems

In this paper, we propose an advanced joint transceiver design for block-diagonal geometric-mean-decomposition (BD-GMD) based multiuser multiple-input-multiple-output (MIMO) systems. First, we use the lattice reduction (LR) method to design the BD-GMD-based advanced detection and precoding for an uplink and a downlink, respectively. Then, we exploit the vector perturbation (VP) technique to further improve the system performance of the multiuser downlink. To directly reduce the high complexity of VP by a sphere encoder, we provide an LR-based sphere encoder and LR-based approximations for perturbation symbols. Performance and complexity analyses are given to show the advantages of the proposed schemes. Particularly, the diversity-gain analysis shows some insights of the existing and proposed schemes. Simulation results verify the performance improvement as well as the theoretical analysis.

Block diagonal geometric mean decomposition (BD-GMD) for MIMO broadcast channels

In recent years, the research on multiple-input multiple-output (MIMO) broadcast channels has attracted much interest, especially since the discovery of the broadcast channel capacity achievable through the use of dirty paper coding (DPC). In this paper, we propose a new matrix decomposition, called the block diagonal geometric mean decomposition (BD-GMD), and develop transceiver designs that combine DPC with BD- GMD for MIMO broadcast channels. We also extend the BD- GMD to the block diagonal uniform channel decomposition (BD- UCD) with which the MIMO broadcast channel capacity can be achieved. Our proposed schemes decompose each user's MIMO channel into parallel subchannels with identical SNRs/SINRs, thus equal-rate coding can be applied across the subchannels of each user. Numerical simulations show that the proposed schemes demonstrate superior performance over conventional schemes.