sparse.rar_excel_文件格式下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62572d8560196e4b849cbb18/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572d8560196e4b849cbb18/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Progress In Electromagnetics Research M, Vol. 77, 103–113, 2019</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls1 ws0">Two-Stage Hybrid Precoding Algorithm Based on Switch Network</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls2 ws0">for Millimeter Wave MIMO Systems</div><div class="t m0 x1 h4 y4 ff3 fs2 fc0 sc0 ls3 ws0">Fulai Liu</div><div class="t m0 x4 h5 y5 ff4 fs3 fc0 sc0 ls4 ws0">1, 2, *,</div><div class="t m0 x5 h6 y6 ff5 fs4 fc0 sc0 ls5 ws0">†</div><div class="t m0 x6 h4 y4 ff3 fs2 fc0 sc0 ls3 ws0">, Xiaodong Kan</div><div class="t m0 x7 h5 y5 ff4 fs3 fc0 sc0 ls4 ws0">1, 2,</div><div class="t m0 x8 h6 y6 ff5 fs4 fc0 sc0 ls5 ws0">†</div><div class="t m0 x9 h4 y4 ff3 fs2 fc0 sc0 ls6 ws0">, Xiaoyu Bai</div><div class="t m0 xa h5 y5 ff4 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 xb h4 y4 ff3 fs2 fc0 sc0 ls7 ws0">,RuiyanDu</div><div class="t m0 xc h5 y5 ff4 fs3 fc0 sc0 ls4 ws0">1, 2</div><div class="t m0 xd h4 y4 ff3 fs2 fc0 sc0 ls8 ws0">, and Yanshuo Zhang</div><div class="t m0 xe h5 y5 ff4 fs3 fc0 sc0 ls4 ws0">1, 2</div><div class="t m0 x1 h7 y7 ff3 fs2 fc0 sc0 ls9 ws0">Abstract—Owing to the hardware cost and power consumption limitation, hybrid precoding has been</div><div class="t m0 x1 h7 y8 ff6 fs2 fc0 sc0 lsb ws0">recently considered as an alternative to the fully digital precoding in millimeter wave (mmWave) large-</div><div class="t m0 x1 h7 y9 ff6 fs2 fc0 sc0 lsc ws0">scale multiple-input multiple-output (MIMO) systems. Although the number of radio frequency (RF)</div><div class="t m0 x1 h7 ya ff6 fs2 fc0 sc0 lsd ws0">chains is reduced to a certain extent in the hybrid precoding structure, a great number of phase shifters</div><div class="t m0 x1 h7 yb ff6 fs2 fc0 sc0 lse ws0">are still needed. In this paper, we present a new hybrid precoding architecture based on switch network</div><div class="t m0 x1 h7 yc ff6 fs2 fc0 sc0 lsf ws0">to decrease the power consumption of hybrid precoder by reducing the number of phase shifters greatly.</div><div class="t m0 x1 h7 yd ff6 fs2 fc0 sc0 lsf ws0">The new hybrid precoding architecture consists of three parts, a digital precoder, an analog precoder,</div><div class="t m0 x1 h7 ye ff6 fs2 fc0 sc0 ls10 ws0">and a switch network, in which the switch network is used to oﬀer a dynamic connection from phase</div><div class="t m0 x1 h7 yf ff6 fs2 fc0 sc0 lse ws0">shifters to antennas. Afterwards, a two-stage algorithm is proposed to determine each part of the</div><div class="t m0 x1 h7 y10 ff6 fs2 fc0 sc0 ls11 ws0">hybrid precoding implementation. Speciﬁcally, the product of the analog precoding matrix and digital</div><div class="t m0 x1 h7 y11 ff6 fs2 fc0 sc0 ls12 ws0">precoding matrix is viewed as a whole matrix ﬁrstly, thereby the original problem is simpliﬁed into</div><div class="t m0 x1 h7 y12 ff6 fs2 fc0 sc0 ls13 ws0">a two-variable problem which is relatively easy to be solved. Then, the decomposition of the analog</div><div class="t m0 x1 h7 y13 ff6 fs2 fc0 sc0 ls14 ws0">precoding matrix and digital precoding matrix is considered in the second stage. Simulation results show</div><div class="t m0 x1 h7 y14 ff6 fs2 fc0 sc0 ls15 ws0">that the presented implementation can not only provide a better trade-oﬀ between hardware complexity</div><div class="t m0 x1 h7 y15 ff6 fs2 fc0 sc0 ls16 ws0">and system performance, but also achieve higher energy eﬃciency with far fewer phase shifters than</div><div class="t m0 x1 h7 y16 ff6 fs2 fc0 sc0 ls16 ws0">previous works.</div><div class="t m0 x1 h4 y17 ff3 fs2 fc0 sc0 ls17 ws0">1. INTRODUCTION</div><div class="t m0 x1 h7 y18 ff6 fs2 fc0 sc0 ls12 ws0">Millimeter wave (mmWave) communication systems, operating in the spectrum from 30 GHz to 300 GHz,</div><div class="t m0 x1 h7 y19 ff6 fs2 fc0 sc0 lse ws0">have attracted extensive attention over the past years [1–3]. Multiple-input multiple-output (MIMO) is</div><div class="t m0 x1 h7 y1a ff6 fs2 fc0 sc0 lsb ws0">one of the promising techniques, which can exploit large-scale antenna elements at transceivers to achieve</div><div class="t m0 x1 h7 y1b ff6 fs2 fc0 sc0 lse ws0">high beamforming gains and combat huge attenuation and penetration loss at mmWave frequencies [4].</div><div class="t m0 x1 h7 y1c ff6 fs2 fc0 sc0 ls10 ws0">However, increased power consumption and hardware cost make a fully digital precoder infeasible for</div><div class="t m0 x1 h7 y1d ff6 fs2 fc0 sc0 lsd ws0">large-scale mmWave MIMO systems [5]. To overcome this shortcoming, a hybrid precoding architecture,</div><div class="t m0 x1 h7 y1e ff6 fs2 fc0 sc0 ls13 ws0">which only adopts a limited number of RF chains to connect a low-dimensional digital baseband precoder</div><div class="t m0 x1 h7 y1f ff6 fs2 fc0 sc0 ls13 ws0">and a high-dimensional analog RF precoder, has recently received much consideration [6, 7].