4.2 Uplink

Consider the antenna array CDMA system described in (1.13). In the presence of noise, the baseband signal received at the mth receiver is given by:

The additive noise { v _m( t)} is assumed to be of power ? _n ² and is independent to the signals.

To facilitate our analysis, we shall cast the above CDMA system into a multi-input multi-output (MIMO) framework of Figure 4.1, with { d _i( n)} denoting the spread chip sequences and { h _mi} the composite channel responses of maximum length L _cT _c The antenna outputs can be expressed in vector convolution form below:

where h _i( t) = [ h _{1 i}( t) h _Mi( t)] ^T and v( t)= [ v ₁( t) v _M( t)] ^T represent the noise vector.

Note the modulated chip sequence from the ith user:

The chip delay index n _i, 0 ? n _i < L, accounts for the relative discrete-time offset between users. In practice, this offset is usually known to the receiver after coarse synchronization during the initial access. The exact timing (within a fraction of a chip duration) of the direct-path signal, incorporated in h _i(t) is assumed to he unknown.

Sampling each antenna output at the chip...