TEL AVIV UNIVERSITY Gaddi Blumrosen

The error probability bound in Rayleigh fading model is:
NT 1
Pe
2
j 11 j/ 4
NT
j
j1
2
1/ 4
Where r is the rank of A.
A
j
(3.20)
Since are the coding matrix eigenvalues, the first term in the multiplication in
Nr
NT
(3.20), j , can be interrupted as coding gain (coding factor) and the second
j1
exponent of the second term, r m
A , is the SNR factor of each sub-channel or spatial
diversity gain.
A design criteria for uncorrelated Rayleigh fading, account also for all cases, of slow
fading with low values of rN R was obtained in [19]. Other criteria should be applied
to other cases such as fast fading or large values of rN R
The design criteria for uncorrelated Rayleigh fading consists of two stages:
1. The Rank Criterion
In order to achieve the maximum diversity, the matrix has to maximize the minimum
rank over the set of all two distinct codewords.
2. The Determinant Criterion
Maximize the minimum determinant of the matrix A, along the pairs of distinct
codewords with the minimum rank.
If the channel coefficients are correlated, we face degradation in performance due to
the decrease in system diversity order. With the same expressions and design
criterions are used for the correlated case [19], there is the following penalty in coding
gain and consequently to the over all gain, expressed in Decibels:
L 10/( N N ) log10
det( )
(3.21)
los
h
where E(
H H)
.
Nr Nr
R
T
3.3.3 Orthogonal Space-time codes (OSTBC)
In this section we will examine the properties of a family of STC, OSTBC which are
derived from the performance criterion in (3.20). When the transmitted data is
encoded using a OSTBC, the encoded data is split into NT
streams from each antenna
which tend to be independent as much as and thus designed to achieve the maximum
diversity order. OSTBC enable simple maximum-likelihood decoding algorithm,
which is based only on linear processing at the receiver rather than joint detection.
A simple transmit OSTBC for two antennas was first derived in [20].
The classical mathematical framework of orthogonal designs is applied to construct
space–time block codes [21], [22].
In orthogonal code matrix,
I N i j
H
T
XX j
0 N i j
T
(3.22)
Where X ,
, are the i‟th and j‟th columns respectively.
i X j
rm
A