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# Increasing BW of BPF at Receiver Improves False Alarm Performance?

## Increasing BW of BPF at Receiver Improves False Alarm Performance?

(OP)
I'm trying to justify my empirical finding with an intuitive and mathematical explanation.

I am receiving an LFM centered at 100kHz with fmin=95kHz, fmax=105kHz.  My receiver is a matched filter with a pre-defined threshold at the output that decides there is a detection if the threshold is exceeded.
Before the matched filter, at my receiver is a BPF centered at 100kHz with variable BW.  Initially, I thought to maximize the SNR going to the matched filter by minimizing the noise being received, so I made the BW of my BPF slightly larger than the BW of my LFM, i.e. 1.75 times the BW of my LFM or 17.5kHz.  I then started performing False Alarm tests to determine what threshold I needed to achieve a false alarm rate of 1detect/day.
I then re-ran the false alarm tests with a BW of the BPF at 50kHz.  The threshold for the 1 detect/day was substantially smaller.

My question is why?  Intuitively I can explain it as the reduction of the BW of the BPF colors the noise to within the BW of what the matched filter is detecting.
But how do I explain it in terms of Kay's probability of detection equation:
Pd = Q(Q^-1(Pfa)-sqrt(d^2))
d^2 is the deflection coefficient
d^2 = intergral of the signal power spectrum divided by the PSD of the noise, i.e. the signal to noise ratio.

Thanks,
klieberschnitzel

### RE: Increasing BW of BPF at Receiver Improves False Alarm Performance?

(OP)
My confusion is with the fact that the probability of detection is improved upon by increasing the SNR so it seems counter-intuitive that increasing the BW of the BPF improves the probability of detection since increasing the BW of the BPF increases the noise energy and hence decreases the SNR.

### RE: Increasing BW of BPF at Receiver Improves False Alarm Performance?

Is this a simulation or real-world performance?  If this is real world your wider filter might have better out-of-band rejection than your narrow filter.

John D

### RE: Increasing BW of BPF at Receiver Improves False Alarm Performance?

(OP)
That is a good point about the out of band rejection.

The filter is being generated via Labview simulation, and the output is inputted to the real system under test.  I did not create this filter and I have been suspicious of its performance.  I'm going to go with your hint and measure the performance with a spectrum analyzer.

I'll let you know. Thanks

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