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linear precoding Design for OTFS Systems in Time/Frequency Selective Fading Channels

IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第3期14卷 816-820页

作者： Ge, Yao Meng, Lingsheng Gonzalez, G. David Wen, Miaowen Guan, Yong Liang Fan, Pingzhi Nanyang Technol Univ ContinentalNTU Corp Lab Singapore 639798 Singapore Continental AG Wireless Commun Technol Grp D-65936 Frankfurt Germany South China Univ Technol Sch Elect & Informat Engn Guangzhou 510641 Peoples R China Southwest Jiaotong Univ CSNMT Int Cooperat Res Ctr MoST Key Lab Informat Coding & Transmiss Sichuan Prov Chengdu 610031 Peoples R China

Even orthogonal time frequency space (OTFS) has been shown as a promising modulation scheme for high mobility doubly-selective fading channels, its attainability of full diversity order in either time or frequency selective fading channels has not been clarified. By performing pairwise error probability (PEP) analysis, we observe that the original OTFS system can not always guarantee full exploitation of the embedded diversity in either time or frequency selective fading channels. To address this issue and further improve system performance, this letter proposes linear precoding solutions based on algebraic number theory for OTFS systems over time and frequency selective fading channels, respectively. The proposed linear precoded OTFS systems can guarantee the maximal diversity and potential coding gains in time/frequency selective fading channels without any transmission rate loss and do not require the channel state information (CSI) at the transmitter. Simulation results are finally provided to illustrate the superiority of our proposed precoded OTFS over both the original unprecoded and the existing phase rotation OTFS systems in time/frequency selective fading channels.

关键词： Diversity gain time/frequency selective fading channels linear precoding OTFS PEP analysis Diversity gain time/frequency selective fading channels linear precoding OTFS PEP analysis

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A Low Complexity linear precoding Method for Extremely Large-Scale MIMO Systems

IEEE OPEN JOURNAL OF VEHICULAR TECHNOLOGY

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IEEE OPEN JOURNAL OF VEHICULAR TECHNOLOGY 2025年 6卷 240-255页

作者： Berra, Salah Benchabane, Abderrazak Chakraborty, Sourav Maruta, Kazuki Dinis, Rui Beko, Marko Kasdi Merbah Ouargla Univ Dept Elect & Telecommun Lab LAGE Ouargla 30000 Algeria Univ Lusofona COPELABS P-1749024 Lisbon Portugal Cooch Behar Govt Engn Coll Dept Elect & Commun Engn Cooch Behar 736170 India Tokyo Univ Sci Fac Engn Dept Elect Engn Tokyo 1628601 Japan FCT UNL Inst Telecomunicacoes P-2825515 Caparica Portugal Univ Lisbon Inst Super Tecn P-1649004 Lisbon Portugal

Massive multiple-input multiple-output (MIMO) systems are critical technologies for the next generation of networks. In this field of research, new forms of deployment are emerging, such as extremely large-scale MIMO (XL-MIMO), in which the antenna array at the base station (BS) is of extreme dimensions. As a result, spatial non-stationary features emerge as users view just a section of the antenna array, known as the visibility regions (VRs). The XL-MIMO systems can achieve higher spectral efficiency, improve cell coverage, and provide significantly higher data rates than standard MIMO systems. It is a promising technology for future sixth-generation (6G) networks. However, due to the large number of antennas, linear precoding algorithms such as Zero-Forcing (ZF) and regularized Zero-Forcing (RZF) methods suffer from unacceptable computational complexity, primarily due to the required matrix inversion. This work aims to develop low-complexity precoding techniques for the downlink XL-MIMO system. These low-complexity linear precoding methods are based on Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) techniques, which avoid calculating the complex matrix inversion and lead to stable linear precoding performance. To further enhance linear precoding performance, we incorporate the Chebyshev acceleration method with the SOR and GS methods, referred to as the Cheby-SOR and Cheby-GS methods. As these proposed methods require optimizing parameters, we create a deep unfolded network (DUN) to optimize the algorithm parameters. Our performance results demonstrate that the proposed method significantly reduces computational complexity from to O(K-2), where $K$ represents the number of users. Moreover, our approach outperforms the original algorithms, requiring only a few iterations to achieve the RZF bit error rate (BER) performance.

