Performance of Coherent Mary Signaling ENSC 428 Spring

Performance of Coherent M-ary Signaling ENSC 428 – Spring 2007

Digital Communication System

1. M-ary PSK T sin

cont …

cont …

Integration over IQ plane

cont …

cont …

2. M-ary Orthogonal Signaling

cont … 3 -ary orthogonal signal space

cont … assume equally likely M-ary symbols a priori

cont … assume equally likely symbols a priori

cont … union bound

cont …

cont … Performance improves as M increases (? ? ) p In the limit (M ∞), error probability can be made arbitrarily small as long as Eb/N 0 > ln 2 (-1. 59 d. B). p n n p Proof in Gallager Lecture 19 section 4. 3 In fact, Information Theory also proves that we cannot achieve error probability arbitrarily small if Eb/N 0 < ln 2. Most practical systems use non-coherent FSK rather than coherent FSK. We will discuss non-coherent FSK soon.

Biorthogonal Signaling

cont … 6 -ary biorthogonal signal constellation

Simplex Signaling

cont … 3 -ary simplex signal constellation

cont …

3. M-ary QAM 16 -ary QAM

cont …

cont …

Symbol Error Rate (SER) or SEP

Bit Error Rate (BER) or BEP (cf SEP, symbol error probability)

Orthogonal signaling BEP e e e k bits, M=2 k, each bit error pattern corresponds to a unique symbol, which is not the transmitted.

Example: 8 -ary PSK

Gray Coding

Gray-coded MPSK

cont …

cont …

Gray code (Reflected binary code by Frank Gray) generation p Can be generated recursively by reflecting the bits (i. e. listing them in reverse order and concatenating the reverse list onto the original list), prefixing the original bits with a binary 0 and then prefixing the reflected bits with a binary 1.

Gray code generation: another view