Space-Time Block Codes for Wireless Systems - The ...

[
3 1314 2447 3246
8PSK u
0
8 u 0 ] [
8 u
2
8 u 4 ] [
u 0 8 u 3 8 u
4
8 u 6 ] [
8 u 4 8 u 2 8 u
6
8 u 2 ]
8 u 1 8 u 7 8
8 u 5 8 u 6 8
8 14469 33744 47965
16PSK [ u 0 16 u 0 ] [
16 u
3
16 u 8 ] [
u 0 16 u 8 16 u
8
16 u 3 ] [
16 u 8 16 u 5 16 u
11
16 u 13
16 u 0 16 u 11 ]
16
16 u 5 16 u 13
16
Table 2.3: Detailed Structure of rate 1 OMM 2×2 8PSK and 16PSK Codes. ( u n = e i 2π n )
ρ c
=0.3
2X2 BPSK
2X2 16PSK
10 −2
Union Bound
10 −1 SNR
10 −3
10 −4
6 7 8 9 10 11 12 13 14 15 16
Figure 2.9: Rate 1 OMM 2 × 2 BPSK and 16PSK codes for ρ c = 0.3.
2. It is unitary, but, it does not form a group under matrix multiplication, neither is it a
subset of group unitary codes [SHHS01]. The detailed structure of the OMM 8PSK
and 16PSK (Table 2.3) suggests that as more degrees of freedom are introduced,
code tends to be more unitary. This agrees with the general structure suggested in
[MH99].
3. The 16PSK optimal code is actually “correlation free”. It is OMM for all ρ!
The rate 1 OMM 3 × 3 BPSK codes are listed in Table 2.4. We make the following
observations:
1. There are 3 equivalence classes which are OMM codes for ρ c = 0.3, but their multiplicity
of the minimum metric in the distance spectra, N p , are different. The
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