Error rate curve for M-ary othogonal signaling

[pangpangfish]

I always have one unanswered question on the error rate curves for M-ary othogonal signaling. Notice that the there is a cross-over in the error rate curve in the region near -1.6 dB. In other words, in low SNR region, why a 16-ary orthogonal signaling performs worse than a binary orthogonal signaling?

 

[senaydud]

Do you have any reference plot? I checked the book of proakis (Dig. Comm. - Figure 5-2-5) and there seems to be no cross-over between 16-ary and 2-ary ort. signals.

 

[pangpangfish]

Your observation is right about Fig. 5.2-5 in Proakis. Since he didn't plot the error rates above 0.1, pretty useless region.

If you look at Fig. 3.20 (page 127) of a recent book by Madhow (can be downloaded from edaboard), you will see the cross over behavior I described.

 

[senaydud]

yes I have seen the plot on Madhow's book, thanks for the reference. Well, I have no idea sorry, I hope someone tells us a sensible reason for that.

 

[cwjcwjcwj]

I couldn't understand what you mean by M-ary signal constellation systems performed worse comparing to that of 2-ary signal constellation systems in low SNR.....

From my understanding, M-ary signal constellation systems always performed worse in all the region when comparing to that of 2-ary. Cause M-ary signal constellation systems used more average transmitted power than 2-ary.

 

[pangpangfish]

If you read my original post carefully, we were discussing M-ary *othogonal* signalings. You are probably thinking of 2-dimensional M-ary constellations.

M-ary orthogonal signalings can actually achieve the Shannon limit (without using any channel coding) when M approaches infinity, as long as SNR per bit is above a threshold ln2 (or -1.6dB). M-ary orthogonal signaling achieves high power efficiency at the cost of letting the bandwidth efficiency go to zero.

I couldn't understand what you mean by M-ary signal constellation systems performed worse comparing to that of 2-ary signal constellation systems in low SNR.....

From my understanding, M-ary signal constellation systems always performed worse in all the region when comparing to that of 2-ary. Cause M-ary signal constellation systems used more average transmitted power than 2-ary.