低复杂度无延迟选择性子带自适应过滤算法

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"A Low-Complexity Delayless Selective Subband Adaptive Filtering Algorithm是关于信号处理的一篇学术论文,探讨了在高计算复杂度需求的应用场景,如声学回声消除和宽频带主动噪声控制中,如何降低自适应滤波器的复杂度。文章主要介绍了无延迟的子带自适应滤波器部分更新方案,该方案旨在仅更新最不匹配的子带滤波器,以实现全带滤波器的快速收敛,同时避免子带分割引入的时间延迟。通过均方误差分析,证明了这种方法能显著提高全带滤波器的收敛速度。作者包括Christian Schüldt、Fredric Lindstrom和Ingvar Claesson,他们都是IEEE的成员。" 这篇论文关注的是自适应滤波器在高复杂度环境下的优化问题。传统的高阶自适应滤波器虽然能有效处理复杂信号,但其计算量大,对实时性要求高的应用(如声学回声消除和宽频带主动噪声控制)构成挑战。为了解决这个问题,研究者提出了子带自适应过滤方法,这是一种将全带信号分解为多个子带并分别进行处理的技术,能有效减少计算负担。 论文进一步提出了一种无延迟的子带自适应滤波器部分更新策略。该策略的核心思想是在每个时间步只更新那些与输入信号匹配度最低的子带滤波器,而不是全部更新。这种选择性的更新不仅减少了计算量,还保持了输出的无延迟特性,即避免了子带分解和重组过程中可能出现的时间延迟问题。 为了评估这个新方法的性能,论文进行了均方误差分析,结果表明,尽管只更新部分子带滤波器,但整个全带滤波器的收敛速度得到了显著提升。这意味着在保持滤波效果的同时,可以更快地调整滤波器参数以适应变化的信号环境,这对于实时性和效率要求极高的应用是非常有利的。 这篇论文为降低复杂自适应滤波器的计算负担和提高其在实际应用中的性能提供了一个创新解决方案,尤其适合于那些对时间和计算资源有限制的领域。

Algorithm 1: The online LyDROO algorithm for solving (P1). input : Parameters V , {γi, ci}Ni=1, K, training interval δT , Mt update interval δM ; output: Control actions 􏰕xt,yt􏰖Kt=1; 1 Initialize the DNN with random parameters θ1 and empty replay memory, M1 ← 2N; 2 Empty initial data queue Qi(1) = 0 and energy queue Yi(1) = 0, for i = 1,··· ,N; 3 fort=1,2,...,Kdo 4 Observe the input ξt = 􏰕ht, Qi(t), Yi(t)􏰖Ni=1 and update Mt using (8) if mod (t, δM ) = 0; 5 Generate a relaxed offloading action xˆt = Πθt 􏰅ξt􏰆 with the DNN; 6 Quantize xˆt into Mt binary actions 􏰕xti|i = 1, · · · , Mt􏰖 using the NOP method; 7 Compute G􏰅xti,ξt􏰆 by optimizing resource allocation yit in (P2) for each xti; 8 Select the best solution xt = arg max G 􏰅xti , ξt 􏰆 and execute the joint action 􏰅xt , yt 􏰆; { x ti } 9 Update the replay memory by adding (ξt,xt); 10 if mod (t, δT ) = 0 then 11 Uniformly sample a batch of data set {(ξτ , xτ ) | τ ∈ St } from the memory; 12 Train the DNN with {(ξτ , xτ ) | τ ∈ St} and update θt using the Adam algorithm; 13 end 14 t ← t + 1; 15 Update {Qi(t),Yi(t)}N based on 􏰅xt−1,yt−1􏰆 and data arrival observation 􏰙At−1􏰚N using (5) and (7). i=1 i i=1 16 end With the above actor-critic-update loop, the DNN consistently learns from the best and most recent state-action pairs, leading to a better policy πθt that gradually approximates the optimal mapping to solve (P3). We summarize the pseudo-code of LyDROO in Algorithm 1, where the major computational complexity is in line 7 that computes G􏰅xti,ξt􏰆 by solving the optimal resource allocation problems. This in fact indicates that the proposed LyDROO algorithm can be extended to solve (P1) when considering a general non-decreasing concave utility U (rit) in the objective, because the per-frame resource allocation problem to compute G􏰅xti,ξt􏰆 is a convex problem that can be efficiently solved, where the detailed analysis is omitted. In the next subsection, we propose a low-complexity algorithm to obtain G 􏰅xti, ξt􏰆. B. Low-complexity Algorithm for Optimal Resource Allocation Given the value of xt in (P2), we denote the index set of users with xti = 1 as Mt1, and the complementary user set as Mt0. For simplicity of exposition, we drop the superscript t and express the optimal resource allocation problem that computes G 􏰅xt, ξt􏰆 as following (P4) : maximize 􏰀j∈M0 􏰕ajfj/φ − Yj(t)κfj3􏰖 + 􏰀i∈M1 {airi,O − Yi(t)ei,O} (28a) τ,f,eO,rO 17 ,,actor模型和critic模型在哪

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