</div><div class="t m0 xf h7 y20 ff6 fs2 fc0 sc0 lsb ws0">In general, the hybrid precoding is categorized into fully-connected and partially-connected</div><div class="t m0 x1 h7 y21 ff6 fs2 fc0 sc0 lsb ws0">structures with phase shifters (FC-PSs and PC-PSs). Recently, several hybrid precoding algorithms</div><div class="t m0 x1 h7 y22 ff6 fs2 fc0 sc0 ls18 ws0">have been presented for FC-PSs. The spatially sparse precoding algorithm in [7] reformulates the</div><div class="t m0 x1 h7 y23 ff6 fs2 fc0 sc0 lse ws0">hybrid precoding problem as a sparse reconstruction problem and solves it by the orthogonal matching</div><div class="t m0 x1 h7 y24 ff6 fs2 fc0 sc0 ls18 ws0">pursuit (OMP). Codebook-based hybrid precoding algorithm in [8] involves an iterative searching process</div><div class="t m0 x1 h7 y25 ff6 fs2 fc0 sc0 ls15 ws0">in a predeﬁned codebook to ﬁnd the optimal hybrid precoding matrix. The works in [9–12] devise</div><div class="t m0 x1 h7 y26 ff6 fs2 fc0 sc0 ls19 ws0">hybrid precoding algorithm by matrix decomposition and alternative minimization, respectively, and</div><div class="t m0 x2 h8 y27 ff7 fs3 fc0 sc0 ls1a ws0">Received 28 October 2018, Accepted 6 Decemb er 2018, Scheduled 29 Decemb er 2018</div><div class="t m0 x1 h5 y28 ff8 fs3 fc0 sc0 ls1b ws0">* Corresponding author: Fulai Liu (fulailiu@126.com).</div><div class="t m0 x1 h6 y29 ff9 fs4 fc0 sc0 ls5 ws0">1</div><div class="t m0 x2 h5 y2a ff8 fs3 fc0 sc0 ls1c ws0">Engineer Optimization & Smart Antenna Institute, Northeastern University at Qinh uangdao, Qinhuangdao, China.</div><div class="t m0 x10 h6 y29 ff9 fs4 fc0 sc0 ls5 ws0">2</div><div class="t m0 x11 h5 y2a ff8 fs3 fc0 sc0 ls1d ws0">Sc hool of</div><div class="t m0 x1 h5 y2b ff8 fs3 fc0 sc0 ls1e ws0">Computer Science and Engineering, Northeastern University, Shenyang, China.</div><div class="t m0 x12 h6 y2c ff5 fs4 fc0 sc0 ls5 ws0">†</div><div class="t m0 x13 h5 y2d ff8 fs3 fc0 sc0 ls1f ws0">Fulai Liu and Xiaodong Kan have made the same</div><div class="t m0 x1 h5 y2e ff8 fs3 fc0 sc0 ls20 ws0">cont ributions on this paper.</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572d8560196e4b849cbb18/bg2.jpg"><div class="t m0 x1 h2 y1 ffa fs0 fc0 sc0 ls21 ws0">104 Liu et al.</div><div class="t m0 x1 h7 y2f ff6 fs2 fc0 sc0 ls12 ws0">the objective of achieving spectral eﬃciency is close to that of fully digital solutions. The iterative</div><div class="t m0 x1 h7 y30 ff6 fs2 fc0 sc0 lse ws0">column maximization algorithm and iterative coordinate descent algorithm for FC-PSs are studied</div><div class="t m0 x1 h7 y31 ff6 fs2 fc0 sc0 ls15 ws0">in [13] and [14], respectively.</div><div class="t m0 xf h7 y32 ff6 fs2 fc0 sc0 ls16 ws0">The hybrid precoding scheme based on FC-PSs enjoys fully beamforming gain, since each RF chain</div><div class="t m0 x1 h7 y33 ff6 fs2 fc0 sc0 lsd ws0">is connected to all antenna elements via phase shifters. However, the number of required phase shifters</div><div class="t m0 x1 h7 y34 ff6 fs2 fc0 sc0 lsa ws0">is as large as the product of the numbers of RF chains and antenna elements, which leads to excessive</div><div class="t m0 x1 h7 y35 ff6 fs2 fc0 sc0 ls18 ws0">hardware cost and power consumption. To improve the hardware eﬃciency, the hybrid precoding scheme</div><div class="t m0 x1 h7 y36 ff6 fs2 fc0 sc0 ls23 ws0">based on PC-PSs is one possible way to signiﬁcantly reduce the number of phase shifters, in which each</div><div class="t m0 x1 h7 y37 ff6 fs2 fc0 sc0 ls23 ws0">RF chain is only connected to a subset of antennas.</div><div class="t m0 xf h7 y38 ff6 fs2 fc0 sc0 ls24 ws0">In [15, 16], a codebook-based design of hybrid precoders for PC-PSs is proposed for narrow-band</div><div class="t m0 x1 h7 y39 ff6 fs2 fc0 sc0 ls15 ws0">and orthogonal frequency division multiplexing systems, respectively. The design complexity of these</div><div class="t m0 x1 h7 y3a ff6 fs2 fc0 sc0 ls25 ws0">algorithms is low; however, the limited size of the codebook gives rise to an inevitable performance</div><div class="t m0 x1 h7 y3b ff6 fs2 fc0 sc0 ls26 ws0">loss. In [17], a semideﬁnite relaxation (SDR</div><div class="t m0 x14 h7 y3c ff6 fs2 fc0 sc0 ls19 ws0">AltMin) algorithm is introduced by utilizing the idea</div><div class="t m0 x1 h7 y3d ff6 fs2 fc0 sc0 ls27 ws0">of alternating minimization, which can provide substantial performance gains for PC-PSs. Based on</div><div class="t m0 x1 h7 y3e ff6 fs2 fc0 sc0 ls28 ws0">realistic PC-PSs with low complexity, an iterative hybrid precoding algorithm is studied in [8], where</div><div class="t m0 x1 h7 y3f ff6 fs2 fc0 sc0 ls26 ws0">successive interference cancellation is exploited to obtain the analog RF precoding matrix. In addition,</div><div class="t m0 x1 h7 y40 ff6 fs2 fc0 sc0 ls16 ws0">to improve the system performance for PC-PSs, a greedy hybrid precoding algorithm and a modiﬁed</div><div class="t m0 x1 h7 y41 ff6 fs2 fc0 sc0 lse ws0">K-means-based hybrid precoding algorithm are developed to dynamically optimize the sub-arrays in [18]</div><div class="t m0 x1 h7 y42 ff6 fs2 fc0 sc0 lse ws0">and [19], respectively.