In CI/MC-CDMA system described in Section 2, N length CI codes support N orthogonal users and additional N users are added by pseudo-orthogonal CI codes [21, 22]. To support more users, a high-capacity CI/MC-CDMA system is proposed in [29], where the capacity is increased up to 3N users through the splitting of pseudo-orthogonal CI (PO-CI) codes. As defined earlier, the CI code for k th user (1 <= k <= K) is given by . This code is divided into odd and even parts. Further, orthogonal subcarriers are also divided into odd and even parts. The odd/even partitioning of PO-CI and odd/even separation of available subcarriers are useful in adding extra users and hence the system capacity.
In multimedia communication, users transmit at variable data rate. In this paper, different data rate users are broadly grouped into high data rate users (HDR) and low data rate users (LoDR). HDR users are assigned by N contiguous subcarriers. Non-orthogonal odd/even subcarriers with odd/even CI code are allocated to LoDR users. In multipath fading channel, if some of the subcarriers are passed through deep fade, then other subcarriers are used to ensure low BER. The non-contiguous odd-even subcarrier allocation ensures better performance in deep fade as compared to contiguous subcarrier allocation. Proper user allocation algorithm [29] is maintained to minimize the cross-correlation between different user sets. In multirate high-capacity system model, there are five user sets.
U1 : assigned normal CI; transmit through all subcarriers
U2: assigned odd CI codes; transmit through odd subcarriers
U3: assigned even CI codes; transmit through odd subcarriers
U4: assigned odd CI codes; transmit through even subcarriers
U5: assigned even CI codes; transmit through even subcarriers
The transmitted signal for multirate high-capacity system can be expressed as
(31)
It is assumed that HDR users transmit data at 'q' times higher than LoDR users. The angles ΔΦ1, ΔΦ2, ΔΦ3 and ΔΦ4 are phase shift for the different LoDR sets (U
i
, i = 2, 3, 4, 5) with respect to HDR users assigned by normal CI codes. Different angles are shown in Figure 1.
(32)
These phase angles are chosen such that the interferences between different sets is reduced. Let us assume that R1,2(j, k) represents the cross-correlation between j th user in group 1 and k th user in group 2.
(33)
Here, the cross-correlation between j th user in orthogonal group 1 and all the users in group 2 is identical to the cross-correlation between (j + 1)th user in orthogonal group 1 and all the users in group 2. The total numbers of users in group 1 and group 2 are K1 and K2, respectively.
Let R1,2(j) is the total cross-correlation between j th user and all the users in group 2.
(34)
(35)
In CI-based system, R1,2(j) = R1,2(j + 1), i.e., every user in one set has same total cross-correlation from users of the other set. If both sets have same number of users, i.e., K1 = K2, then the total cross-correlation between j th user in orthogonal group 1 and all the users in group 2 is identical to the cross-correlation between k' th user in orthogonal group 2 and all the users in group 1. Total cross-correlation between group 1 and group 2 can be written as
(36)
If K1 = K2 = N, then R1,2 becomes
(37)
Let refers to cross-correlation between j th spreading sequence in U
x
user set and k th spreading sequence in U
y
user set. For real signal, the expression is
(38)
(39)
Total cross-correlation between j th user and all the user of U2 set becomes
(40)
where represents total number of users in U
x
set. In general,
(41)
(42)
and
(43)
So, total cross-correlation between j th user in U1 set and all the users in other set is given by
(44)
From Equation (44), it is clear that the users of the same set of subcarrier used by U1 user set create interference to the j th user of U1. set. Assuming orthogonality is maintained in subcarrier, there is no cross-correlation between [U2, U4] set and [U2, U5] set. U2 and U3 user sets are using different set of subcarriers that is utilized by U4 and/or U5 sets. In same subcarriers, the cross-correlation between two different user set is minimized by proper phase separation described in Equation (32). For U2 user set, all users from U1 set and U3 user create interference on odd subcarrier. Then, total interference for j th user in U2 user is obtained by
(45)
In multipath channel, intercarrier interference (ICI) occurs due to non-orthogonality between subcarrier. So, MAI in multipath fading channel is more than AWGN channel due to ICI.