function [x_pre] = precode(Mt, x_mod, V, N);% [x_pre] = precode(Mt, x_mod, V, N);%% Function precodes the modulated symbols prior to sending through the IFFT module.  The precoder% left-multiplies the channel at each tone, to eliminate the right unitary matrix in the SVD% decomposition of the channel.%%   Mt - # transmit antennas%   x_mod - modulated symbols for each tone (the symbols are grouped together in tones, ie: for 3%           MIMO subchannels per tone, have 3 consecutive x_mod symbols)%   V - the matrix of right unitary matrices of the channel, in row order%   N - # subchannelsx_pre =[];for i = 1:N    x_pre = [x_pre; [V(:,(i-1)*Mt+1:i*Mt)]*transpose(x_mod((i-1)*Mt+1:i*Mt))];endx_pre = transpose(x_pre);