</div><div class="t m0 xf h7 y43 ff6 fs2 fc0 sc0 ls29 ws0">However, while the PC-PSs are studied substantially, there still exist an inevitable gap compared</div><div class="t m0 x1 h7 y44 ff6 fs2 fc0 sc0 ls14 ws0">with the performance of FC-PSs [17]. To achieve the tradeoﬀ among power consumption, hardware</div><div class="t m0 x1 h7 y45 ff6 fs2 fc0 sc0 ls18 ws0">complexity and spectral eﬃciency of the hybrid precoder, in this paper, we focus on a novel hardware-</div><div class="t m0 x1 h7 y46 ff6 fs2 fc0 sc0 lsd ws0">eﬃcient hybrid precoding architecture with switch network instead of phase shifters in mmWave MIMO</div><div class="t m0 x1 h7 y47 ff6 fs2 fc0 sc0 ls13 ws0">systems. The main contributions of this paper can be summarized as follows.</div><div class="t m0 x15 h9 y48 ffb fs2 fc0 sc0 ls5 ws0">• Firstly, a new hybrid architecture based on switch network is proposed in the analog processing</div><div class="t m0 xf h7 y49 ff6 fs2 fc0 sc0 ls14 ws0">stage. The objective of the proposed architecture is to further reduce power consumption of</div><div class="t m0 xf h7 y4a ff6 fs2 fc0 sc0 ls2a ws0">mmWave MIMO systems. Compared with the existing FC-PSs and PC-PSs, a dynamic switch</div><div class="t m0 xf h7 y4b ff6 fs2 fc0 sc0 ls15 ws0">network is added to connect the phase shifters and antenna elements in the proposed scheme, which</div><div class="t m0 xf h7 y4c ff6 fs2 fc0 sc0 ls14 ws0">can signiﬁcantly reduce the number of phase shifters and achieve substantial hardware eﬃciency</div><div class="t m0 xf h7 y4d ff6 fs2 fc0 sc0 ls2b ws0">gain.</div><div class="t m0 x15 h9 y4e ffb fs2 fc0 sc0 ls5 ws0">• Secondly, because it is challenging to jointly optimize the switch network matrix, digital precoding</div><div class="t m0 xf h7 y4f ff6 fs2 fc0 sc0 ls27 ws0">matrix, and RF precoding matrix, a two-stage alternating minimization algorithm is introduced</div><div class="t m0 xf h7 y50 ff6 fs2 fc0 sc0 ls19 ws0">to facilitate the solution of each part of the proposed scheme in this paper. In the ﬁrst stage, the</div><div class="t m0 xf h7 y51 ff6 fs2 fc0 sc0 lsa ws0">binary switch network matrix is derived analytically, and then, the decomposition of the digital</div><div class="t m0 xf h7 y52 ff6 fs2 fc0 sc0 ls15 ws0">precoding matrix and RF precoding matrix is considered in the second stage.</div><div class="t m0 x15 h9 y53 ffb fs2 fc0 sc0 ls5 ws0">• Finally, we evaluate the performance of the proposed hybrid precoding architecture based on switch</div><div class="t m0 xf h7 y54 ff6 fs2 fc0 sc0 ls23 ws0">network in comparison with FC-PSs and PC-PSs. Simulation results show that the proposed hybrid</div><div class="t m0 xf h7 y55 ff6 fs2 fc0 sc0 lsf ws0">precoding scheme based on switch network can yield reasonable reduction in the power consumption.</div><div class="t m0 xf h7 y56 ff6 fs2 fc0 sc0 ls26 ws0">The rest of this paper is organized as follows. Section 2 brieﬂy introduces the mmWave system</div><div class="t m0 x1 h7 y57 ff6 fs2 fc0 sc0 ls11 ws0">model and proposed hybrid precoding implementation. The proposed hybrid precoding algorithm is</div><div class="t m0 x1 h7 y58 ff6 fs2 fc0 sc0 lsd ws0">developed in detail and followed by the problem formulation in Section 3. Section 4 presents several</div><div class="t m0 x1 h7 y59 ff6 fs2 fc0 sc0 ls19 ws0">simulation results to verify the performance of the proposed algorithm. Finally, Section 5 provides a</div><div class="t m0 x1 h7 y5a ff6 fs2 fc0 sc0 ls10 ws0">concluding remark to summarize the paper.</div><div class="t m0 xf h7 y5b ff6 fs2 fc0 sc0 lse ws0">Throughout this paper, bold upper-case letters and bold lower-case letters are used for matrix and</div><div class="t m0 x1 h7 y5c ff6 fs2 fc0 sc0 lsb ws0">vector, respectively. For example, a and A stand for a column vector and a matrix, respectively. A</div><div class="t m0 x16 ha y5d ffc fs3 fc0 sc0 ls2e ws0">i,j</div><div class="t m0 x17 h7 y5e ff6 fs2 fc0 sc0 ls2f ws0">is</div><div class="t m0 x1 h7 y5f ff6 fs2 fc0 sc0 lsb ws0">the element (i, j)th of A. The transpose, conjugate transpose and Moore-Penrose pseudo-inverse of A</div><div class="t m0 x1 h7 y60 ff6 fs2 fc0 sc0 ls31 ws0">are represented by A</div><div class="t m0 x18 ha y61 ffc fs3 fc0 sc0 ls5 ws0">T</div><div class="t m0 x19 h7 y62 ff6 fs2 fc0 sc0 ls5 ws0">, A</div><div class="t m0 x1a ha y61 ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x1b h7 y62 ff6 fs2 fc0 sc0 ls2d ws0">and A</div><div class="t m0 x1c h5 y61 ffe fs3 fc0 sc0 ls5 ws0">†</div><div class="t m0 x1d h9 y62 ff6 fs2 fc0 sc0 ls5 ws0">. |A| and A</div><div class="t m0 x1e ha y63 ffc fs3 fc0 sc0 ls5 ws0">F</div><div class="t m0 x1f h7 y62 ff6 fs2 fc0 sc0 ls32 ws0">denote the determinant and Frobenius norm of A.