关键词： precoding Massive MIMO Downlink Iterative methods Computational complexity Signal processing algorithms Chebyshev approximation Interference Vehicular and wireless technologies Artificial neural networks XL-MIMO non-stationary linear precoding Chebychev acceleration low-complexity iterative method deep unfolding

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linear precoding in Cooperative MIMO Cellular Networks with Limited Coordination Clusters

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2010年第9期28卷 1446-1454页

作者： Ng, Chris T. K. Huang, Howard Alcatel Lucent Bell Labs Holmdel NJ 07733 USA

In a cooperative multiple-antenna downlink cellular network, maximization of a concave function of user rates is considered. A new linear precoding technique called soft interference nulling (SIN) is proposed, which performs at least as well as zero-forcing (ZF) beamforming. All base stations share channel state information, but each user's message is only routed to those that participate in the user's coordination cluster. SIN precoding is particularly useful when clusters of limited sizes overlap in the network, in which case traditional techniques such as dirty paper coding or ZF do not directly apply. The SIN precoder is computed by solving a sequence of convex optimization problems. SIN under partial network coordination can outperform ZF under full network coordination at moderate SNRs. Under overlapping coordination clusters, SIN precoding achieves considerably higher throughput compared to myopic ZF, especially when the clusters are large.

关键词： Cellular network convex optimization cooperation interference mitigation linear precoding multiple-antenna

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linear precoding versus linear multiuser detection in downlink TDD-CDMA systems

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2007年第3期6卷 780-786页

作者： Berenguer, Inaki Wang, Xiaodong Donaire, Manuel Reynolds, Daryl Host-Madsen, Anders Univ Cambridge Dept Engn Cambridge CB2 1PZ England Columbia Univ Dept Elect Engn New York NY 10027 USA Univ Cambridge Dept Appl Math & Theoret Phys Cambridge CB2 1PZ England W Virginia Univ Dept Comp Sci & Elect Engn Morgantown WV 26506 USA Univ Hawaii Dept Elect Engn Honolulu HI 96817 USA

In this paper, we compare two classes of linear interference suppression techniques for downlink TDD-CDMA systems, namely, linear multiuser detection methods (receiver processing) and linear precoding methods (transmitter processing). For the linear precoding schemes, we assume that the channel state information (CSI) is available only at the transmitter but not at the receiver (i.e., ultra simple receivers). We propose several precoding techniques and the corresponding power control algorithms. The performance metric used in the comparisons is the total power required at the transmitter to achieve a target SINR at the receiver. Our results reveal that in general multinser detection and precoding offer similar performance;but in certain scenarios (e.g, low BER requirements or use of random spreading sequences), precoding can bring a substantial performance improvement. These results motivate the use of precoding techniques to reduce the complexity of the system and the mobile terminals (only a matched-filter to the own spreading sequence is required without CSI). Moreover, it is shown that the proposed chip-wise linear MMSE precoding method is optimal in the sense that it requires the minimum total transmitted power to meet a certain receiver SINR performance.

关键词： downlink CDMA linear multiuser detection linear precoding power control

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linear precoding with Resource Allocation for MIMO Relay Channels

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2013年第11期12卷 5704-5716页

作者： Monroy, Edwin Choi, Sunghyun Jabbari, Bijan Seoul Natl Univ Coll Engn Int IT Policy Program Seoul South Korea Seoul Natl Univ Dept Elect & Comp Engn Seoul South Korea Seoul Natl Univ INMC Seoul South Korea George Mason Univ Dept Elect & Comp Engn Fairfax VA 22030 USA

This paper considers a half-duplex relay channel with a single source, relay, and destination, where each node has multiple antennas and the relay operates in decode-and-forward (DF) mode. The additional degrees of freedoms introduced by the MIMO channels entail increased complexity in comparison with the single antenna case. We propose a new transmission strategy for the relay channel that is able to take advantage of the MIMO gains while employing practical techniques that help reduce complexity. In the proposed scheme, the source splits its message in two parts and sends them to the destination, one part directly and the other with help from the relay. For such a transmission strategy, we formulate the problem of obtaining the rate-maximizing linear precoding matrices with time, power, and spatial stream allocation and transform the problem into a convex form. We also propose a suboptimal algorithm that provides simplifying expressions to solve the resulting problem with far less computational complexity. The numerical results show that the achievable rate of our scheme is greater than the DF rate in certain scenarios, as well as that of other practical existing strategies. In addition, the rate obtained by the suboptimal method approximates the optimal rate extremely well in all considered scenarios.

关键词： MIMO Relay linear precoding convex optimization resource allocation

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linear precoding for space-time coded systems with known fading correlations

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IEEE COMMUNICATIONS LETTERS 2002年第6期6卷 239-241页

作者： Sampath, H Paulraj, A Iospan Wireless Inc Palo Alto CA 94301 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

We design an optimal linear precoder for a space-time coded system assuming knowledge of only the transmit antenna fading correlations. Assuming a flat fading channel and a maximum-likelihood receiver, we show that the linear precoder transmits power on the eigenmodes of the transmit antenna correlation matrix. The power allocation on the eigenmodes is a form of waterpouring policy. Simulation results are presented to show performance improvement on a space-time coded system.

