# Noise Bandwidth of multichannel system

I have a question that troubles me a little( Maybe it is quite simple to answer though). Its about the noise bandwidth of a multichannel receiver.

Let's assume we have a multichannel receiver with e.g. 4 channels. Each channel has a BW of e.g. 20 MHz and the channels are next to each other.

Quesetion 1: If I design now the system such that I first have preselection filter that selects the 80 MHz Bw of interest (with subsequent power amplifier and, image rejection filter, etc...) and subsequentially a channel selection filter that selects e.g. one of the channels with 20 MHz that I want to receive/decode/process what will be the bandwidth to calculate the thermal noise power of the system before quantization?(aka: -174dBm/Hz + 10*log10(?Hz)) Would this then be 80 MHz or 20 MHz. It should be 20 MHz right, because the system works at 20 MHz after all. I know there are other possibilities to design such a receiver(direct conversion), but that question troubles me a little.

Question 2: Also, if I would digitize the signals with an ADC firstly (with a high enough resolution and sampling frequency double the BW of all channels => 160MHz) and do the channilization in digital domain (by an e.g. FIR filter) , what would be the bandwidth here? I.e, I quantize the 80 MHz signal and then I use channelization for 20MHz. Will the noise then also be calculated with 20MHz BW?

Maybe this question is rather easy to answer, but unfortunatelly I didn't find a discussion of this problem so far. Thanks so much steve

thank you very much for your answer! I still have a question though.

It is more concerning the sensitivity of the receiver now. So if I now think of a system with an overall noise figure of e.g. 10dB and i consider one 20 MHz channel of the 80 MHz, then the noise power can be calulated by -174dBm/Hz + 73(=10*log10(20000000))dBHz + 10dB = -91dBm; So if I want to decode a modulation scheme that requires e.g. 10 dB Eb/N0 for a certain (wanted) BER i would need an input power of at least -81dBm. So far so good.

And now I am still a little bit confused. What if now I would ADC all four channels (=> 80 MHz) and do then signal processing of a 20 MHz channel in digital domain after quantization, what is the sensitivity of the system then? Input noise power of the ADC would -174dBm/Hz + 79dBHz(80MHz) + 10dB = -79dBm. So this is the noise the ADC sees. If I assume, that the ADC does not add any quantization noise would this mean that in this case I would need an input power of at least -69dBm to be able to decode the 20 MHz channel with the same BER, or does it mean that, because i use a 20MHz filter in the digital domain, the noise bandwidth is reduced again to 20MHz and the sensitivity is still -81dBm?

I hope the question is clear so far.

• Wall of text. Didn't read. Please improve the formatting. Thanks! – AaronD Oct 26 '15 at 20:12
• Thx! I edited the questions. Hope it is more readable and clear! – steve_0 Oct 26 '15 at 21:03
• Much better! I can follow it now, but I'm having a hard time visualizing what you're trying to do. A schematic would be nice, preferably from the CircuitLab button (pencil and components next to the other formatting buttons), but it could be an image of your own. Welcome to SE! – AaronD Oct 26 '15 at 21:09
• Thx for the tip! And thanks for welcoming me!! :) I'll try to add a schematic of the problem later on. The thing is that the editor doesn't seem to have building blocks like mixer, etc. This makes it not so easy to draw the picture. – steve_0 Oct 27 '15 at 9:21
• Yeah, you have to be creative sometimes. I've been surprised myself with what it doesn't have and then built what I needed out of what it does. Never tried to simulate; my purpose was purely visual. – AaronD Oct 27 '15 at 15:20