</div><div class="t m0 x1 h9 y64 ff6 fs2 fc0 sc0 ls26 ws0">tr(A) and vec(A) indicate the trace and vectorization of A. a</div><div class="t m0 x20 h5 y65 ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x21 h7 y66 ff6 fs2 fc0 sc0 ls33 ws0">denotes the 2-norm of a. I</div><div class="t m0 x22 ha y67 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x23 h7 y66 ff6 fs2 fc0 sc0 ls34 ws0">stands for</div><div class="t m0 x1 h9 y68 ff6 fs2 fc0 sc0 ls26 ws0">the N × N identity matrix. Expectation is introduced by E [·], and the real part of a complex variable</div><div class="t m0 x1 h9 y69 ff6 fs2 fc0 sc0 ls26 ws0">is represented by {·}. CN (μ, σ</div><div class="t m0 x24 h5 y6a ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x25 h7 y6b ff6 fs2 fc0 sc0 ls23 ws0">) is the complex Gaussian distribution with mean μ and variance σ</div><div class="t m0 x17 h5 y6a ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x26 h7 y6b ff6 fs2 fc0 sc0 ls5 ws0">,</div><div class="t m0 x1 h9 y6c ff6 fs2 fc0 sc0 ls2d ws0">and U(a, b) represents the uniform distribution between a and b.</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572d8560196e4b849cbb18/bg3.jpg"><div class="t m0 x1 h2 y1 ffa fs0 fc0 sc0 ls39 ws0">Progress In Electromagnetics Research M, Vol. 77, 2019 105</div><div class="t m0 x1 h7 y6d ff3 fs2 fc0 sc0 ls3a ws0">Figure 1. A single-user mmWave MIMO system with hybrid precoder and combiner implementation.</div><div class="t m0 x1 h4 y6e ff3 fs2 fc0 sc0 ls3b ws0">2. SYSTEM MODEL</div><div class="t m0 x1 h7 y6f ff6 fs2 fc0 sc0 ls25 ws0">Consider a single-user mmWave MIMO system model as shown in Fig. 1, in which N</div><div class="t m0 x27 ha y70 ffc fs3 fc0 sc0 ls5 ws0">s</div><div class="t m0 x28 h7 y71 ff6 fs2 fc0 sc0 ls3c ws0">independent</div><div class="t m0 x1 h7 y72 ff6 fs2 fc0 sc0 ls24 ws0">data streams are sent and collected from N</div><div class="t m0 x29 ha y73 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x2a h7 y74 ff6 fs2 fc0 sc0 ls2b ws0">antenna elements at the transmitter and N</div><div class="t m0 x2b ha y75 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x2c h5 y76 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x2d h7 y74 ff6 fs2 fc0 sc0 ls17 ws0">RF chains</div><div class="t m0 x1 h7 y77 ff6 fs2 fc0 sc0 ls26 ws0">to N</div><div class="t m0 xf ha y78 ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 x2e h7 y79 ff6 fs2 fc0 sc0 lse ws0">antenna elements at the receiver and N</div><div class="t m0 x2f ha y7a ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 x30 h5 y7b ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x31 h7 y79 ff6 fs2 fc0 sc0 lsc ws0">RF chains. In this model, only a small number of RF</div><div class="t m0 x1 h7 y7c ff6 fs2 fc0 sc0 lsb ws0">chains are available, i.e., N</div><div class="t m0 x32 ha y7d ffc fs3 fc0 sc0 ls5 ws0">s</div><div class="t m0 x33 h9 y7e ffb fs2 fc0 sc0 ls5 ws0">≤ N</div><div class="t m0 x34 ha y7f ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x35 h5 y80 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x36 h9 y7e ffb fs2 fc0 sc0 ls5 ws0">≤ N</div><div class="t m0 x9 ha y7d ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x37 h7 y7e ff6 fs2 fc0 sc0 ls2d ws0">and N</div><div class="t m0 x38 ha y7d ffc fs3 fc0 sc0 ls5 ws0">s</div><div class="t m0 x39 h9 y7e ffb fs2 fc0 sc0 ls5 ws0">≤ N</div><div class="t m0 x3a ha y7f ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xa h5 y80 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x3b h9 y7e ffb fs2 fc0 sc0 ls5 ws0">≤ N</div><div class="t m0 x3c ha y7d ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 x3d h7 y7e ff6 fs2 fc0 sc0 ls33 ws0">. In the proposed implementation, it</div><div class="t m0 x1 h7 y81 ff6 fs2 fc0 sc0 ls13 ws0">can be seen that the signal from each RF chain is transmitted by N</div><div class="t m0 x3e ha y82 ffc fs3 fc0 sc0 ls5 ws0">c</div><div class="t m0 x3f h7 y83 ff6 fs2 fc0 sc0 ls10 ws0">available phase shifters, where</div><div class="t m0 x1 hb y84 ffd fs2 fc0 sc0 ls5 ws0">N</div><div class="t m0 x2 ha y85 ffc fs3 fc0 sc0 ls5 ws0">c</div><div class="t m0 x40 h9 y86 ffb fs2 fc0 sc0 ls5 ws0"> N</div><div class="t m0 x41 ha y85 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x42 h7 y86 ff6 fs2 fc0 sc0 lsf ws0">, which can improve the energy eﬃciency eﬀectively. Compared with high-resolution phase</div><div class="t m0 x1 h7 y87 ff6 fs2 fc0 sc0 lsf ws0">shifters, the switch network only has binary on-oﬀ states, thus, the implementation of an