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)