Optimal Space-Time Multiuser Detection
In Section 5.2, we considered
(linear) spatial processing as a mechanism for separating multiple users sharing
identical temporal signatures. In the remainder of this chapter we examine the
situation in which both temporal and spatial signatures of the users differ and
consider the joint exploitation of these differences to separate users. Such
joint processing is known as space-time
processing. In this and the following sections, we discuss such
processing in the context of multiuser detection in a CDMA system with multipath
channel distortion and multiple receive antennas. We begin in this section with
consideration of optimal (nonlinear) processing, turning in subsequent sections
to linear and adaptive linear methods. The materials in this and the next
sections first appeared in [554].
5.3.1 Signal Model
Consider a DS-CDMA mobile radio network with K users, employing normalized spreading waveforms s1, s2, . . . sK, and transmitting sequences of BPSK
symbols through their respective multipath channels. The transmitted baseband
signal due to the kth user is given by
Equation 5.42
where M is the number of data
symbols per user per frame, T is the symbol
interval, bk[i] 
{+1, –1} is the
ith symbol transmitted by the kth user, and Ak and sk(t) denote,
respectively, the amplitude and normalized signaling waveform of the kth user. It is assumed that sk(t) is
supported only on the interval [0,T] and has unit
energy. (Here, for simplicity, we assume that periodic spreading sequences are
employed in the system. The generalization to the aperiodic spreading case is
straightforward.) It is also assumed that each user transmits independent
equiprobable symbols and that the symbol sequences from different users are
independent. Recall that in the direct-sequence spread-spectrum multiple-access
format, the user signaling waveforms are of the form
Equation 5.43
where N is the processing gain,
{cj,k: j = 0, . . ., N – 1} is
a signature sequence of ±1's assigned to the kth
user, and y is a
normalized chip waveform of duration Tc = T/N.
At the receiver an antenna array of P elements is employed. Assuming that each transmitter
is equipped with a single antenna, the baseband multipath channel between the
kth user's transmitter and the base station
receiver can be modeled as a single-input/multiple-output channel with the
following vector impulse response:
Equation 5.44
where L is the number of paths
in each user's channel, a
,k and tl,k are,
respectively, the complex gain and delay of the lth path of the kth
user's signal, and al,k = [al,k,1 ···
al,k,P]T is the array response vector corresponding to
the lth path of the kth user's signal. The total received signal at the
receiver is then the superposition of the signals from the K users plus the additive ambient noise, given by
Equation 5.45
where * denotes convolution; n(t) = [n1 (t) ···
nP(t)]T is a
vector of independent zero-mean complex white Gaussian noise processes, each
with power spectral density s2.
Sections
