This document analyzes the performance of a new 8-level signal constellation compared to standard 8-PSK. It calculates the average symbol energies and minimum distances between symbols for each constellation. Simulation results show the bit error rate decreases as the signal-to-noise ratio increases for both constellations, but the rate of decrease is slightly lower for the new constellation compared to standard 8-PSK. The 8-PSK constellation is concluded to be better since its bit error rate drops more compared to the new constellation, due to having a higher minimum distance between symbols despite a higher average symbol energy.

1. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
Performance Analysis of a new 8-level Signal
Constellation with reference to 8-PSK
G.W.C. Saumya (100488C), P.R. Senanayaka (100490B)
R.M.A.U. Senerath (100495U), D.P.D. Senaratna (100496A)
Department of Electronic and Telecommunication Engineering,
University of Moratuwa, Sri Lanka
August 18, 2013

2. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
GRAY CODING SCHEMES
Figure : 8 - PSK Constellation Figure : New Constellation

3. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
CALCULATIONS
Average Symbol Energies:
New Constellation
= 3
8 ∗ (A
2 )2 + 5
8 ∗ A2 = 23
32 ∗ A2
Standard 8-PSK Constellation
= (A
2 )2
Minimum Distance Between Symbols:
New Constellation
= 0.5 ∗ A
Standard 8-PSK Constellation
= 0.765 ∗ A
Number of Bits used: 30,000
The MATLAB code simulating the above constellations can be found here

4. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
EFFECTS OF NOISE
(Es
N ) New Constellation 8 - PSK Constellation
No Noise
0.6 dB

5. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
EFFECTS OF NOISE, CONTINUED.
(Es
N ) New Constellation 8 - PSK Constellation
3 dB
6 dB

6. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
COMPARISON OF THE TWO CONSTELLATIONS
Figure : Bit Error Rate Vs (Eb
N )

7. INTRODUCTION BACKGROUND METHODOLOGY RESULTS CONCLUSION
PERFORMANCE ANALYSIS
In the reference 8-PSK scheme, the Bit error rate (BER)
drops fast when (Eb
N ) is increased. In the new constellation
also, the Bit error rate (BER) decreases as(Eb
N ) is increased;
but in a slightly lower rate than that of the reference 8-PSK
scheme.
The reference 8-PSK scheme is a better scheme since its Bit
error rate (BER) drops slightly higher compared to the
new constellation.
Even though 8-PSK has a higher average symbol energy
than the new constellation, it has the higher minimum
distance between symbols. So the cumulative effect has
caused this observation.