Abstract

This chapter describes transceiver design methods for simultaneous wireless power transmission (WPT) and information transmission in two typical multiuser MIMO networks, that is, the MIMO broadcasting channel (BC) and interference channel (IC) networks. The design problems are formulated to minimize the transmit power consumption at the transmitter(s) while satisfying the quality of service (QoS) requirements of both the information decoding (ID) and WPT of all users. The mean-square error (MSE) and the signal-to-interference-noise ratio (SINR) criteria are adopted to characterize the ID performance of the BC network and the IC network, respectively. The designs are cast as nonconvex optimization problems due to the coupling of multiple variables with respect to transmit precoders, ID receivers, and power splitting factors, which are difficult to solve directly. The feasibility conditions of these deign problems are discussed, and effective solving algorithms are developed through alternative optimization (AO) framework and semidefinite programming relaxation (SDR) techniques. Low-complexity algorithms are also developed to alleviate the computation burden in solving the semidefinite programming (SDP) problems. Finally, simulation results validating those proposed algorithms are included.

Keywords: wireless power transfer (WPT), energy harvesting, multiuser MIMO, transceiver design, alternating optimization, semidefinite programming relaxation (SDR)

#### 1. Introduction

Wireless power transfer (WPT) through radio frequency (RF) signals has been redeemed as one of the promising techniques to provide perpetual and costeffective power supplies for mobile devices [1–4]. Compared with traditional energy harvesting (EH) methods depending on external sources, such as solar power and wind energy, the RF WPT is able to power the wireless devices at any time. Moreover, since RF signals carry energy as well as information, wireless devices can be charged while communicating. These merits of WPT bring great convenience and provide quality of service (QoS) guarantee for wireless devices.

On the other hand, multiple-input, multiple-output (MIMO) techniques are widely used in many wireless communication systems such as WiFi and the fifth generation mobile (5G) systems, due to their potential in providing increased link capacity and spectral efficiency combined with improved link reliability. Moreover, the evolution of MIMO techniques to the massive MIMO systems, where tens or hundreds of antennas are equipped at transmitters or/and receivers, accompanied by shrinking coverage of base stations (BSs) in the future wireless systems, makes it possible to transmit wireless power with higher efficiency. It is envisaged that the power line connected to the mobile devices would be eliminated completely in future wireless communications by combing WPT with MIMO wireless information transmission (WIT) system [5–9].

determinant of matrix A. A ¼ diag a1, … , ai ð Þ , aiþ1, … , aN is a N � N diagonal matrix with the i-th diagonal elements being ai. ½ �� denotes the statistical expectation. ∥ � ∥<sup>2</sup> and ∥ � ∥<sup>F</sup> denote the two-norm and Frobenius norm, respectively.

Transceiver Design for Wireless Power Transfer for Multiuser MIMO Communication Systems

2. Joint transceiver design and power splitting optimization based on

A downlink MIMO BC channel network shown in Figure 1, where one base station (BS) serves K mobile stations (MSs) simultaneously through spatial multiplexing, is considered. The number of antennas of the BS and the kth (k∈f g 1, 2, … ,K ) user are denoted as M and Lk, respectively. Nk represents the number of data stream for the kth user, and the total number of data streams served

. It is assumed that ss<sup>H</sup> � � <sup>¼</sup> <sup>I</sup>d. The BS transmits the signal s to users, and the received baseband signal at the

where <sup>G</sup> <sup>∈</sup>C<sup>M</sup>�<sup>d</sup> denote the transmit precoding matrix, <sup>H</sup><sup>k</sup> <sup>∈</sup> <sup>C</sup>Lk�<sup>M</sup> denotes the channel propagation matrix from the BS to the <sup>k</sup>th user and <sup>n</sup><sup>k</sup> <sup>∈</sup> <sup>C</sup>Lk�<sup>1</sup> denotes the noise vector, elements of which are assumed to be independent and identically

As shown in Figure 1, each user divides the received signal into two parts through power splitters, one part is for information decoder (ID) and the other is for EH. For easy analysis, solution, and implementation, we adopt the uniform PS model [11] in this chapter, that is, the power splitters of all the antennas of a user have the same PS factor. Denote 0 ≤ρ<sup>k</sup> ≤1 as the PS factors for the kth user, the

(i.i.d.) zero mean complex Gaussian random variables with variance σ<sup>2</sup>

transmit power of the BS can be calculated as <sup>P</sup> <sup>¼</sup> <sup>∥</sup>G∥<sup>2</sup>

rID <sup>k</sup> ¼ ffiffiffiffiffi ρk

<sup>k</sup>¼<sup>1</sup>Nk <sup>≤</sup> <sup>M</sup>. Let <sup>s</sup><sup>k</sup> <sup>∈</sup> <sup>C</sup>Nk�<sup>1</sup> denote the data vector transmitted to the

r<sup>k</sup> ¼ HkGs þ nk, (1)

F.

