# interpretation of simulation results : capacity with precoder

I am studying the concept of computation the capacity. I have early asked about the difference between CSI unknown/ known to transmitter here.

In the book about Matlab implementation OFDM system, the equation for capacity with CSI is known to the transmitter is given. $$C = \max \log_2 \det (I_{N_R} + \frac{E_x}{N_T \cdot N_0} H \cdot H^H)$$ I would like to rewrite the above equation for the case if the signal is precoded and have got :

$$C = \max \log_2 \det (I_{N_R} + \frac{E_x}{N_T \cdot N_0} H \cdot V \cdot V^H \cdot H^H)$$

I have simulated it in Matlab and got : dashed line - with precoder ; line - wihout precoder

I see, as SNR increases, the precoder provides a larger improvement in capacity and also decrease the bit error rate (BER).

what conclusions can I make else?

• What am I looking at in this plot? Adding x-axis and y-axis labels would help – Engineer Feb 10 at 16:59
• @Engineer It is BER vs SNR – Jang Lee Feb 11 at 12:37
• Hmm..could you add some code snippets if they are relatively small? There are some weird things happening: (1) BER will be in the range 0-1, not 2-16, and (2) BER shouldn't be higher for a better SNR – Engineer Feb 11 at 13:42
• @Engineer I have mistaken. In Figure Capacity vs SNR is given... – Jang Lee Feb 12 at 8:07
• What is the question then? The capacity looks to be increasing like $\text{log}(1+x)$. If you're doubting your result then adding how you generated the plot to the question would be helpful – Engineer Feb 12 at 13:16

You could try to work with BER instead of SER.