mohatta2015.pdf

20 INTRODUCTION
The K = 4 main block sequences of length NMB = 4 are given in Table 1.4. Similar
to CDM, the main block sequences are orthogonal when time aligned, i.e.,
NM„-1
Σ cl(n)c k ,(n) = N MB 6(ki-k 2 ). (1.41)
n=(l
They have an additional property in that a circular shift of the sequence is
equivalent to applying a phase shift to the original sequence. Specifically,
Λ(ηθί) = exp (j2nk(n - g)/K)
= exp(-j2nke/K)exp{j2nkn/K)
= exp(-j2nke/K)f k (n). (1.42)
where Θ denotes subtraction modulus NMB- This property implies that the sequences
are also orthogonal with circular shifts of one another, i.e.,
N M „-1
Σ cl 1 (n)c k2 (n®e) = N MB 6(k l -k 2 ), (1.43)
where ® denotes modular addition using modulus NMB- We will see in the next
chapter that the use of a cyclic prefix and discarding of certain receive samples
makes delayed versions of the symbol appear as circular shifts. This allows orthogonality
to be preserved in a dispersive channel. (From a CDM point of view, the
CP makes interference a function of periodic crosscorrelations, which are "perfect"
in this case.)
Table 1.4 Main block OFDM soquonc