I have a channel matrix, H, which contains the complex entries. I want to obtain the quantization of this matrix. For instance,
H=[1+2i,2-3i;5+3i,9-8i]; Q(H)?
Where Q is a quantization function. I found something on google but it is only to deal with a vector having real numbers. The code is given below.
t = [0:.1:2*pi]; % Times at which to sample the sine function
sig = sin(t); % Original signal, a sine wave
partition = [-1:.5:1]; % 2 bit quantizer
codebook = [-1.5:.5:1]; % 2 bit quantizer
[index,quants] = quantiz(sig,partition,codebook); % Quantize.
plot(t,sig,'x',t,quants,'.')
legend('Original signal','Quantized signal');
I am not sure I understand what is quantization in this context. But if you want real values out of your channel matrix and then approximate it to nearest values, I have 2 ideas.
(1) Separate the matrix into two, one for amplitude of the H (|H|) and other for phase of H (angle(H)). Since they are real values. you can quantize them to nearest value to lower the resolution of the information.
(2) Create a time-frequency plot of the each individual channel vectors (row or column depending on your assignment. You can use different methods like STFT, WT or CT, then quantize the time and frequency information separately. Finally, recombine them again.
I think either method would be fairly easy with inbuilt matlab functions.
I hope this answers your question.
Thanks, Sekhar Rajendran. Method 1 seems easy. I will try it out and will share the MATLAB code here so that it could be beneficial for others too.
Muhammad Karam Shehzad, alternatively, you could quantize the complex numbers in Cartesian form directly from H instead of converting them into Polar form. That is, quantize separately the Real and Imaginary parts of each element from H.
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