# FSK Rx sensitivity with different deviations

I used an RF generator transmitting FSK packets with a datarate of 50 kbps. The deviation was 12.5 kHz. With this combination of datarate and deviation the modulation index is 0.5. I found that my device undertest had an Rx sensitivity of ~102 dBm. The IF BW is approximately 100 kHz.

I left DUT settings untouched. I changed the deviation of the signal sent by the generator from 12.5 kHz to 25 kHz. Datarate remained 50 kbps. This equals to modulation index = 1.

I found out that the sensitivity was a few dB's better. Someone told me that it is because the symbols are further apart from each other in the freq plane, and thus it is easier for the radio to demodulate it. My question is, why the wider deviation is easier for the radio?

The radio uses low IF receiver. RF is fed to an I/Q- down conversion mixer. The I/Q signals are sampled by IF ADC.

• I edited your question to indicate that the receive sensitivity is in dBm instead of dB. If that is not correct, please re-edit it. Sep 25 '17 at 7:25

Your receiver has very wide, excessive bandwidth. The amount of noise power reaching the demodulator is a function of receiver bandwidth. With a narrow band transmitted signal, the noise power dominates the demodulated signal. As your transmitted signal becomes wider in bandwidth, it occupies more of the demodulated bandwidth so the signal to noise ratio is improved.

It may be helpful to think about this in the frequency domain and dividing the received bandwidth spectrum into FFT buckets. Each bucket can be described as having a signal to noise ratio. In those buckets with no signal, the SNR is 0. In the other buckets where there is a signal, the SNR is >0. If we now average the SNR of all of the buckets, we have the SNR of the entire received bandwidth. This analogy shows that for a given receiver and received bandwidth, the more buckets that contain the signal, the better the SNR as viewed over the entire received bandwidth.

It is worth noting that your two examples transition between narrow band FM and wide band FM. When the DFSK modulation index, h, is >=1 the signal transitions from having two sidebands to a larger, potentially infinite, number of sidebands. It is also worth noting that the actual bandwidth of your DFSK signal will depend heavily on the keying shape or algorithm of your signal generator. An FM transmitter keyed directly with high dV/dt modulating signals will have a wide transmitted spectrum.

The so called Carson rule states that 98% of the signal power of an FM transmitter is contained within a bandwidth equal two times the sum of the deviation frequency and the modulation frequency, This is considered the minimum bandwidth to prevent excess distortion:

$$BW_{98\%} = 2 \times \left( \Delta F + FM \right)$$

If you would like to see an improvement in received signal sensitivity, use the minimum necessary transmit bandwidth and narrow your receiver IF bandwidth accordingly. This will minimize the noise power entering your demodulator and thus raise the SNR (Signal to Noise Ratio) of the receiver. As an example, going from a 100 kHz receive bandwidth to a 15 kHz bandwidth will improve the SNR by over 8 dB.

$$10 \times log \left( \frac{BW_A}{BW_B} \right) = \Delta SNR$$

• Thanks for the answer. But, I kept the IF bandwidth constant, just widening the deviation for the signal that is being modulated. Thus, the receiver noise is kept constant. Somehow the receiver manages to demodulate the signal with lower SNR when the deviation is wider. Sep 25 '17 at 9:05
• Yes, I understand. That was addressed in the first paragraph. Perhaps I should elaborate? Sep 25 '17 at 11:55
• I got better sensitivity with wider Tx bandwidth, and worse with narrower tx bandwidth. Seems to contradict your answer. Sep 26 '17 at 10:15
• @Mikey I added some detail to my answer that should help. Sep 26 '17 at 16:55
• Thanks for your answer Glenn. Could you also comment that for 2FSK, modulation index 0.5, and a datarate of 50 kbps, what is the minimum necessary IF bandwidth that I should even consider? With carsons rule, BW(98%) = 2 * (12.5 kHz + 50 kHz) = 150 kHz, sounds too wide.. Sep 29 '17 at 4:39