# ADC sampling rate and signal bandwidth for FHSS

If i am correct; for a radio receiver the ADC sample rate will have to be higher than at least twice the BW of the data (disregarding sparse sampling techniques). So for frequency hopping spread spectrum (FHSS),when the receiver is unaware of the transmitter's hopping pattern, does that mean the ADC sample rate needs to be higher than twice the entire hopping bandwidth?

Let's say I use amplitude shift keying, data BW is 500kbps, and the entire hopping bandwidth is 24MHz. If I use a 2Msps (4x data BW) ADC it looks like I will still recover my data; sure it under-samples some of MHz modulated frequency but it does capture entirely my data

correct? if not do I miss something?

So for frequency hopping spread spectrum (FHSS),when the receiver is unaware of the transmitter's hopping pattern, does that mean the ADC sample rate needs to be higher than twice the entire hopping bandwidth?

Yes.

If I use a 2Msps (4x data BW) ADC it looks like I will still recover my data; sure it under-samples some of MHz modulated frequency but it does capture entirely my data.

No. See above. It'll alias whatever is in the entire 24MHz band into the 1MHz that it can resolve, or you'll precede it with an anti-alias filter and lose $$\frac{23}{24}$$ of your signal.

On the bright side, if you're taking 24MHz worth of bandwidth and only using 1MHz of it, that's close to $$14\mathrm{dB}$$ of processing gain, so while you need an ADC that's 24 times faster, it can be 4 bits narrower.

• thanks. I am not formally taught in DSP, can you point me to an article/text book/website that teaches the conversions that you had done (BW, processing gain, number of bits?)?
– j c
Mar 2 '21 at 4:10
• This app note may help. It just states processing gain (they call it "process gain") as a thing without explaining it. Basically, process gain happens because you're taking wideband noise (like what comes out of a spread spectrum despreader) and running it through a bandpass filter. That filtering tends to average out the noise, which reduces it, while allowing the signal to pass unmolested -- so your SNR goes up, and that increase is your processing gain. Mar 2 '21 at 23:46

So for frequency hopping spread spectrum (FHSS),when the receiver is unaware of the transmitter's hopping pattern, does that mean the ADC sample rate needs to be higher than twice the entire hopping bandwidth?

If you have no interferers in that band, AND know the frequencies and bandwidths, just not the sequence that you use to hop to these frequencies, you can use a lower sampling rate that aliases the hops to the same frequency (or a small set of frequencies). However, that's a bit of a gamble, because it really doesn't make frequency synchronization any easier.

If I use a 2Msps (4x data BW) ADC it looks like I will still recover my data; sure it under-samples some of MHz modulated frequency but it does capture entirely my data

correct? if not do I miss something?

You're missing the fact that even if you can live with the SNR reduction due to undersampling, you still need your undersampling to produce aliases at the right frequency, so, frequency grid and sample rate need to be linked, inherently, and you're not defining the distance in frequency of the hops.

(Yes, you could technically do a complicated carrier frequency recovery for every hop, but you don't know when you hop where, so that's going to be hard to realize well, and in the times where you're still trying to guess the right frequency, you'll lose data. If you can do this offline after the fact, you might be able to live with that. Whether or not the technical complexity of that justifies not simply using a larger-bandwidth ADC to begin with – up to your system design.)

Let's say I use amplitude shift keying, data BW is 500kbps, and the entire hopping bandwidth is 24MHz

Suboptimal, but I've seen it in legacy systems. I can't think of a scenario where you'd want to do that: 24 MHz basically says "frequency selective for any scenario where you'd use FHSS in"; so some of your hops have different attenuation than others, and that's not cool for ASK, unless each of your hops has a channel sensing period of its own, or you have something differential going on with enough FEC.