Increasing BW of BPF at Receiver Improves False Alarm Performance?

[klieberschnitzel]

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

 

[klieberschnitzel]

An addendum to this is:
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.

 

[zappedagain]

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

 

[klieberschnitzel]

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