Effective Signal to Noise Ratio (ESNR)

From a signal processing standpoint, demodulation error and capacity degradation may happen when there is a change of interference distribution, even though the received SNR γ is the same. The BER performance of regular QPSK/QPSK becomes deteriorated in Fig. 7 when ζQPSK/QPSK increases. However, with optimally rotating the enhancement-layer signal constellation, the performance loss can be recovered. This kind of recovery is more significant with large ζ. In order to quantify and understand this kind of BER performance loss due to interference and receiver design, one approach we propose for capturing this kind of degradation is to calculate the effective signal-to-noise ratio (ESNR) of the whole transceiver chain, which is defined by ˜γ (γ) ≡ Ψ−1 (pe(γ)) ,

where pe(γ) is the demodulation BER of the signal with SNR γ, and Ψ−1 (∗) denotes the inverse function of Ψ(·), the demodulation error probability function with no ILI. The ESNR for the QPSK-modulated base layer or enhancement layer of any hierarchical modulation can be calculated by ˜γQPSK/QPSK = 2 Q−1 (pe(γ)) 2 . (10)

More specifically, the ESNR for the base layer of regular QPSK/QPSK hierarchical modulation with ML demodulator is given by ˜γB QPSK/QPSK(γ) = 2

Q−1

Q((1− √ ζ)γ)+Q((1+ √ ζ)γ) 2

2 . (11)