Investigation of the method of suppression of random noise by coherent signal accumulation
Purpose - to identify opportunities for the coherent accumulation for cases of stationary and quasi-stationary signal. Suppose that the input is the mixture of observed signal and a random white noise (i.e. noise with uniform spectral density). The signal is stationary and is described from sample to sample by constant function (for example, a sinusoidal signal with a constant frequency and constant initial phase). In this case, the input noise in it amplitude is several times greater than the amplitude of the signal. By coherent accumulation of the input mix for a number of samples it possible to increase the signal/noise ratio.
- According to the results of modeling build a relationship: a) The signal/noise ratio in the output mix with respect to duration of accumulation, ie accumulated number of samples at a constant signal/noise ratio at the input , ( the number of samples of accumulation varies ) b) the signal/noise ratio at the output with respect to signal/noise ratio at the input for a fixed number of samples (M = 10, 25 , 50 ) (SNR at the input vary)
- Repeat item "1" for the case of quasi-stationary signals. As a useful signal you should set a rectangular pulse of constant duration, which offset from the origin varies from sample to sample by a linear law.
- To develop a functional diagram of a device that filters the signal by accumulation.
Type of signal: The sum of two harmonic signals; S/N ratio: 0.2; The number of cycles of accumulation: up to 500; Limits of change in the signal / noise ratio: 0.1-2.
THEORY The method of accumulation is applicable if the useful signal during the reception time constant or a periodic function. The method is consist of many times repeated signal and summation of its individual realizations in the receiver. Let the transmission of the desired signal implemented in two levels.
In the interval Tx signal is constant. In the observation interval Tx sample values of the received signal are accumulated.
y1=x+r1 y2=x+r2 ............... yn=x+rn
and these values are summed.
We introduce two assumptions: 1) counts of interference ri are independent of each other; 2) The obstacle is stationary (its characteristics do not depend on time) and lets find (Px/Pr)out on the output of the accumulator, ie