有限碼長域下針對多用戶大規(guī)模MIMO系統(tǒng)速率優(yōu)化的高效功率分配算法
doi: 10.11999/JEIT240241
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武漢大學(xué)電子信息學(xué)院 武漢 430000
基金項(xiàng)目: 國家重點(diǎn)研發(fā)計(jì)劃(2023YFE0206600)
Efficient Power Allocation Algorithm for Throughput Optimization of Multi-User Massive MIMO Systems in Finite Blocklength Regime
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Electronic Information School, Wuhan University, Wuhan 430000, China
Funds: The National Key R&D Plan (2023YFE0206600)
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摘要: 第六代(6G)移動(dòng)通信網(wǎng)絡(luò)需要為大規(guī)模節(jié)點(diǎn)提供高可靠低時(shí)延通信(URLLC)服務(wù)。為此，該文針對多用戶大規(guī)模多輸入多輸出(MIMO)技術(shù)輔助的URLLC下行通信場景，基于有限碼長( FBL)域理論表征系統(tǒng)性能，以用戶速率公平性為目標(biāo)，提出一種高效的功率分配算法。具體而言，該文首先針對傳統(tǒng)MIMO中基于全局奇異值分解(SVD)的線性預(yù)編碼方案復(fù)雜度高、不能兼顧用戶公平性等問題，設(shè)計(jì)基于局部SVD的預(yù)編碼方案，以相對較低的復(fù)雜度實(shí)現(xiàn)對MIMO用戶間干擾和用戶內(nèi)干擾的有效抑制。其次，該文以功率分配因子為優(yōu)化變量、以最大化最小用戶速率(MMR)為目標(biāo)構(gòu)建優(yōu)化問題。為解決所構(gòu)建的高維變量耦合非凸問題，該文通過引入輔助變量、分段McCormick包絡(luò)將目標(biāo)函數(shù)中香農(nóng)容量相關(guān)項(xiàng)凸松弛處理，實(shí)現(xiàn)MMR問題重構(gòu)。進(jìn)而該文提出基于連續(xù)凸近似(SCA)的優(yōu)化算法有效求解MMR問題。仿真結(jié)果驗(yàn)證了所提優(yōu)化算法的收斂性與準(zhǔn)確性，同時(shí)也表明所提優(yōu)化方案相比于現(xiàn)有方案在系統(tǒng)MMR性能和魯棒性上均具有優(yōu)勢。
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關(guān)鍵詞:
- 超可靠低時(shí)延通信(URLLC) /
- 多用戶MIMO /
- 有限碼長(FBL) /
- 連續(xù)凸近似(SCA)
Abstract:Objective The 6th Generation (6G) mobile communication network aims to provide Ultra-Reliable and Low Latency Communication (URLLC) services to a large number of nodes. To support URLLC for massive users, Multiple-In-Multiple-Out (MIMO) technology has become a key enabler for improving system performance in 6G. However, URLLC systems typically operate with Finite BlockLength (FBL) codes, which pose unique challenges for resource allocation design due to their deviation from traditional methods in the infinite blocklength regime. Although prior studies have explored resource allocation strategies for MIMO-assisted URLLC, power allocation design that considers user fairness remains unresolved. This paper proposes an efficient power allocation algorithm for multi-user MIMO systems in the FBL regime, addressing the issue of user fairness. Methods This study investigates the MIMO-assisted URLLC downlink communication scenario. The system performance is first characterized based on FBL theory, revealing the achievable rate of MIMO downlink users, which introduces significant nonconvexity compared to the infinite blocklength regime. Given the base station's limited power resources, setting system throughput as the optimization objective fails to ensure user fairness. To address this, a Maximum Minimum Rate (MMR) optimization problem is formulated, with power allocation factors as the optimization variables, subject to a total power constraint. The formulated problem is highly nonconvex due to the nonconvex terms in the objective function. To develop an efficient power allocation design for the MMR problem, a low-complexity precoding strategy is first proposed to mitigate both inter-user and intra-user interference. This precoding strategy, based on the local Singular Value Decomposition (SVD) method, reduces complexity compared with the traditional global SVD precoding strategy and effectively suppresses interference. To address the nonconvexity introduced by the Shannon capacity and channel dispersion terms in the objective function, convex relaxation and approximation techniques are introduced. The convex relaxation involves auxiliary variables and piecewise McCormick envelopes to manage the Shannon capacity term, transforming the MMR problem into an optimization problem where only the channel dispersion term remains nonconvex. For the relaxed problem, the channel dispersion term is then approximated by an upper bound function, rigorously shown to be convex through analytical findings. Based on this convex relaxation and approximation, the original MMR problem can be approximated by a convex subproblem at a given feasible point and efficiently