基于修正牛顿法的大规模MIMO低复杂度混合预编码算法

doi:10.11959/j.issn.1000-0801.2023186

Abstract

Abstract:

A phase tracking algorithm was proposed for massivemultiple-input multiple-output(MIMO) systems based on the modified Newton (MN) method, which effectively reduced the high computational complexity in traditional high-performance hybrid precoding schemes.The algorithm optimized the analog precoding matrix from the perspective ofsub-dimensional vector recovery.In each sub-dimension optimization, the phase tracking method was used to transform the recovery of the analog precoding vectors into an unconstrained nonlinear optimization problem, which was then solved using the MN method.Concurrently, this strategy led to a marked reduction in the computational intricacy pertaining to both the computation of correction factors and the inversion of the Hessian matrix within the framework of the MN method.This was achieved through the insightful incorporation of Gerschgorin’s Disk theorem and the Hermitian matrix block-inverse lemma.Simulation results show that the proposed algorithm has higher spectral efficiency and lower computational complexity than several conventional high-performance hybrid precoding schemes.

Key words: massive MIMO, hybrid precoding, phase tracking, modified Newton method

CLC Number:

TN928

Bo HU, Anding WANG, Guiyi WEI. Low complexity hybrid precoding algorithm for massive MIMO based on modified Newton method[J]. Telecommunications Science, 2023, 39(11): 80-95.

Figures/Tables 12

操作		复数乘法和除法个数
算法1（外部迭代）	$F_{RF}^{(k)^{†}} F_{opt}$	$N_{t} (N_{t}^{RF})^{2} + N_{t} N_{t}^{RF} N_{s} + f_{inv} (N_{t}^{RF})$
算法2（内部子迭代）	$g_{i}^{(k)}$	$(N_{t}^{RF})^{2} (N_{s} + 1) + N_{t}^{RF} N_{s} + f_{\exp} (N_{t}^{RF})$
	$H_{i}^{(k)}$	$\frac{1}{2} (N_{t}^{RF})^{2}$
	$d_{i}^{(k)}$	$α (\frac{1}{6} (4 N_{t}^{RF} - 1) (N_{t}^{RF} + 1) \cdot N_{t}^{RF} + (N_{t}^{RF})^{2} \begin{array}{l} \end{array})$

算法	计算开销
MN-AltMin	$N_{iter}^{o} (N_{t} (N_{t}^{RF})^{2} + N_{t} N_{t}^{RF} N_{s} + f_{inv} (N_{t}^{RF})) +$
	$N_{iter}^{i} N_{t} (\frac{1}{6} (N_{t}^{RF})^{3} + (N_{s} + \frac{15}{8}) (N_{t}^{RF})^{2} +$
	$(N_{s} - \frac{1}{24}) N_{t}^{RF} + f_{\exp} (N_{t}^{RF}))$
CG-AltMin	$N_{iter}^{o} (N_{t} (N_{t}^{RF})^{2} + N_{t} N_{t}^{RF} N_{s} + f_{inv} (N_{t}^{RF})) +$
	$N_{iter}^{i} N_{t} (4 N_{s} N_{t} N_{t}^{RF} + 11 N_{t}^{RF})$
BB-AltMin	$N_{iter}^{o} (N_{t} (N_{t}^{RF})^{2} + N_{t} N_{t}^{RF} N_{s} + f_{inv} (N_{t}^{RF})) +$
	$N_{iter}^{i} N_{t} (2 N_{s} N_{t} N_{t}^{RF} + 8 N_{t}^{RF})$
GP-AltMin	$N_{iter}^{o} (N_{t} (N_{t}^{RF})^{2} + N_{t} N_{t}^{RF} N_{s} + f_{inv} (N_{t}^{RF})) +$
	$N_{iter}^{i} N_{t} (2 N_{s} N_{t} N_{t}^{RF} + 2 N_{t}^{RF})$

N_RF	MN-AltMin		CG-AltMin		GP-AltMin		BB-AltMin
N_RF	$T_{\max}^{i}$	$N_{iter}^{o}$	$N_{iter}^{i}$	$N_{iter}^{o}$	$N_{iter}^{i}$	$N_{iter}^{o}$	$N_{iter}^{i}$	$N_{iter}^{o}$
2	30.69	9.31	226.97	9.28	420.50	9.41	265.17	9.28
3	57.01	6.77	286.31	6.73	310.91	7.22	451.69	6.87
4	368.86	5.70	656.80	5.73	269.60	6.39	1 726.77	5.72
5	390.89	4.96	511.46	4.92	233.52	5.67	1 276.47	4.91
6	398.55	4.45	482.52	4.50	241.25	5.82	1 229.23	4.49

ε		$T_{\max}^{i}$
ε		2	4	8	16	32	64	128	512
10^-2	$N_{iter}^{i}$	8.36	11.98	15.56	18.23	20.62	21.40	22.82	23.55
	$N_{iter}^{o}$	5.18	4.09	3.74	3.69	3.67	3.63	3.68	3.67
10^-3	$N_{iter}^{i}$	17.60	24.64	31.84	37.66	40.96	45.52	47.33	46.16
	$N_{iter}^{o}$	9.81	7.77	7.28	7.006	6.74	6.85	6.80	6.84
10^-4	$N_{iter}^{i}$	47.14	63.89	81.18	93.50	104.88	108.83	130.32	125.36
	$N_{iter}^{o}$	24.57	20.17	18.86	18.39	18.03	17.70	18.78	17.36
10^-5	$N_{iter}^{i}$	131.88	170.87	227.27	243.51	289.60	326.18	326.11	319.09
	$N_{iter}^{o}$	66.85	56.60	56.34	50.69	52.35	53.64	51.96	50.23

References 26

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Low complexity hybrid precoding algorithm for massive MIMO based on modified Newton method

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