# PPM Variant - Analytic symbol error probability

I'm trying to calculate symbol error probability of variant of pulse position modulation considering only AWGN channel. The decoder is maximum likelihood so the implementation of the detector is by using vector correlators. $$\arg \max_{x} <y,x>.$$ Attached is the waveforms vector representation of the transceiver & receiver. I didn't find any general term for the inner product that will lead me to solve the probability problem and from there to find the analytic solution. Any help will be appreciated.

• Your last equation should read $\lt y,s_m \gt$, I think. You want to compare the inner product of y with $s_m$ for $m=1,2,\ldots,M$, not always with $s_M$. Is this homework? Or self-study? If so, please tag it as such. – Peter K. Oct 31 '13 at 13:37
• @PeterK. Hi , you are right. fixed it. don't know how to tag it as self-study... – UdiW Oct 31 '13 at 13:54
• Also, if you're generating the image in Latex, you can put it straight here and it'll render... – Peter K. Oct 31 '13 at 13:59
• :) struggling with Latex. this one produced with Word... – UdiW Oct 31 '13 at 14:02
• Also asked on electronics.SE. – Dilip Sarwate Oct 31 '13 at 14:36