SNR Signal to noise ratio of Pseudo random bit sequence (PRBS)
To estimate the Signal to Noise Ratio you can use the normalized correlation coefficient to the reference time-aligned sequence. I detail this approach further at this post here including the relationship between correlation coefficient and SNR. Note that "noise" in this context is any deviation of the received signal from the reference sequence such as multipath effects and band-limiting. To negate those effects modify the reference sequence to also include that or use equalization techniques on the received sequence to match the reference. In many cases these effects are second order and may be neglected. 

Noise detection

If you can assume the noise is White, and you can assume the PRBS is a rectangular waveform (with a Sinc function spectrum) then the equivalent 2-sided brick-wall noise bandwidth of the Sinc with nulls at 1/T (where T is the pulse width) is 1/T. If your signal level is sufficiently in far excess of the total noise power (such as 15 dB or more) then you can estimate the signal power from total power received and compute the noise power over that equivalent bandwidth (1/T) using the estimate of the noise floor far from the signal. Pay attention to the resolution bandwidth setting on the spectrum analyzer to then determine power values / Hz (for example if you are using a 1 KHz resolution band width and a pixel displays a power level of -70 dBm, this is -100 dBm/Hz since $10Log10(1000) = 30$ dB.) For lower signal powers you can resolve the signal to noise by knowing the total power is the additive power of signal plus noise (for example if the signal is only 10 dB higher the noise, the total power measured will be 0.4 dB higher than the signal alone given $10Log(1+10^{-10/10})= 0.4$, and for 15 dB higher will be 0.14 dB from  $10Log(1+10^{-15/10}) = 0.14$)