Flat vs frequency selective fading in MC-CDMA?

Question

I am trying to simulate an MC-CDMA system. I have NXK matrix $S$ which consists of subcarriers ($s_n,_k$ represents subcarrier $n$ of user $k$) and KX1 vector $X$ consists of user symbols. So my received signal is $Y=SX+N$. To include the channel response I am confused in flat fading and frequency selective fading.

• $\:$ For flat fading i.e., coherence bandwidth $>$ signal bandwidth, and I have a 3 tap channel impulse response in time domain. So in frequency domain I have NX1 vector $h_k$ for user $k$.

  Now to include the channel fading for user $k$,

  • Should I do S(:,k) .* H(:,k) %% H is channel matrix i.e., each subcarrier is multiplied by a different channel coefficient while coeffecients have nearly same magnitude, or
  • S(:,k)*h(k) i.e., multiplying whole sequence by a single coefficient. and what that h(k) value should be ?

• For frequency selective fading does only the values of channel coefficient will change or I will have multiple taps for each subcarrier and will need to convolve in frequency domain?

Answer 1

It would help if you mentioned where your references for MC-CDMA and your channel model come from.

The short answer is that it depends on the level of abstraction you want. For a flat channel, you would multiply by a complex-valued gain. For a frequency-selective channel, I would typically form the time domain signal and convolve with an impulse response (generated from some channel model that reflects your target environment). Perhaps if you provide us with a reference, I can provide additional assistance.