CANONICAL SPACE-TIME COORDINATES FOR MULTIUSER WIRELESS COMMUNICATIONS Eko N. Onggosanusi, Akbar M. Sayeed, and Barry D. Van Veen Department of Electrical and Computer Engineering University of Wisconsin{Madison Madison, WI 53706
[email protected],fakbar,
[email protected] ABSTRACT We propose a space-time multiuser detection scheme for wireless communications that projects the received signal onto a xed set of basis signals. The basis signals are dictated by a canonical characterization of channel propagation dynamics in terms of discrete multipath delays, Doppler shifts, and directions of arrival. They capture the essential degrees of freedom in the received signal. The canonical space-time coordinates induced by the underlying basis provide a natural framework for multi-access interference suppression and diversity processing. The signal of the desired user is concentrated in a subset of coordinates, while the interference generally occupies the entire space-time coordinate system. It is demonstrated that MAI suppression can be improved by incorporating a subset of coordinates where the desired user is absent. 1. INTRODUCTION The use of antenna arrays for enhancing the capacity and delity of multiuser wireless communication systems has spurred signi cant interest in space-time signal processing techniques [1]. Most existing space-time receiver designs employ \ideal" processing matched to all the dominant multipaths and corresponding direction of arrivals (DOAs). In addition to su ering from high computational complexity in dense multipath environments, such receivers rely heavily on accurate estimation of the delay and DOA parameters of dominant scatterers. In [2] we introduced a canonical characterization of the received signal in terms of the essential degrees of freedom in the channel that are observable at the receiver. These degrees of freedom are captured by a xed basis corresponding to certain discrete multipath delays, Doppler shifts, and DOAs of the signaling waveform. The received signal is projected onto this basis by sampling the outputs of a space-time matched
lter bank. Our approach inherently eliminates the need for estimating arbitrary delays and DOAs, and instead only requires estimates of the channel coecients. The canonical space-time coordinates induced by the underlying basis provide a natural framework for interference suppression and diversity processing as the desired user is concentrated in a subset of coordinates that depend on its delay, angle, and Doppler spreads. The signal of the desired user is known to be present in some canonical coecients, termed \active" coordinates, and absent from other canonical coecients, termed \inactive" coordinates. Multi-access interference (MAI) occupies both active and inactive coordinates. While the active coordinates capture the essential diversity and energy of the desired user, they only provide limited MAI suppression. Additional MAI suppression can be obtained by incorporating a set of inactive coordinates in the detection process. In this paper we present a decentralized interference suppression scheme1 that exploits this idea. The next section describes the canonical space-time representation and the notion of active-inactive coordinates that underlie the proposed multiuser receivers. A generic receiver based on the proposed scheme is presented in Section 3. Examples illustrating the performance of the proposed receiver are given in Section 4. 2. CANONICAL COORDINATE REPRESENTATION Consider a time and frequency-selective channel with K users. The baseband signal received at a R-element sensor array within one signaling interval [0; T ) can be 1 A decentralized receiver processes the received signal in the desired user's canonical space-time coordinates without incorporating the channnel parameters and signaling waveforms of the interfering users.
written as
written as
r(t) = sk(t) =
K X
r(t) =
p
bk Ek sk (t ? k ) + n(t);
k=1 Sk+ Z Dk
Z
Z
Tk
Hk ( ; ; )a( ) Sk? ?Dk 0 qk (t ? )ej 2td dd ;
(1)
where bk , Ek and k are the symbol, energy, and delay of the k-th user, and a( ) is the array response vector for direction-of-arrival (DOA) . We assume a onedimensional array without loss of generality. Hk ( ; ; ) is the time-frequency spreading function of the channel [2], and qk (t) is the signaling waveform, [Sk? ; Sk+ ], [?Dk ; Dk ], [0; Tk ] are the angular, Doppler, and delay spread for the k-th user, respectively. Here we assume fbk g 2 f?1; +1g are IID equiprobable Bernoulli random variables and the noise n(t) is a zero-mean complex Gaussian random vector with E [n(t)nH (t0)] = N0 IR (t ? t0 ) 2 and uncorrelated with fbk g. Due to the time-limited and essentially bandlimited nature of qk (t), the k-th user signal admits a representation [2]
sk(t ? k )
P+
k X
Mk X
dkX +L k
p=Pk? m=?Mk l=dk
(k ) (k ) Hpml qpml (t); (2)
l k (t) = a(' )ej 2mt T qk t ? qpml p B ; 0t