adaptive</div><div class="t m0 x1 h7 y88 ff6 fs2 fc0 sc0 lsf ws0">switch network is much easier than phase shifters [20]. The transmitted signal vector x can be given</div><div class="t m0 x1 h7 y89 ff6 fs2 fc0 sc0 ls3e ws0">by x = F</div><div class="t m0 x4 h5 y8a ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x43 h4 y8b ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x44 h5 y8a ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x45 h4 y8b ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x5 h5 y8a ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x46 h7 y8b ff3 fs2 fc0 sc0 ls5 ws0">s [21], where F</div><div class="t m0 x47 h5 y8a ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x48 h9 y8b ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x9 ha y8c ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x49 h6 y8d ff10 fs4 fc0 sc0 ls5 ws0">t</div><div class="t m0 x29 h5 y8c ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x4a h6 y8d ff10 fs4 fc0 sc0 ls5 ws0">c</div><div class="t m0 x4b h7 y8b ff6 fs2 fc0 sc0 ls5 ws0">, F</div><div class="t m0 x4c h5 y8a ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x4d h9 y8b ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x4e ha y8c ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x4f h6 y8d ff10 fs4 fc0 sc0 ls5 ws0">c</div><div class="t m0 x50 h5 y8c ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x13 h6 y8e ff10 fs4 fc0 sc0 ls5 ws0">t</div><div class="t m0 x51 h6 y8f ff9 fs4 fc0 sc0 ls40 ws0">RF</div><div class="t m0 x52 h7 y8b ff6 fs2 fc0 sc0 ls2d ws0">and F</div><div class="t m0 x53 h5 y8a ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x54 h9 y8b ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x55 ha y8c ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x56 h6 y8e ff10 fs4 fc0 sc0 ls5 ws0">t</div><div class="t m0 x57 h6 y8f ff9 fs4 fc0 sc0 ls40 ws0">RF</div><div class="t m0 x58 h5 y8c ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x59 h6 y8d ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 x2b h7 y8b ff6 fs2 fc0 sc0 ls31 ws0">stand for the</div><div class="t m0 x1 h7 y90 ff6 fs2 fc0 sc0 lsf ws0">binary switch network matrix, analog RF precoding matrix and digital baseband precoding matrix,</div><div class="t m0 x1 h9 y91 ff6 fs2 fc0 sc0 ls25 ws0">respectively. s ∈ C</div><div class="t m0 x5a ha y92 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x5b h6 y93 ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 x5c h5 y92 ffe fs3 fc0 sc0 ls5 ws0">×1</div><div class="t m0 x3 h7 y94 ff6 fs2 fc0 sc0 ls25 ws0">is the symbol vector such that E</div><div class="t m0 x5d hc y95 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x5e h4 y94 ff3 fs2 fc0 sc0 ls41 ws0">ss</div><div class="t m0 x5f ha y92 ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x60 hc y96 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x61 h7 y97 ff6 fs2 fc0 sc0 ls5 ws0">=</div><div class="t m0 x62 h5 y98 ff8 fs3 fc0 sc0 ls5 ws0">1</div><div class="t m0 x63 ha y99 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x64 h6 y9a ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 x65 h4 y94 ff3 fs2 fc0 sc0 ls5 ws0">I</div><div class="t m0 x66 ha y9b ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x67 h6 y9c ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 xc h7 y94 ff6 fs2 fc0 sc0 ls26 ws0">. Since the analog RF precoder</div><div class="t m0 x1 h7 y9d ff6 fs2 fc0 sc0 ls23 ws0">is implemented using phase shifters, which can only adjust the phases of the signals, all entries of</div><div class="t m0 x1 h4 y9e ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x68 h5 y9f ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x69 h7 ya0 ff6 fs2 fc0 sc0 ls2b ws0">are subjected to constant modulus constraint. To reﬂect that, the constraint can be given by</div><div class="t m0 x1 h9 ya1 ffb fs2 fc0 sc0 ls5 ws0">|(F</div><div class="t m0 x6a h5 ya2 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x6b h7 ya3 ff6 fs2 fc0 sc0 ls5 ws0">)</div><div class="t m0 x6c ha ya2 ffc fs3 fc0 sc0 ls2e ws0">i,j</div><div class="t m0 x41 h9 ya3 ffb fs2 fc0 sc0 ls5 ws0">| =1,i=1, 2, ···,N</div><div class="t m0 x6d ha ya2 ffc fs3 fc0 sc0 ls5 ws0">c</div><div class="t m0 x6e h9 ya3 ffd fs2 fc0 sc0 ls46 ws0">,j=1, 2, ···,N</div><div class="t m0 x4b ha ya4 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x14 h5 ya5 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x38 h7 ya3 ff6 fs2 fc0 sc0 ls16 ws0">. The normalized total transmit power constraint is</div><div class="t m0 x1 h9 ya6 ff6 fs2 fc0 sc0 ls26 ws0">given by F</div><div class="t m0 x6f h5 ya7 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x70 h4 ya8 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x71 h5 ya7 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x72 h4 ya8 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x73 