I've read in a couple sources that in a channel consisting of only additive white Gaussian noise (AWGN), at low SNR, QPSK31 is actually worse than BPSK31.
By doing simulations in a computer, and tests on the bench with a noise generator, it has been found that when the bit error-rate is less than 1% with BPSK, it is much better than 1% with QPSK and error-reduction, but when the BER is worse than 1% on BPSK, the QPSK mode is actually worse than BPSK. Therefore, if we are dealing with radio paths where the signal is just simply very noisy, there is actually no advantage to QPSK at all!
Computer simulation with BPSK in white noise shows that when the SNR is good, the error-correction system does win, reducing the low error rate to very low levels, but at the SNR levels that are acceptable in live amateur contacts, it's better to transmit the raw data slowly in the narrowest bandwidth. It also takes up less band space of course!
The reasoning seems to be that the switch from BPSK to QPSK degrades the SNR:
Suppose I devise an error-correcting system that doubles the number of transmitted bits. If I wanted to keep the traffic throughput the same, I would need to double the bit rate. But with BPSK that means doubling the bandwidth, so I lose 3dB of signal-to-noise ratio and get more errors. The error-correction system will have to work twice as hard just to break even! It is no longer obvious that error-correction wins. It is interesting to note that with FSK, where the bandwidth is already much wider than the information content, you can double the bit-rate without doubling the bandwidth, and error-correction does work.
I'm skeptical. Doubling the symbol rate in FSK halves the duration of the symbols, and thus halves Eb/N0. Switching from BPSK to QPSK while holding the symbol rate the same splits the transmitter between two orthogonal systems, so again halving Eb/N0. I don't see any reason error correction would work for FSK but not QPSK.
But then, the channel decoding in QPSK31 combines two bits on the air into one bit received. So this is a doubling of energy per bit, for a net effect of no change in Eb/N0.
What's the basis for this claim that BPSK31 is worse than QPSK31 in an AWGN channel? Is there any formal proof or published empirical results to back it up?