In OFDM system, I need to transmit a signal $x$ in SIMO channel $H$ of single Tx antenna and $4$ Rx antennas. The initial equation for that convolution is $r = Hx + n$ where $n$ is the noise.
As known, in OFDM, after serial/Parallel conversion with dimension $(Number of subcarriers, Number of symbols)$, we perform the $IFFT$ and then add Cyclic prefix. Than, P/S conversion in order to do convolution between signal and channel. In case if we are using SISO system, we perform in $MATLAB$ the command $conv(H,x)$, regardless the dimensions in length of channel and transmitted signal, but the problem I'm facing now, what's about if we are using SIMO channel? the convolution operation should be replaced by product since we have matrices, as mentioned, $r = Hx$
Below is the code, the issue is in the last line, how can I get the received signal $r$ in case if $H$ and $x$ don't have similar dimensions to do the matrices product operation?
clear all; clc; N = 128; %Number of subcarriers P = 32; % CP length Q = N + P; % subcarriers + CP AA = 1000; %number of symbole M = 15; % IR order p = 4; % # of Rx antennas sn=sign(randn(N,AA))+1i*sign(randn(N,AA)); %generate a signal () xn=ifft(sn); % FFT cp(1:P,1:AA)=xn(N-P+1:N,1:AA); % Get CP x=[cp;xn]; %Add cp into signal H = (randn(p,M+1)+1i*randn(p,M+1)); % randum channle (4x16) r = H*x; %% The received signal should be conv(H,x)