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Low Complexity Non-Linear Precoding Schemes for the Multi-Stream Multi-User MIMO systems

Low Complexity Non-Linear Precoding Schemes for the Multi-Stream Multi-User MIMO systems

초록/요약

Multi-Stream Multi-User Multiple Input Multiple Output (MS-MU-MIMO) systems are an emerging topic in wireless communications. They can achieve very high data-rate by spatially multiplexing independent data-streams to geographically dispersed users. They improve the spectral efficiency of the MIMO broadcast channel significantly however performance of MU-MIMO is limited by presence of high amount of interference in addition to the presence of noise. This problem is solved efficiently by employing precoding schemes or beamforming techniques at the Base Station (BS). Precoding scheme utilize Channel State Information (CSI) at the BS to pre-process the signal to take most advantage of Spatial Division Multiple Access (SDMA) and mitigate interference in the system. Precoding algorithms perform the most complex processing at the BS which leads to simple low complexity mobile receiver design. Precoding techniques can be classified into linear and non-linear precoding algorithms. Linear precoding algorithms are simple and non-iterative in structure. However they offer suboptimal performance and fail to achieve high throughput gain for MS-MU-MIMO systems. Block Diagonalization (BD), Successive Minimum Mean Square Error (SMMSE),Per-User Successive Minimum Mean Square Error (PU-SMMSE),Signal-to-Jamming-plus-Noise-Ratio (SJNR) algorithms are some classic linear precoding schemes. On the other hand, non-linear precoding algorithms are iterative in nature and provide high throughput gains. They give near-optimal performance. However, they have very high computation complexity which limits their applicability. Non Linear precoding schemes involve Vector Perturbation (VP), Dirty Paper Coding (DPC) and Tomlinson-Harashima Precoding (THP) scheme. Recent research have shown that the throughput and performance of MU-MIMO system can be improved significantly by combining linear precoding techniques with THP algorithm. By using such combination, a part of interference is pre-equalized at transmitter by THP precoding scheme and other part is mitigated by linear precoding function. Hence they combine the benefits of both schemes and improve system performance significantly. SO-THP and SMMSE-THP are efficient examples of such combination, they provide capacity achieving performance. However precoding algorithms of such structure have very high computational complexity which makes it impossible to use them for practical implementation In this dissertation we solve the problem of low-complexity efficient non-linear precoding algorithms. We propose two cost-efficient THP based precoding algorithms which give near-optimal performance for MS-MU-MIMO systems. We also perform computational analysis for each precoding scheme to show its computational efficiency The first proposed scheme combines THP precoding with Per-User Successive MMSE (PU-SMMSE) precoding scheme. PU-SMMSE is sub-optimal linear precoding technique based on MMSE optimization criterion. PU-SMMSE is a simplification of successive MMSE (SMMSE) precoding scheme. PU-SMMSE reduces computation effort of SMMSE without any performance degradation. It evaluates precoding matrices on a per-user basis instead of per-receiver antenna basis. In this work we have further reduced complexity of PU-SMMSE algorithm by introducing matrix inversion updates to calculate per-user channel inverses. We have introduced an iterative approach to calculate the mmse nulling matrix for each user, which significantly reduces the computational effort of original PU-SMMSE algorithm. Then this low-complexity proposed PU-SMMSE is combined with THP to propose an efficient non-linear precoding scheme. Proposed scheme PU-SMMSE-THP combines the array and diversity gain of both precoding schemes. Simulation results show that it gives near-optimal performance and reaches sum-rate bound of MIMO broadcast channels at low SNRs The second proposed scheme combines an improved Signal-to-Jamming-and-Noise Ratio (SJNR) precoding scheme with THP. SJNR precoding scheme takes both MUI and noise into account and uses a leakage based criterion which maximizes signal to jamming and noise ratio for all users [4]. Jamming or leakage refers to the impact of interference caused by one user on other users. This approach leads to de-coupled per-user optimization problem and leads to a closed form solution. In this work we have modified this SJNR criterion by extending jamming term to power of interference posed by one user on the whole MU-MIMO channel to get Signal-to-Whole-Jamming-and-Noise Ratio (SWJNR) precoding scheme. The main advantage of proposed algorithm comes in the form of complexity reduction. Original SJNR algorithm rigorously calculates channel inverse for each user separately. Proposed SWJNR algorithm calculates the inverse of whole regularized MU-MIMO channel only once. Hence it reduces computation effort of SJNR algorithm significantly. The advantage of using this criterion is that the resulting effective channel matrix in both precoding schemes is diagonal, hence there is no major performance gain or loss. Complexity analysis shows that the proposed algorithm has lower computation cost than other linear precoding algorithms and it outperforms other linear precoding techniques for all SNR ranges. This linear precoding algorithm is extended to non-linear precoding by combining it with THP algorithm. A SJNR based ordering criterion is introduced to re-order users in order to maximize sum rate for each user. Proposed scheme SWJNR-THP combines benefits of both precoding schemes. It gives near-optimal performance for all SNR ranges and does not impose any restriction on the number of antennas at the transmitter or receiver terminal. Quantitative computation analysis shows that SJNR-THP has lowest complexity than other non-linear precoding techniques of similar structure. These benefits make it highly efficient for practical applications.

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목차

Chapter 1. Introduction. 1
1.1 Background and Motivation 1
1.2 Thesis Contributions. 4
1.3 Thesis Organization 6
Chapter 2. Multi-User MIMO. 7
2.1 MU-MIMO 7
2.2 System Model 10
2.3 Capacity of MU-MIMO downlink Channel 14
2.4 Computational Complexity Analysis. 16
Chapter 3. Conventional MU-MIMO Precoding Algorithms 18
3.1 Block Diagonalization (BD). 20
3.1.1 Computational Complexity Analysis for BD 23
3.2 Successive Minimum Mean Square Error (SMMSE) . 24
3.2.1 Computational Complexity Analysis for SMMSE 28
3.3 Per User Successive MMSE (PU-SMMSE) 29
3.3.1 Computational Complexity Analysis for PUSMMSE 32
3.4 Signal to Jamming plus Noise Ratio (SJNR) 33
3.4.1 Computational Complexity Analysis for SJNR. 35
3.5 Tomlinson Harashima Precoding (THP) scheme 36
3.5.1 Computational Complexity Analysis for THP 38
3.6 Successive Optimization THP (SO THP) 39
3.6.1 Computational Complexity Analysis for SOTHP. 42
3.7 Successive MMSE THP (SMMSE THP) 44
3.7.1 Computational Complexity Analysis for SMMSE 48
Chapter 4. PUSMMSE-THP Precoding Technique 49
4.1 Simplified PUSMMSE Precoding Scheme 50
4.2 PU-SMMSE-THP Precoding Scheme. 57
4.3 Computational Complexity for PUSMMSE-THP 59
Chapter 5. SWJNR-THP Precoding Technique 62
5.1 SWJNR Precoding Scheme. 62
5.2 Performance Analysis of SWJNR scheme 67
5.3 SWJNR-THP Precoding Scheme. 71
5.4 Computational Complexity for SWJNR-THP. 73
Chapter 6. Simulation Results. 75
Chapter 7. Conclusion. 88
Reference 90

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