Furthermore, SKR for both the 4-PSK and 8-PSK modulation formats under collective attack  are depicted in Figure 4(a).
Caption: Figure 4: Calculated QKD secure key rates as a function of transmission distance for (a) 4-PSK and 8-PSK modulation and (b) single-channel (1-Ch) 4-PSK modulation and 12-channel WDM 4-PSK modulation with 25 and 50 GHz channel spacing.
1 shows the average SER versus SNR of the considered HSTRN, for infrequent light shadowing (satellite-relay LMS channel), with multiple values of CCI (-5 dB, 0 dB and 5dB) using different M-PSK modulation schemes: BPSK, QPSK and 8-PSK. It is assumed that [[sigma].sup.2.sub.1] = [[sigma].sup.2.sub.2]; and on the x-axis of Fig.
We observe that the increase in SER is more prominent for higher-order modulation such as 8-PSK than that of lower-order modulation scheme of BPSK.
The ERS calculates the PER of the measured signal using the four principal modulation schemes used in recent satellite communication technologies, namely, QPSK, 8-PSK, 16-QAM, and 32-QAM.
Figure 9(a) shows the output of the ERS for the rainy period shown in Figure 5, which shows that under 8-PSK, the PER increased only during the heavy-rain rate period.
The tailbiting codes search results for 4-PSK, 8-PSK and 16-QAM modulation are presented in Section 4.
An object of search in this article were tailbiting convolutional codes over ring [Z.sub.2] generated by concatenation of the systematic encoders with feedback with code rate R=1/2 and R=2/3 for 4-PSK and 8-PSK modulators, and tailbiting convolutional codes over ring [Z.sub.4] generated by concatenation of the systematic encoders with feedback with code rate R=1/2 for 16-QAM.
The contributions of this paper are the following: We first derive the accurate analytical expressions of average bit and symbol error probability for different modulation schemes (B-PSK, B-FSK, Q-PSK, 8-PSK
, 4-QAM and 16-QAM (square constellations) under Nakagami-m fading channels.
With EDGE modulation, the change from a constant envelope modulation format to 8-PSK
has implications on VCO pulling which must be investigated further.
The evolution of GSM (EDGE) and the linear modulation used (8-PSK
) with both amplitude and gain variations come with new specification requirements regarding system linearity.
An evolution of the current GSM standard to provide higher data rates is GSM EDGE (812.5 kbps) where the modulation scheme to be used is pulse-shaped (Gaussian) 3[Pi]/8 offset 8-PSK
as opposed to GSM (270.8 kbps), which uses Gaussian minimum-shift keying (GMSK).