h5 ya7 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x74 h9 ya8 ffb fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x75 h5 ya9 ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x75 ha yaa ffc fs3 fc0 sc0 ls5 ws0">F</div><div class="t m0 x76 h7 ya8 ff6 fs2 fc0 sc0 ls5 ws0">= N</div><div class="t m0 x33 ha ya7 ffc fs3 fc0 sc0 ls5 ws0">s</div><div class="t m0 x77 h7 ya8 ff6 fs2 fc0 sc0 lse ws0">. For simplicity, a narrow-band block-fading propagation channel model</div><div class="t m0 x1 h7 yab ff6 fs2 fc0 sc0 ls26 ws0">is considered, and the received signal after decoding processing is expressed as [21]</div><div class="t m0 x75 h7 yac ff3 fs2 fc0 sc0 ls5 ws0">y =</div><div class="t m0 x78 h9 yad ffb fs2 fc0 sc0 ls5 ws0">√</div><div class="t m0 x33 hb yae ffd fs2 fc0 sc0 ls5 ws0">ρW</div><div class="t m0 x25 ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x25 h5 yb0 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x1d h4 yae ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x79 ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x79 h5 yb0 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x7a h4 yae ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x29 ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x29 h5 yb0 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x2a h4 yae ff3 fs2 fc0 sc0 ls47 ws0">HF</div><div class="t m0 x31 h5 yb1 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x7b h4 yae ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 x7c h5 yb1 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x4d h4 yae ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xa h5 yb1 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x7d h7 yae ff3 fs2 fc0 sc0 ls5 ws0">s + W</div><div class="t m0 x7e ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x7e h5 yb0 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x7f h4 yae ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x67 ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x67 h5 yb0 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x53 h4 yae ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x80 ha yaf ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x80 h5 yb0 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x81 h7 yae ff3 fs2 fc0 sc0 ls5 ws0">n, (1)</div><div class="t m0 x1 h9 yb2 ff6 fs2 fc0 sc0 ls2c ws0">where ρ represents the average received power, and n is the vector of i.i.d. CN(0,σ</div><div class="t m0 x82 h5 yb3 ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x82 ha yb4 ffc fs3 fc0 sc0 ls5 ws0">n</div><div class="t m0 x83 h7 yb5 ff6 fs2 fc0 sc0 ls49 ws0">)noise,inwhichσ</div><div class="t m0 x84 h5 yb3 ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x84 ha yb4 ffc fs3 fc0 sc0 ls5 ws0">n</div><div class="t m0 x1 h7 yb6 ff6 fs2 fc0 sc0 ls10 ws0">stands for the noise power. H denotes the N</div><div class="t m0 x2a ha yb7 ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 x85 h9 yb6 ffb fs2 fc0 sc0 ls5 ws0">× N</div><div class="t m0 x86 ha yb7 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x87 h7 yb6 ff6 fs2 fc0 sc0 ls4a ws0">channel matrix, W</div><div class="t m0 x88 h5 yb7 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x89 h9 yb6 ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x8a ha yb8 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x8b h6 yb9 ff10 fs4 fc0 sc0 ls5 ws0">r</div><div class="t m0 x8c h5 yb8 ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x8d h6 yb9 ff10 fs4 fc0 sc0 ls5 ws0">c</div><div class="t m0 x8e h7 yb6 ff6 fs2 fc0 sc0 ls5 ws0">, W</div><div class="t m0 x8f h5 yb7 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x90 h9 yb6 ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x91 ha yb8 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x92 h6 yb9 ff10 fs4 fc0 sc0 ls5 ws0">c</div><div class="t m0 x93 h5 yb8 ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x94 h6 yba ff10 fs4 fc0 sc0 ls5 ws0">r</div><div class="t m0 x95 h6 ybb ff9 fs4 fc0 sc0 ls40 ws0">RF</div><div class="t m0 x1 h7 ybc ff6 fs2 fc0 sc0 ls2d ws0">and W</div><div class="t m0 x96 h5 ybd ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x43 h9 ybc ffb fs2 fc0 sc0 ls5 ws0">∈ C</div><div class="t m0 x45 ha ybe ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x5 h6 ybf ff10 fs4 fc0 sc0 ls5 ws0">r</div><div class="t m0 x97 h6 yc0 ff9 fs4 fc0 sc0 ls40 ws0">RF</div><div class="t m0 x73 h5 ybe ffe fs3 fc0 sc0 ls5 ws0">×N</div><div class="t m0 x98 h6 yc1 ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 x99 h7 ybc ff6 fs2 fc0 sc0 ls26 ws0">stand for the switch matrix, RF combining matrix and baseband combining</div><div class="t m0 x1 h7 yc2 ff6 fs2 fc0 sc0 ls26 ws0">matrix, respectively. The RF combiner is also subjected to the constant modulus constraint, i.e.,</div><div class="t m0 x1 h9 yc3 ffb fs2 fc0 sc0 ls5 ws0">|(W</div><div class="t m0 x9a h5 yc4 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x9b h7 yc5 ff6 fs2 fc0 sc0 ls5 ws0">)</div><div class="t m0 x9c ha yc4 ffc fs3 fc0 sc0 ls2e ws0">i,j</div><div class="t m0 x9d h9 yc5 ffb fs2 fc0 sc0 ls5 ws0">| =1,i=1, 2, ··· ,N</div><div class="t m0 x9e ha yc4 ffc fs3 fc0 sc0 ls5 ws0">c</div><div class="t m0 x9f h9 yc5 ffd fs2 fc0 sc0 ls43 ws0">,j=1, 2, ···,N</div><div class="t m0 x4b ha yc6 ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 x14 h5 yc7 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x38 h7 yc5 ff6 fs2 fc0 sc0 ls5 ws0">.