An Optimal Number of Indices Aided gOMP Algorithm for Multi-user Detection in NOMA System
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摘要:
作为5G的关键技术之一，非正交多址(NOMA)通过非正交方式访问无线通信资源，以实现提高频谱利用率、增加用户连接数的目的。该文提出将压缩感知(CS)及广义正交匹配追踪(gOMP)算法引入上行免调度NOMA系统，从而增强NOMA系统活跃用户检测及数据接收的性能。通过每次迭代识别多个索引，gOMP算法实际上是传统的正交匹配追踪(OMP)算法的扩展。为了获得最优性能，研究分析了在gOMP算法信号重构的每次迭代中所应选择的最优索引数目。仿真结果表明：与其它的贪婪追踪算法及梯度投影稀疏重构(GPSR)算法相比，最优索引gOMP算法具有更优异的信号重构性能；并且，对于不同的活跃用户数或过载率等参数配置的NOMA系统，均表现出最优的多用户检测性能。
Abstract:As one of the key 5G technologies, Non-Orthogonal Multiple Access (NOMA) can improve spectrum efficiency and increase the number of user connections by utilizing the resources in a non-orthogonal manner. In the uplink grant-free NOMA system, the Compressive Sensing (CS) and generalized Orthogonal Matching Pursuit (gOMP) algorithm are introduced in active user and data detection, to enhance the system performance. The gOMP algorithm is literally generalized version of the Orthogonal Matching Pursuit (OMP) algorithm, in the sense that multiple indices are identified per iteration. Meanwhile, the optimal number of indices selected per iteration in the gOMP algorithm is addressed to obtain the optimal performance. Simulations verify that the gOMP algorithm with optimal number of indices has better recovery performance, compared with the greedy pursuit algorithms and the Gradient Projection Sparse Reconstruction (GPSR) algorithm. In addition, given different system configurations in terms of the number of active users and subcarriers, the proposed gOMP with optimal number of indices also exhibits better performance than that of the other algorithms mentioned in this paper.
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表 1 最优索引gOMP检测算法
算法1 最优索引gOMP检测算法 输入 ${{y}}$, ${{H}}$, $S$, ${C_{{\rm{opt}}}}$. 初始化：${{{r}}^0} = {{y}}$,${{{\varGamma}} ^0} = \varnothing $,$t = 0$. (1) While ${\left\| {{{{r}}^t}} \right\|_2} > e$ 且$t \le S$ do (2) $t = t + 1$;
(3) $\eta {\rm{(}}i{\rm{)}} = \mathop {{\rm{argmax}}}\limits_{j:j \in \varOmega \backslash {\rm{\{ }}\eta {\rm{(}}i - 1{\rm{)}}, \cdots ,\eta {\rm{(2)}},\eta {\rm{(}}1{\rm{)\} }}} \left| { < {{{r}}^{t - 1}},{{{\varphi}} _j} > } \right|$;(4) ${{{\varGamma}} ^t} = {{{\varGamma}} ^{t - 1}} \cup {\rm{\{ }}\eta {\rm{(1),}}\eta {\rm{(2),}} ··· ,\eta {\rm{(}}{C_{{\rm{opt}}}}{\rm{)\} }}$; (5) ${\hat {{x} }_{ { {{\varGamma} } ^t} } } = \mathop { {\rm{argmin} } }\limits_{ u} {\left\| { {{y} } - { {{H} }_{ { {{\varGamma} } ^t} } }{{u} } } \right\|_2} = {{H} }_{ { {{\varGamma} } ^t} }^{\rm{† } }{{y} }$; (6) ${{{r}}^t} = {{y}} - {{{H}}_{{{{\varGamma}} ^t}}}{\hat {{x}}_{{{{\varGamma}} ^t}}}$ end while
输出 ${\hat {{x} }_{ { {{\varGamma} } ^t} } } = \mathop { {\rm{argmin} } }\limits_{ u} {\left\| { {{y} } - { {{H} }_{ { {{\varGamma} } ^t} } }{{u} } } \right\|_2}$
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