solved using the Successive Convex Approximation (SCA) algorithm. Convergence and optimality analyses of the proposed algorithm are provided. Results and Discussions The proposed power allocation design is evaluated and validated through numerical simulations. To demonstrate the superiority of the proposed design, several benchmarks are introduced for comparison. For the proposed precoding design based on local SVD, the global SVD precoding method is included to validate its advantage in terms of complexity. The Shannon-rate-oriented rate maximization methods are also introduced to verify the accuracy of the proposed convex relaxation design. Moreover, the suboptimality of the SCA-based algorithm is validated through comparisons with other benchmarks, including the exhaustive search method. First, the low-complexity advantage of the proposed precoding design is demonstrated ( Fig. 2 ). The proposed precoding strategy exhibits low complexity in both small-scale and large-scale user scenarios. The performance of the suboptimal solutions obtained using the proposed SCA-based algorithm is compared with the globally optimal solutions from the exhaustive search method (Fig. 3 ). The results confirm the accuracy of the proposed algorithm, with a performance loss of less than 3%. The effect of the base station's antenna number on both the MMR problem and the system throughput maximization problem is illustrated (Fig. 4 ), further validating the effectiveness and applicability of the local SVD precoding strategy. The tightness of the convex relaxation is examined (Fig. 5 ), confirming that the proposed design becomes more advantageous as the user antenna number increases. The effect of blocklength on MMR performance is explored (Fig. 6 ), while the variation trend of MMR with respect to average transmit power is shown (Fig. 7). The influence of antenna number at both base station and user sides on MMR performance is investigated (Fig. 8 ), while the effect of user number on MMR performance is demonstrated (Fig. 9 ).Conclusions This paper investigates the optimization of user rate fairness in downlink MIMO-assisted URLLC scenarios. The system performance in the FBL regime is characterized, and based on this modeling, an MMR optimization problem is formulated under a sum power constraint, which is inherently nonconvex. To address this nonconvexity, a local SVD-based precoding design is proposed to reduce precoding complexity while ensuring fairness. Furthermore, convex relaxation is applied by introducing auxiliary variables and piecewise McCormick envelopes. The relaxed objective function is then approximated by an upper bound function, whose convexity is rigorously proven. Building on this relaxation and approximation, an SCA-based algorithm is developed to effectively solve the MMR problem. The proposed design is validated through numerical simulations, where its validity and parameter influence on system performance are discussed. The approach can be extended to other URLLC scenarios, such as multi-cell MIMO, and provides valuable insights for solving nonconvex optimization problems in related fields. -
1 基于連續(xù)凸近似的MMR功率分配算法
(1) 初始化功率分配因子向量${{\boldsymbol{\beta}} ^{(0)}}$，設(shè)置閾值$ \varepsilon$； (2) 初始化迭代次數(shù)$m = 0$，根據(jù)${{\boldsymbol{\beta}} ^{(0)}}$計(jì)算${\gamma _{gk}}$，得到$\gamma _{gk}^{(0)}$； (3) 根據(jù)${\boldsymbol{\beta}} _{gk}^{^{(0)}}$，$\gamma _{gk}^{(0)}$求解凸子優(yōu)化問題(SP1.3)，得到$\gamma _{gk}^{(1)}$, ${\boldsymbol{\beta}} _{gk}^{^{(1)}}$,
$R_{\min }^{(1)}\,$；(4) for $m = 2,3, \cdots $ (5) 根據(jù)${\boldsymbol{\beta}} _{gk}^{^{(m - 1)}}$，$\gamma _{gk}^{(m - 1)}$求解優(yōu)化問題(SP1.3)，得到$\gamma _{gk}^{(m)}$,
${\boldsymbol{\beta}} _{gk}^{^{(m)}}$, $R_{\min }^{(m)}\,$；(6) if $\left\| R_{\min}^{(m)} -R_{\min}^{(m-1)} \right\| \ge \varepsilon $, then 更新$m \leftarrow m + 1$再次進(jìn)
入步驟5并繼續(xù)計(jì)算；(7) else 根據(jù)${{\boldsymbol{\beta}} ^{(m)}}$計(jì)算目標(biāo)函數(shù)$ {{\boldsymbol{R}}}_{\mathrm{min}}({\boldsymbol{\beta}} ) $，得到問題
(OP1)的有效解，終止迭代并返回結(jié)果；(8) end 
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