</div><div class="t m0 xf h7 yc8 ff6 fs2 fc0 sc0 lsb ws0">Assume that perfect channel state information (CSI) is known at both the transmitter and</div><div class="t m0 x1 h7 yc9 ff6 fs2 fc0 sc0 lse ws0">receiver [21]. When Gaussian symbols are transmitted over the channel, and the achievable spectral</div><div class="t m0 x1 h7 yca ff6 fs2 fc0 sc0 lse ws0">eﬃciency can be given by</div><div class="t m0 x6c h7 ycb ffd fs2 fc0 sc0 ls5 ws0">R =log</div><div class="t m0 xa0 h5 ycc ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 xa1 hc ycd ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xa2 hc yce ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xa2 hc ycf ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xa2 hc yd0 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xa2 hc yd1 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xa3 h4 yd2 ff3 fs2 fc0 sc0 ls5 ws0">I</div><div class="t m0 xa4 ha yd3 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 xa5 h6 ycc ff10 fs4 fc0 sc0 ls5 ws0">s</div><div class="t m0 xa6 h7 yd4 ff6 fs2 fc0 sc0 ls5 ws0">+</div><div class="t m0 xa7 hb yd5 ffd fs2 fc0 sc0 ls5 ws0">ρ</div><div class="t m0 xa8 hb yd6 ffd fs2 fc0 sc0 ls5 ws0">σ</div><div class="t m0 xa9 h5 yd7 ff8 fs3 fc0 sc0 ls5 ws0">2</div><div class="t m0 x1a ha yd8 ffc fs3 fc0 sc0 ls5 ws0">n</div><div class="t m0 x78 hb yd6 ffd fs2 fc0 sc0 ls5 ws0">N</div><div class="t m0 xaa ha yd9 ffc fs3 fc0 sc0 ls5 ws0">s</div><div class="t m0 x77 h7 yd4 ff6 fs2 fc0 sc0 ls5 ws0">(W</div><div class="t m0 x35 h5 yd3 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 xab h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x48 h5 yd3 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 xac h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 xad h5 yd3 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x2a h7 yd4 ff6 fs2 fc0 sc0 ls5 ws0">)</div><div class="t m0 xae h5 yda ffe fs3 fc0 sc0 ls5 ws0">†</div><div class="t m0 x14 h4 yd4 ff3 fs2 fc0 sc0 ls47 ws0">HF</div><div class="t m0 x86 h5 yd3 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 xaf h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xb0 h5 yd3 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x3a h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xb1 h5 yd3 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 xb2 h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xb3 ha yda ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 xb3 h5 ydb ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 x3d h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xb4 ha yda ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 xb4 h5 ydb ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 x66 h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">F</div><div class="t m0 xb5 ha yda ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 xb5 h5 ydb ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 xb6 h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">H</div><div class="t m0 xb7 ha yda ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 xb8 h7 yd4 ff6 fs2 fc0 sc0 ls5 ws0">(W</div><div class="t m0 xb9 h5 yd3 ff8 fs3 fc0 sc0 ls5 ws0">S</div><div class="t m0 x55 h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 xba h5 yd3 ff8 fs3 fc0 sc0 ls3d ws0">RF</div><div class="t m0 xbb h4 yd4 ff3 fs2 fc0 sc0 ls5 ws0">W</div><div class="t m0 x2c h5 yd3 ff8 fs3 fc0 sc0 ls3f ws0">BB</div><div class="t m0 xbc h7 yd4 ff6 fs2 fc0 sc0 ls5 ws0">)</div><div class="t m0 x2d hc ydc ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x2d hc ydd ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x2d hc yde ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x2d hc ydf ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xbd hc ye0 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x91 h7 yd4 ffd fs2 fc0 sc0 ls5 ws0">. (2)</div><div class="t m0 xf h7 ye1 ff6 fs2 fc0 sc0 ls18 ws0">Based on the Saleh-Valenzuela model [7], the mmWave channel matrix H is assumed to be a sum</div><div class="t m0 x1 h7 ye2 ff6 fs2 fc0 sc0 ls2d ws0">of N</div><div class="t m0 x9a h5 ye3 ff8 fs3 fc0 sc0 ls4d ws0">cl</div><div class="t m0 x2e h7 ye4 ff6 fs2 fc0 sc0 lsc ws0">clusters, each of which consists of N</div><div class="t m0 xbe h5 ye5 ff8 fs3 