Autocorrelation and SNR for the Output of a Square-Law Device and Low-Pass Filter With Square-Law SSB Plus Gaussian Noise at the Input

Powers´ square-law single-sideband (SSB) signal is shown to be to ordinary SSB roughly what amplitude modulation (AM) with carrier is to amplitude-modulation suppressed carrier (AMSC) signaling. That is, both SSB and AMSC require coherent demodulation at the receiver to recover the information signal properly and this requires the slaving of the receiver to the transmitter or at least the use of expensive phase-locking circuitry. A carrier is added to the AMSC signal to make possible inexpensive incoherent demodulation at the receiver (envelope detection) and the resulting transmission inefficiency and loss of SNR in the receiver are accepted to achieve this simple detection. In the same manner, Powers´ square-law SSB allows inexpensive incoherent demodulation at a loss in transmission efficiency and receiver SNR. This loss in SNR is found to always be within 3 dB of that in AM envelope detection for large SNR when equal input-signal power and noise spectraldensity levels are assumed. Further, there are situations for which the SNR performance is better than AM envelope detection (i.e., 100 percent tone modulation is one such case). The main difference is that AM with carrier and AMSC require twice the transmission bandwidth of SSB or Powers´ square-law SSB.