Problem about gain of the phased.matchedFilter.
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mage bryan
2024-4-16
I have 2 questions about the phased.matchedFilter.
(1). when you use phased.matchedFilter as follow:
mfilter = phased.MatchedFilter();
[Y,GAIN] = mfilter(X)
I found that the output 'GAIN' is not defined as the SNR gain in the radar handbook, but the total signal power gain. When I normalized the 'Coefficients' of the phased.matchedFilter by its power, the 'GAIN' will be zero, which is demonstrated in the code below.
(2). The pulse compression gain is defined by the waveform's time-bandwidth product. However, in the simulation below, the SNR gain equals the product of sampling rate and bandwidth, which is not consistent with the radar handbook.
% parameter specification
c = 3e8;
fc = 10e9;
PRT = 50e-6;
PRF = 1/PRT;
tw = 10e-6;
bandwidth = 200e6;
fs = 500e6;
% waveform specification
wav = phased.LinearFMWaveform();
wav.SampleRate= fs;
wav.DurationSpecification= 'Pulse width';
wav.PulseWidth= tw;
wav.PRF= PRF;
wav.PRFSelectionInputPort= false;
wav.SweepBandwidth= bandwidth;
wav.SweepDirection= 'Up';
wav.SweepInterval= 'Symmetric';
wav.Envelope= 'Rectangular';
wav.FrequencyOffsetSource= 'Property';
wav.FrequencyOffset= 0;
wav.OutputFormat= 'Pulses';
wav.NumPulses= 1;
wav.PRFOutputPort= false;
wav.CoefficientsOutputPort= false;
% matched filter
mf = phased.MatchedFilter();
coe = getMatchedFilter(wav);
mf.Coefficients = coe./norm(coe);
mf.GainOutputPort = true;
% receiver
rx = phased.Receiver();
rx.Gain = 0;
rx.NoiseFigure = 3;
rx.SampleRate = fs;
% simulation
sig_in = wav();
sig_out = rx(sig_in);
[sig_mf, gain] = mf(sig_out)
sig_mf =
0.0044 + 0.0134i
0.0027 + 0.0083i
-0.0027 - 0.0083i
-0.0044 - 0.0135i
-0.0000 - 0.0001i
0.0044 + 0.0134i
0.0028 + 0.0085i
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0.0044 + 0.0133i
0.0029 + 0.0087i
-0.0026 - 0.0078i
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-0.0003 - 0.0008i
0.0043 + 0.0131i
0.0030 + 0.0091i
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0.0043 + 0.0129i
0.0032 + 0.0096i
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0.0042 + 0.0125i
0.0034 + 0.0103i
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gain = 0
% noise power
noiseSig = sig_out(15000: end);
noisePow = pow2db(mean(noiseSig.*conj(noiseSig)))
noisePow = -117.0121
% signal power before and after matched filter
sigPowBeforeMF = max(db(sig_out));
sigPowAfterMF = max(db(sig_mf));
% measured SNR gain
SNR_before = sigPowBeforeMF - noisePow
SNR_before = 117.0122
SNR_after = sigPowAfterMF - noisePow
SNR_after = 154.0018
SNR_gain_measured = SNR_after - SNR_before
SNR_gain_measured = 36.9897
% theoretical SNR gain
SNR_gain_theoretical = pow2db(bandwidth*tw)
SNR_gain_theoretical = 33.0103
SNR_gain = pow2db(fs*tw)
SNR_gain = 36.9897
figure;
plot(db(sig_out));
hold on;
plot(db(sig_mf));
hold off;
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