Two type IDs for SWIPT and only zero or one Energy Beamforming is needed

Date: 2024.04.10 11:29 Author: Joffrey LC

Multiuser MISO Beamforming for Simultaneous Wireless Information and Power Transfer. Jie Xu et.al. IEEE Transactions on Signal Processing, September 2014 (pdf) (Citations 387)

Quick Overview

Note that all the analysis is under the assumption of independently distributed user channels.

Type I: without the capability of cancelling the interference from energy signals.
Type II: with the capability of cancelling the interference from energy signals.
No dedicated energy beam is used for the case of Type I; and employing no more than one energy beam is optimal.
Establish a new form of the celebrated uplink-downlink duality for the downlink beamforming problems and thereby develop alternative algorithms to obtain the same optimal solutions as by SDR

System model

the SINR of two types:

The two types can be formulated as:

Both problems can be shown to maximize a convex quadratic function with \(\mathbf{G}\) being positive semidefinite, subject to various quadratic constrains; thus they are both non-convex QCQPs.

Check on their feasibility

code varify

clc;clear;close all;
P = 1;
M = 10;
K = 4;
los = generate_channel_simple(M, K, -pi+2*pi*rand, -pi+2*pi*rand, -pi+2*pi*rand);
nlos = sqrt(1/2)*(randn(K, M)+1j*randn(K, M));
kappa = 0;
G_all = sqrt(kappa/(1+kappa))*los+sqrt(1/(1+kappa))*nlos;

G = 0;
for k=1:1:K
    G = G + G_all(k, :)'*G_all(k, :);
end

[U, S] = eig(G);
optimal_w = U(:, 1);
optimal_w = optimal_w/norm(optimal_w)*P;


trace(optimal_w*optimal_w'*G)

close_form = S(1,1)*P


cvx_begin quiet
    variable V(M,M) hermitian semidefinite
    rece_power = 0;
    rece_power = rece_power+ real(trace(V*G));
    maximise rece_power
    subject to
    total_power = 0;
    trace(V)<= P;
cvx_end


[U2, S2] = eig(V);
re_w = U2(:, end);
re_w = re_w/norm(re_w)*P;
re_power = trace(re_w*re_w'*G)