关键词： fading correlations linear precoding MIMO space-time coding

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linear precoding Techniques for OFDM-Based NOMA over Frequency-Selective Fading Channels

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IETE JOURNAL OF RESEARCH 2017年第4期63卷 536-551页

作者： Khan, Arsla Shin, Soo Young Kumoh Natl Inst Technol KIT Sch Elect Dept IT Convergence WENS Lab Gumi South Korea

Non-orthogonal multiple access (NOMA) is one of the potential candidates for future radio access to address the increasing demands of mobile traffic. NOMA-based systems employ orthogonal frequency division multiplexing (OFDM) for multicarrier modulation which induces peak-to-average power ratio (PAPR). High PAPR makes conventional NOMA systems spectrally and energy inefficient. Thus, in this paper, precoded NOMA system is proposed to overcome the PAPR problem in downlink NOMA. Different unitary transforms such as Walsh Hadamard transform (WHT), Zadoff chu transform (ZCT), and discrete Hartley transform are applied as linear precoding techniques to overcome the PAPR problem in NOMA. Moreover, a new precoding technique -transform is also proposed which is a hybrid combination of WHT and ZCT. Link-level performance of power domain NOMA is analysed in terms of PAPR, spectral efficiency, bit error rate, and computational complexity. Simulation results show that in the presence of linear precoding techniques, performance of classic NOMA systems improve at the cost of slight increment in complexity.

关键词： Bit error rate Computational complexity linear precoding Non-orthogonal multiple access Orthogonal frequency division multiplexing Peak-to-average power ratio Spectral efficiency Unitary transforms

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linear precoding for high-K-factor channels exploiting channel mean and covariance information

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2007年第5期56卷 2581-2589页

作者： Oteri, Oghenekome Yoon, Eunchul Paulraj, Arogyaswami Freescale Semicond Austin TX 78729 USA Samsung WiBro Syst Dev Grp Suwon South Korea Stanford Univ Dept Elect Engn Stanford CA 94305 USA

In this paper, we consider the high-K-factor Ricean channel, where the channel mean is of arbitrary-rank, and the fading channel components are correlated. We propose two suboptimal linear precoding schemes based on the knowledge of the channel mean and covariance at the transmitter. The first precoder is derived from an approximate ergodic capacity expression for the high-K-factor Ricean channels, whereas the second is derived from Jensen's inequality. We compare the capacity obtained to the true ergodic capacity found by using a numerical convex optimization algorithm. We further investigate the impact of the fading channel covariance, the rank of the channel mean, and the K-factor on the precoding schemes and the achievable ergodic capacity limit.

关键词： linear precoding multiantenna wireless communications

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linear precoding via conic optimization for fixed MIMO receivers

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第1期54卷 161-176页

作者： Wiesel, A Eldar, YC Shamai, SS Technion Israel Inst Technol IL-32000 Haifa Israel

In this paper, the problem of designing linear precoders for fixed multiple-input-multiple-output (MIMO) receivers is considered. Two different design criteria are considered. In the first, the transmitted power is minimized subject to signal-to-interference-plus-noise-ratio (SINR) constraints. In the second, the worst case SINR is maximized subject to a power constraint. It is shown that both problems can be solved using standard conic optimization packages. In addition, conditions are developed for the optimal precoder for both of these problems, and two simple fixed-point iterations are proposed to find the solutions that satisfy these conditions. The relation to the well-known uplink-downlink duality in the context of joint transmit beamforming and power control is also explored. The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders.

关键词： linear precoding multiple-input-multiple-output (MIMO) systems optimization methods

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linear precoding based on polynomial expansion: reducing complexity in massive MIMO

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2016年第1期2016卷 63页

作者： Mueller, Axel Kammoun, Abla Bjornson, Emil Debbah, Merouane Huawei Technol Co Ltd France Res Ctr Math & Algorithm Sci Lab Arcs Seine Batiment A20 Quai Point Jour F-92100 Boulogne France SUPELEC Alcatel Lucent Flexible Radio 3 Rue Joliot Curie F-91190 Gif Sur Yvette France King Abdullah Univ Sci & Technol Thuwal 239556900 Makkah Province Saudi Arabia Linkoping Univ Dept Elect Engn SE-58183 Linkoping Sweden

Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

关键词： Massive MIMO linear precoding Multiuser systems Polynomial expansion Random matrix theory

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