SDMA spread spectrum principle

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

g107-1.gif (1088 bytes) (1)

Where w (t) is called the basic wavelet. In practical applications, usually two wavelets are used, defined as

ψmn (t) ts53.gif (95 bytes) 2m / 2ψ (2mt-n) (2)

According to the nature of the wavelet function, <ψmn.ψkl> = δm, kδn, l, where δi, j = g107-2.gif (387 bytes) For any signal x (t), its discrete binary wavelet transform and inverse transform are

xmn = ∫ + ∞-∞x (t) ψmn (t) dt (3a)
g107-3.gif (662 bytes) (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

g107-4.gif (824 bytes) (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

g107-5.gif (1804 bytes)

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

g107-6.gif (2206 bytes)

Because c (t) is a generalized periodic stationary process, there are

g108-1.gif (1450 bytes) (5)

The power spectral density expression of c (t) is obtained from the Fourier transform of equation (5)

g108-2.gif (1143 bytes) (6)

among them g108-3.gif (591 bytes) And define the spectral density of the information sequence as

g108-4.gif (661 bytes)

Substituting into equation (6) gives a further expression of Φcc (ω)

g108-5.gif (969 bytes) (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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