<sup>p</sup> ð Þþ <sup>H</sup>kGs <sup>þ</sup> <sup>n</sup><sup>k</sup> <sup>w</sup>k, (2)

nk

. The total

MSE criterion for MIMO BC channel

DOI: http://dx.doi.org/10.5772/intechopen.89676

user k, the data vector transmitted by BS can be expressed as

2.1 System model

by BS is <sup>d</sup> <sup>¼</sup> <sup>P</sup><sup>K</sup>

kth receiver is

<sup>1</sup> , … , s<sup>H</sup> K � �<sup>H</sup> <sup>∈</sup>C<sup>d</sup>�<sup>1</sup>

signal received at the ID of the kth user is

<sup>s</sup> <sup>¼</sup> <sup>s</sup><sup>H</sup>

Figure 1.

123

Downlink MU-MIMO SWIPT system.

Transceiver design plays a very important role in achieving this vision. The objective of the transceiver design is to improve the energy and spectral efficiency of the transmitter by optimizing the beam patterns of the transmitting antennas and the filters at the information decoding (ID) receivers. However, it is not a trivial task to design transceivers for multiuser MIMO systems operating in simultaneous wireless information and power transfer (SWIPT) mode due to the presence of inter-user interference. The interference makes the whole design complicated since it is harmful to WIT but beneficial to WPT, and it is very challenging to balance the role of interference in ID and EH. And what makes things worse is that the interference and the PS factors are coupled together, which makes the joint transceiver design and power splitting (JTPS) problems nonconvex. These problems are NPhard in general, so effective algorithms should be found to get feasible solutions.

In this chapter, we will discuss transceiver design methods for SWIPT in two typical multi-user MIMO scenarios, that is, the broadcasting channel (BC) network and interference channel (IC) network. We focus on the QoS-constrained problems that are formulated as minimizing the transmit power consumption subject to both the minimum ID and EH requirements. The mean-square error (MSE) and the signal-to-interference-noise ratio (SINR) criteria are adopted to characterize the ID performance of the two kinds of network, respectively. The formulated optimization problems are nonconvex with respect to the optimization variables, that is, the parameters of transmit precoders, ID receivers, and PS factors. In order to develop effective solutions, the feasibility is first investigated and found to be independent with EH constraints and PS factors. Based on this, we develop an effective initializing procedure for the design problems. Then, effective iterative solving algorithms are developed based on alternative optimization (AO) framework and semidefinite programming relaxation (SDR) techniques. Specifically, we find that the original problems can be equivalently reformulated as convex semidefinite programming (SDP) with respect to the transceivers and PS ratios when the receivers are fixed. On the other hand, when the transmitters and PS factors are fixed, the original problems degenerate to the classical linear MSE minimization receiver design problem for the BC network and the SINR maximization receiver design problem for the IC network, respectively. Since the SDP problems can be solved exactly in polynomial time, feasible solutions can be obtained for the proposed algorithms effectively.

However, the SDP solving is not computationally efficient for large number of variables case [10], and the computational complexity of the SDP-based algorithms is prohibitively high for large number of antenna and user. This greatly restricts its application. To break this, low-complexity schemes should be developed. In this chapter, closed-form power splitting factors with given the transceivers designed from traditional transceiver design algorithms are developed.

Notations: C represents the complex and positive real field. Bold uppercase and lowercase letters represent matrix and column vectors, respectively. Nonbold italic letters represent scalar values. <sup>I</sup><sup>N</sup> is an <sup>N</sup> � <sup>N</sup> identity matrix. <sup>A</sup>H, <sup>A</sup><sup>T</sup> , and A�<sup>1</sup> represent the Hermitian transpose, transpose, and inverse of A, respectively. Trð Þ A and rankð Þ A are the trace and rank of matrix A, respectively. ∣A∣ denotes the

determinant of matrix A. A ¼ diag a1, … , ai ð Þ , aiþ1, … , aN is a N � N diagonal matrix with the i-th diagonal elements being ai. ½ �� denotes the statistical expectation. ∥ � ∥<sup>2</sup> and ∥ � ∥<sup>F</sup> denote the two-norm and Frobenius norm, respectively.
