CC2500 Noise Figure

 Estimate the NF of an RX system by using BER

By measuring a system BER performance for a given bit rate and knowing the RX filter bandwidth it is possible to solve for system noise figure. First we need to know calculate the back ground noise level over a given bandwidth. This determines the lower limit for sensitivity; the level is given by the thermal noise of a 50Ohm resistor at room temperature.

                                                            kTB = -173.8dBm/Hz 

Therefore if you are using a system operating at 250Kb/s using an RX bandwidth of 540KHz, the noise floor is calculated like below.

                                    Noisefloor = kTB*540000Hz = -116.5dBm 

Please note that the reason that you need a higher RX band with than the bit rate indicates is that you need to allow for fact that FSK and even GFSK modulation occupies more bandwidth that 1Hz for every bit/s transmitted. Furthermore we have to allow for XTAL tolerances.

Now for each receiver type (FSK, MSK, QPSK etc, etc) a required signal to noise ratio can be calculated for a given BER. These graphs are typically called “Water fall graphs” because the BER drops quickly at above a certain Signal to noise ratio. 

This figure depicts BER as a function of signal to noise ratio of various receiver architectures; note that the performance of non-coherent FSK is 3dB worse than coherent FSK and therefore the same as OOK/ASK shown on the graph by the red trace.

 Most LPRF radios are specified at 1% packet error rate. Given a packet size of 20 bytes, the BER rate becomes ~0.006%. The type of receiver architecture that is used in most LPRF radios are based on a non-synchronous FSK receiver. From the water fall graphs the required Signal to noise ratio for an ideal FSK receiver is found to be 15dB at 0.006% BER. This information can be used to perform a simple comparison of the sensitivity given in a datasheet versus what a perfect system should perform.

For an ideal system with no noise figure of its own the required signal strength @ 250KB/s becomes 101.5dBm. From the datasheet it can be found to be 87dBm. And therefore the total noise figure of the RX system becomes

NF = 14.5dB

The same equations can be solved for all combinations of bit rates and RX band width, what you will find is that the system NF does not change. This makes sense because its part of the system. Overall this NF number might seem high, but these systems are a compromise between power consumptions, linearity and NF.

/TA

Thanks for the reply. I'm pretty familiar with the analysis above but there are two sources of uncertainty that make this calculation a  SWAG at best . Here's the formula restated:

Sensitivity = -174 dBm/Hz + 10*log (RX bandwidth) + NF + SNR

To work backwards with this equation to determine NF, I need to know rated sensitivity, Rx bandwidth and minimum SNR. Rated sensitivity is easy: -98 dBm. Moving on though, I'm not sure of the receiver bandwidth used by the CC2520 to demodulate the de-spread 250 Kbps data. Based on our experience, I'm guessing it's about 1.5 times the data rate or 375 KHz. But that's really just a guess and I could be off by a factor of 2 (3 dB). Note that unlike the CC2500 or CC1101, receiver bandwidth isn't listed in the data sheet for the CC2520.

As far as SNR goes, that's complicated too. I can find SNR values ranging from 13 dB (your value) to as high as 16 dB depending on method of detection (discriminator, I/Q, coherent, etc.) and post processing filtering (see Digital Modulation Techniques, 2000 by Xiong).

Depending on which BW and SNR numbers I use, my resultant NF can vary by 3 or 4 dB. If I use my best guesses (375 KHz and 14 dB), I get a believable number of 6 dB for the composite NF of the CC2520. So far, so good.

I tried deducing this another way by comparing the sensitivity of another TI chip we've used in the past - the CC2430 - to this one. Turns out there's a 6 dB differential in sensitivity for a given PER. A few years ago, one of the TI App engineers gave us the simulated NF of the CC2430 as 9 dB. That value would imply a 3 dB noise figure for the CC2520 assuming all other things being equal. The 3 dB value sounds too low and is definitely different from the 6 dB arrived at by your method. Not sure if this is a valid approach as it assumes all of the sensitivity enhancements are due to lower NF in the C2520. Again, I don't have enough information to make more than an educated guess.

So, while I appreciate the answer above, would it just be possible to ring up the folks in Oslo and ask them for the actual value?

Thanks,

Mark