A unified approach to multiuser detectors for CDMA and their geometrical interpretations

ቤተ መጻሕፍቲ ባይዱ
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Introduction
CDMA has been recognised as an important access scheme for third generation mobile radio communication systems [1]. However, the attractive flexibility of CDMA comes at the price of multiple access interference (MAI) and also intersymbol interference (ISI) which is magnified in the mobile radio channel where time varying multipath propagation is present [1]. ISI and, more importantly, MAI can be mitigated by multiuser detection techniques, [2]–[8], which are also termed joint detection (JD) techniques [9, 10]. Unfortunately the optimum
Abstract In this paper we align a class of known multiuser detectors for code division multiple access (CDMA) along with some new multiuser detectors in a unified group. The new multiuser detectors are devised by completing the structure of the group. The unified group structure is a binary tree obtained by splitting • sequence and single symbol detection, • maximum a–posteriori (MAP) and maximum likelihood (ML) detection, and • unconstrained as well as constrained detection. The link between sequence and single symbol estimators is explained revealing the increased complexity of single symbol estimators as compared to sequence estimators. Finally, the aforementioned group structure is supported by a geometrical technique depicting the detection process performed by the multiuser detectors.
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A Unified Approach to Multiuser Detectors for CDMA and Their Geometrical Interpretations
Peter Jung
University of Kaiserslautern Department of Electrical Engineering Research Group for RF Communications P.O. Box 3049 D–67653 Kaiserslautern, Germany E-Mail: wowbag@rhrk.uni-kl.de
Paul D. Alexander
University of South Australia Signal Processing Research Institute Mobile Communications Research Centre Warrendi Road, The Levels SA 5095, Australia E-Mail: palex@.au
P. Jung, P. D. Alexander: A Unified Approach to Multiuser Detectors for CDMA and Their Geometrical Interpretations
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multiuser detectors (MD’s) for both sequence detection (SD) and single symbol detection (SSD) are not practical due to the performance/cost ratio exhibited by today’s technology. To alleviate this complexity problem many linear complexity MD’s have been proposed in the literature, cf. e.g. [3], [7]–[11]. These MD’s trade performance for complexity and thus become candidates for implementation in third generation mobile radio systems [1]. The viability of such linear complexity MD’s has already been demonstrated in a recently proposed cellular CDMA mobile radio system applying JD which is termed JD–CDMA [10, 12]. The optimum and linear complexity MD’s have been developed independently and the similarities between them have not been illustrated yet. This shall be done in this paper. Moreover, we shall give an illustrative geometrical description of the detection process carried out by the aforementioned MD’s. To allow a better understanding of the following explanations, we shall first give a definition of the terms detection and estimation. An elaborate presentation of estimation and detection theory can be found in [13]. Detection is the deciding on the cause of an output that is random in character, based on the observation of the mentioned output. For example, the cause could be a data symbol transmitted over a radio channel, resulting in a particular output signal after the channel. This output signal represents the aforementioned observation. Assume that the symbol alphabet has cardinality M . The symbol alphabet is therefore a constrained set. There are M different possible causes that might have resulted in the observation. Hence, the detection outcome is a random variable taken from a constrained set, which is identical to the symbol alphabet. The detection outcome is hence M –ary. Estimation is the determining of the value of a parameter which has influenced the aforementioned observation. The estimation outcome is hence not constrained to a set with finite cardinality. It is rather taken from an unconstrained set. Estimation is hence the continuous extension of detection. In what follows, we will use the term detection in most cases, however, being well aware of the fact that detectors can also be seen as estimators. Two categories of MD’s are conceivable, namely SD based MD’s and SSD based MD’s. In the case of the SD based MD’s the objective is to find that particular data sequence which was most probably transmitted according to some hypothesis criterion. SSD based MD’s try to find that particular data symbol which was most probably transmitted at a particular time, again satisfying some hypothesis criterion. SSD based MD’s are not widely known and to the knowledge of the authors have not yet been studied thoroughly. The authors shall concisely explain the basis of such rather new SSD based MD’s and shall also demonstrate