Adaptive Array Processing in TDMA Systems

Adaptive Array Processing in TDMA Systems

5.2.1 Signal Model

A wireless cellular communication system employing adaptive antenna arrays at the base station is shown in Fig. 5.1, where a base with P antenna elements receives signals from K users. The K users operate in the same bandwidth at the same time. One of the signals is destined to the base. The other signals are destined to other bases, and they interfere with the desired signal; that is, they constitute co-channel interference. Note that although here we consider the uplink scenario (mobile to base), where antenna arrays are most likely to be employed, the adaptive array techniques discussed in this section apply to the downlink (base to mobile) as well, provided that a mobile receiver is equipped with multiple antennas. The general structure can be applied to other systems as well.

Figure 5.1. Wireless communication system employing adaptive arrays at the base station. An array of P antenna elements at the base receives signals from K co-channel users, one of which is the desired user's signal, and the rest are interfering signals.

The received signal at the antenna array is the superposition of K co-channel signals from the desired user and the interferers, plus the ambient channel noise. Assume that the signal bandwidth of the desired user and the interferers is smaller than the channel coherence bandwidth, so that the signals are subject to flat fading. Assume also that the fading is slow, such that the channel remains constant during one time slot containing M data symbol intervals. To focus on the spatial processing, we assume for the time being that all users employ the same modulation waveform,[1] so that after matched filtering with this waveform, the P-vector of received complex signal at the antenna array during the ith symbol interval within a time slot can be expressed as

^[1] In Section 5.3, where we consider both spatial and temporal processing, we drop the assumption.

Equation 5.1

where b_k[i] is the ith symbol transmitted by the kth user, g_k = [g_1,k ··· g_P,k]^T is a complex vector (the steering vector) representing the response of the channel and array to the kth user's signal, and n[i] ~ N_c (0, s² I_P) is a vector of complex Gaussian noise samples. It is assumed that all users employ phase-shift-keying (PSK) modulation with all symbol values being equiprobable. Thus, we have

The nth element of the steering vector g_k can be expressed as

Equation 5.2

where A_k is the transmitted complex amplitude of the kth user's signal, g_n,k is the complex fading gain between the kth user's transmitter and the nth antenna at the receiver, and a_n,k is the response of the nth antenna to the kth user's signal. It is also assumed that the data symbols of all users {b_k[i]} are mutually independent and that they are independent of the ambient noise n[i]. The noise vectors {n[i]} are assumed to be i.i.d. with independent real and imaginary components. Note that, mathematically, the model (5.1) is identical to the synchronous CDMA model of (2.1). However, the different physical interpretation of the various quantities in (5.1) leads to somewhat different algorithms than those discussed previously. Nevertheless, this mathematical equivalence will be exploited in the sequel.