fc0 sc0 ls4e ws0">ray</div><div class="t m0 xbf h7 ye4 ff6 fs2 fc0 sc0 ls4f ws0">rays. Let L = N</div><div class="t m0 x60 h5 ye3 ff8 fs3 fc0 sc0 ls4d ws0">cl</div><div class="t m0 xc0 hb ye4 ffd fs2 fc0 sc0 ls5 ws0">N</div><div class="t m0 xc1 h5 ye5 ff8 fs3 fc0 sc0 ls4e ws0">ray</div><div class="t m0 xc2 h7 ye4 ff6 fs2 fc0 sc0 ls31 ws0">be the total number of propagation</div><div class="t m0 x1 h7 ye6 ff6 fs2 fc0 sc0 ls18 ws0">paths, and the channel matrix H can be expressed as</div><div class="t m0 xc3 h7 ye7 ff3 fs2 fc0 sc0 ls5 ws0">H =</div><div class="t m0 x35 hc ye8 ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 x7 hb ye9 ffd fs2 fc0 sc0 ls5 ws0">N</div><div class="t m0 xc4 ha yea ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xc5 hb ye9 ffd fs2 fc0 sc0 ls5 ws0">N</div><div class="t m0 x8 ha yea ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xc4 hb yeb ffd fs2 fc0 sc0 ls5 ws0">L</div><div class="t m0 xc6 ha yec ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 xc7 h6 yed ff9 fs4 fc0 sc0 ls21 ws0">cl</div><div class="t m0 xc8 hc yee ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xc6 h5 yef ffc fs3 fc0 sc0 ls5 ws0">i=1</div><div class="t m0 x2f ha yf0 ffc fs3 fc0 sc0 ls5 ws0">N</div><div class="t m0 x14 h6 yf1 ff9 fs4 fc0 sc0 ls52 ws0">ray</div><div class="t m0 xc9 hc yee ff11 fs2 fc0 sc0 ls5 ws0"></div><div class="t m0 xae h5 yf2 ffc fs3 fc0 sc0 ls5 ws0">l=1</div><div class="t m0 x1e hb yf3 ffd fs2 fc0 sc0 ls5 ws0">α</div><div class="t m0 x39 ha yf4 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 x87 h4 yf3 ff3 fs2 fc0 sc0 ls5 ws0">a</div><div class="t m0 xca h5 yf5 ff8 fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xcb h7 yf3 ff6 fs2 fc0 sc0 ls5 ws0">(φ</div><div class="t m0 xcc ha yf6 ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xcc ha yf7 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xcd hb yf3 ffd fs2 fc0 sc0 ls45 ws0">,θ</div><div class="t m0 xb2 ha yf6 ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xce ha yf7 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xcf h7 yf3 ff6 fs2 fc0 sc0 ls5 ws0">)a</div><div class="t m0 x13 ha yf6 ffc fs3 fc0 sc0 ls5 ws0">H</div><div class="t m0 x13 h5 yf7 ff8 fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x63 h7 yf3 ff6 fs2 fc0 sc0 ls5 ws0">(φ</div><div class="t m0 xc2 ha yf6 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xc2 ha yf7 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 x66 hb yf3 ffd fs2 fc0 sc0 ls45 ws0">,θ</div><div class="t m0 xd0 ha yf6 ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xd0 ha yf7 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xb6 h7 yf3 ff6 fs2 fc0 sc0 ls5 ws0">), (3)</div><div class="t m0 x1 h7 yf8 ff6 fs2 fc0 sc0 ls2c ws0">where α</div><div class="t m0 xd1 ha yf9 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xd2 h7 yfa ff6 fs2 fc0 sc0 ls53 ws0">denotes the complex path gain of the lth ray in the ith cluster; a</div><div class="t m0 xd3 h5 yfb ff8 fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xd4 h7 yfa ff6 fs2 fc0 sc0 ls5 ws0">(φ</div><div class="t m0 xd5 ha yfc ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xd5 ha yfd ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 x8d hb yfa ffd fs2 fc0 sc0 ls45 ws0">,θ</div><div class="t m0 xd6 ha yfc ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xd6 ha yfd ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xbb h7 yfa ff6 fs2 fc0 sc0 ls54 ws0">)anda</div><div class="t m0 xd7 h5 yfb ff8 fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xd8 h7 yfa ff6 fs2 fc0 sc0 ls5 ws0">(φ</div><div class="t m0 xd9 ha yfc ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xd9 ha yfd ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 x16 hb yfa ffd fs2 fc0 sc0 ls45 ws0">,θ</div><div class="t m0 x94 ha yfc ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x94 ha yfd ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xda h7 yfa ff6 fs2 fc0 sc0 ls5 ws0">)</div><div class="t m0 x1 h7 yfe ff6 fs2 fc0 sc0 ls13 ws0">represent array response vectors of the receiver and transmitter, respectively, where φ</div><div class="t m0 xdb ha yff ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xdb ha y100 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 x59 h7 y101 ff6 fs2 fc0 sc0 ls5 ws0">, θ</div><div class="t m0 xdc ha yff ffc fs3 fc0 sc0 ls5 ws0">r</div><div class="t m0 xdc ha y100 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xdd h7 y101 ff6 fs2 fc0 sc0 ls5 ws0">, φ</div><div class="t m0 x10 ha yff ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 x10 ha y100 ffc fs3 fc0 sc0 ls2e ws0">il</div><div class="t m0 xde h7 y101 ff6 fs2 fc0 sc0 ls2d ws0">and θ</div><div class="t m0 x84 ha yff ffc fs3 fc0 sc0 ls5 ws0">t</div><div class="t m0 xdf ha y100 ffc fs3 fc0 sc0 ls2e ws0">il</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>