Markku Juntti
University of Oulu, Centre for Wireless Communications, P.O. Box 4500, FIN-90014 University of Oulu, Finland markku.junni@ee.oulu.fi
Kari Hooli
University of Oulu, Centre for Wireless Communications, P.O. Box 4500, FIN-90014 University of Oulu, Finland kari.hooli@ee.oulu.fi
Abstract The ideas and basic principles of multiuser receivers for code-division multiple- access (CDMA) systems are summarized and reviewed. Linear multiuser re- ceiver formulation and combination of MAI suppression with multipath and an- tenna combining is the main contribution of the chapter. The multiuser equal- ization can be performed either after maximal ration combining or there can be a separate equalizer in each rake receiver branch. If the latter choice is made, the correlation of noise in the equalizer outputs needs to be taken into considera- tion when selecting the combining weights. Efficient bit error probability (BEP) evaluation methods for such linear receivers with uncoded transmission are also presented. Thirdly, chip equalizers for downlink are described. Their major ad- vantage is that they are applicable also in CDMA systems where the period of spreading sequences is significantly longer than the data symbol period.
Keywords: Multisensor receiver, multiuser receiver, bit error probability, equalizer, code- division multiple-access, receiver design.
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1 INTRODUCTION
The application of direct-sequence (DS) spread-spectrum (SS) code-division multiple-access (CDMA) [1, 2, 3, 4] to commercial cellular communications systems has been initialized in cdmaOne (former IS-95) standard. The third generation cellular communication systems, so called International Mobile Telecommunications 2000 (IMT-2000, or, Universal Mobile Telecommunica- tion Systems (UMTS) in Europe, employ various forms of CDMA in their air interface, which is called UMTS Terrestrial Radio Access (UTRA). The radio access techniques include wideband CDMA (W-CDMA), multicarrier based extension of cdmaOne (called cdma2000), and combined time-division code-division multiple-access (TD-CDMA) to be used in time-division duplex (TDD) operation mode. In addition to the cellular applications, CDMA is used as multiaccess technique in local wireless broadband services, like wireless local area networks in ISM band [5, 6].
In CDMA systems several users transmit their signals at the same frequency at the same times. The user transmissions can be identified by their unique sig- nature signals, which are formed by different spreading sequences or spreading codes. The signature signals are usually designed to pose as low crosscorrela- tion levels as possible. As one extreme the codes can be designed to be totally orthogonal. However, the number of orthogonal spreading sequences is lim- ited to the value of the spreading factor (SF). Therefore, if the number of users or CDMA signals needs to be larger than the value of the SF, all the signa- ture signals cannot be orthogonal. Even if the spreading signals were orthog- onal, asynchronous transmissions of different users or different propagation delays in radio channels of various users make the received spreading signals nonorthogonal. For the reasons described above, in most practical cases, there is multiple-access interference (MAI) present in DS-CDMA systems.
Since the conventional correlator receiver is interference limited [4] and suf- fers a severe performance penalty in DS-CDMA systems, multiuser detection (MUD) has been proposed to improve the receiver performance and CDMA system capacity. Since the optimal multiuser detector [7] has high computa- tional complexity, several suboptimal multiuser detectors have been proposed.
See, e.g., [8, 9, 10] for an overview and further references on multiuser de- tection. A comprehensive textbook treatment is presented in [10]. A brief textbook treatment can be found in [ 1 1 , Chap. 15].
One important approach to improve the performance of a radio communi- cation receiver is to use multiple antennas to implement spatial diversity or beamforming [12, 13]. It has been a hot topic in recent research, and is cur- rently under practical implementation in several commercial communication systems. The diversity can be either transmit [14] or receive diversity. The former is often applied in downlink (DL) (i.e., forward link) while the latter
technique is well suited for uplink (UL) (i.e., reverse link). The idea therein is to have the multiple antenna solution in the base transceiver station (BTS) in both cases. The beamforming is also implemented by BTS antenna arrays both for UL and DL. In CDMA systems, the use of multiple antennas is particularly attractive, since it reduces the required transmit power levels, which directly increases the system capacity [4].
