rfunction out_bits_H = receiver(in_bits_freq, channel_H, index);

%   this function is to do decoding job
%   the input date is a vblast symbel & the channel of frequency field

%   here I will first do the simulation by the paper of M<N

%   input parameter "in_bits_freq " is in_bits_freq is the frequency field symbols after
%   V_blast-OFDM
%   input parameter "channel_H " channel_H is the Channel MAtrix of
%   Frequency field 
%   input parameter "index " is the mapping parameter,such as 64QAM etc..

%----------------------------------------------------------------
%                   Channel 
%----------------------------------------------------------------

if 0
%function channel = firChannel(m_transmitter, n_receiver, n_fir);
chan_h = firChannel(m_transmitter, n_receiver, fir_len);
channel_H = gen_freq_H(chan_h, N_point_FFT);
save channel_H channel_H;

%   first load the channel of frequency field
load Channel_H;
end

%----------------------------------------------------------------
%----------------------------------------------------------------

%----------------------------------------------------------------
%                   Receiver side
%----------------------------------------------------------------
%   as the receiver side,here we use the 
% a(m) = [a_m(1) a_m(2) ... a_m(G)]
% a_tag = [a_tag_1 ......a_tag_M    1: MG

%   Y = S * H + N_f;
Y_out = in_bits_freq * Channel_H;
signal_level_Y = mean(abs(in_bits_freq).^2);
signal_level_Y_dB = 10*log10(signal_level_Y);
decoder_input_Y = awgn(Y_out,(SNR_dB + 10*log10(index)),signal_level_Y_dB);   %   step 1

%   Z = S * A * H + N_f;
% a_tag = gen_tag(m_transmitter, N_point_FFT);
A_tag = diag(gen_tag(m_transmitter, N_point_FFT));
save A_tag A_tag;
%load A_tag;

Z_out = in_bits_freq * A_tag * Channel_H;
signal_level_Z = mean(abs(in_bits_freq).^2);
signal_level_Z_dB = 10*log10(signal_level_Z);
decoder_input_Z = awgn(Z_out,(SNR_dB + 10*log10(index)),signal_level_Z_dB);

R_YY = decoder_input_Y * decoder_input_Y';
R_ZY = decoder_input_Z * decoder_input_Y';

[V,D] = eig(R_YY);  %   step 2

sigma2 = sum(mju(1,M*G+1:K));
if SNR_dB < 50
    %   Y = S .* H + N_f;
	decoder_input = awgn(channel_output,(SNR_dB + 10*log10(index)),signal_level_dB);
else
	decoder_input = channel_output;
end

Y = S .* H + N_f;

sigma_2 = (K - M * G) * sum(mju( M * G + 1 : K);