SDMA spread spectrum principle
The basic theory of wavelet analysis provides a strong theoretical basis for finding a suitable family of orthogonal wavelet functions, and it is also the mathematical basis of SDMA. The wavelet function is defined as
(1)
Where w (t) is called the basic wavelet. In practical applications, usually two wavelets are used, defined as
ψmn (t) 2m / 2ψ (2mt-n) (2)
According to the nature of the wavelet function, <ψmn.ψkl> = δm, kδn, l, where δi, j = 
For any signal x (t), its discrete binary wavelet transform and inverse transform are
xmn = ∫ + ∞-∞x (t) ψmn (t) dt (3a) 
(3b)
Now consider M binary code streams sm ∈ {0, 1}, m = 1, 2, ..., M. For the orthogonal set ψmnT on L2 (R), sm can be combined into
(4)
Where n represents the nth bit of a sequence, and T is the duration of a bit. Therefore, the demodulation of the signal at the receiving end is based on (3b) wavelet transform of c (t) to extract the sequence sm. The following equation ( 4) Start to derive the power spectrum expression of c (t).
The autocorrelation function of c (t) is
Assume that the information sequence {sm (n)}, m = 1,2, ..., M is a generalized stationary process, and its autocorrelation function is defined as Rss (k) = E ï¼»s * m (n) .sm (n + k )],and so
Because c (t) is a generalized periodic stationary process, there are
(5)
The power spectral density expression of c (t) is obtained from the Fourier transform of equation (5)
(6)
among them 
And define the spectral density of the information sequence as
Substituting into equation (6) gives a further expression of Φcc (ω)
(7)
It can be seen from equation (7) that after the information sequence is encoded by wavelet transform, its spectrum is expanded, and the spreading coefficient η = 2m, m> 0. It can be seen that the spreading coefficient of each channel is different.
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