The purpose of this chapter is threefold. First, the ideas and basic principles of multiuser receivers are briefly summarized and reviewed; the various tech- niques are formulated in a unique framework. These issues, and the definition of the system model, are the topics of Section 2. Secondly, the main part of the paper, presented in Section 3, consists of describing the linear multiuser receiver formulation and combination of MAI suppression with multipath and antenna combining. Efficient bit error probability (BEP) evaluation methods for such linear receivers with uncoded transmission are also described. Thirdly, a recent development on the potential application of multiuser receiver princi- ples in downlink is described in Section 5. In Section 6, the chapter is summa- rized and conlusions are drawn.
2 PRELIMINARIES 2.1 SYSTEM MODEL
The system model is defined in this section to set up the further notations used later in the treatment. The conventional CDMA signal description given herein is at its best when uplink (a multiple-access channel) of a typical CDMA system is considered.
The CDMA system is assumed to include K active users whose transmis- sions are received by M different antennas1, or, more generally, sensors. The received CDMA signal in antenna, where is the con- volution of the transmitted signal and the channel impulse response plus the additive channel noise. Thus, the complex envelope of the received signal in antenna can be expressed as
where is the discrete time index referring to the symbol interval, K is the number of users in the CDMA system, L is the number of propagation paths in the channel (assumed equal for all users and antennas for notational sim-
1 The antennas may be closely spaced antenna elements used in adaptive antenna arrays to perform beam- forming, or they may be widely spaced antenna elements used to provide receive diversity. The main emphasis in this paper is given to the diversity case, but the considered receiver principles themselves can be equally applied to antenna arrays as well.
100 WIRELESS TECHNOLOGIES FOR THE 21ST CENTURY
plicity), is the transmitted data symbol at symbol interval (i.e., as is the modulation symbol alphabet,
is the received amplitude of user k in antenna is the energy per sym- bol of the corresponding real bandpass signal in antenna
is the delay of kth user’s received signal in antenna is the complex gain (includes both the impact of Rayleigh fading and direction of arrival) and is the delay of the lth multipath component of user k on sym- bol interval in antenna is the delay spread of the multipath channel,
is complex zero mean additive white Gaussian noise (AWGN) process in antenna with two-sided power spectral density (assumed equal for all antennas for notational simplicity without loss of generality), and is the signature signal2of user k. Since AWGN in the received signal is mostly due to the radio frequency front-end of the antennas, the noise processes in each antenna can usually be assumed to be independent of each other. For con- venience is assumed to be normalized so that
and
It is easy to see that the matched filter (MF) outputs of all antennas for all users and multipath components produce sufficient statistics for the detection of the data symbols. The sampled output of the matched filter of the kth users lth multipath component in antenna on symbol interval is
Let the vectors of MF output samples in antenna for symbol interval be defined as
In the sequel the signal is considered over an observation window of finite length so that the symbol interval of interest is set to n = 0.
The concatenation of MF outputs over the observation window is
The vector of the matched filter outputs has expression
2It has been assumed that the signature signals are periodic over the symbol interval. This assumption is due to notational convenience only. It is easy to generalize to the case of longer signature signals [15,9]. Sim- ilarly, the assumption of a single spreading factor or processing gain for all users can be straightforwardly generalized [16].
where
matrices have elements
is the data-amplitude product vector, and is the noise vector at the MF outputs. Equation (5.2) can be expressed also in the form
where
is the vector of complex channel tap gains in the antenna m,
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is a matrix of products of the data symbols and average amplitudes, and is an identity matrix of size
To combine the observations to a single vector equation, let
is the vector of concatenated MF outputs of all the antennas. By Eq. (5.3) it can be expressed in the form
where