simulation with SINR

Question

I have a DS-CDMA system and the chip width is fixed but every user have a different spreading code length. I want to have a simulation of signal to interference noise ratio (SINR) VS. bit error rate (BER). If I assumed that SINR is given like -25:0 dB. How can I calculate noise power (it is thermal noise) and the interference power?

Answer 1

The SINR characteristics of a DSSS Multiuser Communication are very difficult to approximate theoretically.

1. For the Downlink at least, it is easy enough to characterize it with lesser parameters, but still difficult to obtain any particular derivation. It depends heavily upon the Spreading Sequences(their auto-correlations and cross-correlations), symbols of the interfering users(their average Energy) and so on. As a very decent approximation, $SINR$ is usually computed using random spreading sequences assumption. According to Andreas Goldsmith's textbook "Wireless Communications", for a $K$-user system with $N$ chips per symbol, the $SINR$(assuming Random signal transmissions for every user, again a probabilistic assumption) is given by $SINR = (\frac{N_{o}}{E_{s}}+\frac{K-1}{G})^{-1}$ where $G=N$ approximately.

2. For the Uplink it is even more a difficult task to analyze this. If all users' signals are received with the same power($AWGN$), it can be shown that for those Asynchronous users assuming Random Spreading codes with $N$ Chips per symbol, random start times and random carrier phases, $SINR = (\frac{K-1}{3N}+\frac{N_{0}}{E_{s}})^{-1}$.

For simple simulations, usually people assume that the $SINR$ can be calculated as, $SINR = \frac{E_{s}}{N_{0}+\sum_{i=1}^{K-1}\frac{E_{si}}{G}}$ where G is the processing gain which can be roughly taken to be as $K$. This factor of $G$ applies if the codes are perfectly orthogonal and its approximation to $N$ is usually justified assuming the properties of Spreading codes.

In all the above formulae, $N_{0}$ is the Noise Power which is equal to $2*\sigma^{2}$ for 2-Dimensional Signalling and $E_{s}$ is the average Received Energy of the signal. You can refer to Goldsmith if you to learn any further on the math behind it all. Now you can straight away plugin your numerical value on the LHS of the expressions that are stated above and you can go about calculating the Thermal Noise Power since you know the Received Powers $E_{s}$ for every user's signal. And all these formulae are for $AWGN$ conditions. The difficulty comes from the fact that Interferers cannot be approximated as Random Gaussian Noise.