Non-coherent Multi-User Detection Based on Quantum Search S´ andor Imre, Member, IEEE and Ferenc Bal´ azs, Student Member, IEEE Budapest University of Technology and Economics Department of Telecommunications Mobile Communications Laboratory H-1117 Budapest,Magyar Tud´ osok krt. 2., HUNGARY Abstract— 3G and 4G mobile systems are based on CDMA technology. In order to increase the efficiency of CDMA receivers large amount of effort is invested to develop suitable multi-user detector techniques. However, at this moment there are only sub- optimal solutions available because of the rather high complexity of optimal detectors. One of the possible receiver technologies can be the quantum assisted computing devices which allows high level parallelism in computation. The first commercial devices are estimated by 2004, which meets the advent of 3G and 4G systems. In this paper we introduce a novel quantum computation based Quantum Multi-user detectior (QMUD), employing Grover’s search algorithm, which provides optimal solution. The proposed algorithm is robust to any kind of noise. Keywords — Multi-user detection, Grover’s Algorithm, Quantum Computing, Quantum Signal Processing I. I NTRODUCTION Subscribers of the next generation wireless systems will commu- nicate simultaneously, sharing the same frequency band. All around the world 3G mobile systems apply Direct Sequence - Code Division Multiple Access (DS-CDMA) promising due to its high capacity and inherent resistance to interference, hence it comes into the limelight in many communication systems. Another physical layer scheme, Or- thogonal Frequency Division Access (OFDM), is also often used e.g. for Wireless LANs (WLAN) or HiperLAN, where the subscriber’s sig- nal is transmitted via a group of orthogonal frequencies, providing In- ter Channel Interference (ICI) exemption. Nevertheless due to the fre- quency selective property of the channel, in case of CDMA commu- nication the orthogonality between user codes at the receiver is lost, which leads to performance degradation. Single-User detectors were overtaxed and showed rather poor performance even in multi-path en- vironment [1]. To overcome this problem, in recent years Multi-User Detection (MUD) has received considerable attention and become one of the most important signal processing task in wireless communica- tion. Verdu [1] has proved that the optimal solution is consistent with the optimization of a quadratic function, which yields in MLSE (Maximum-Likelihood Sequence Estimation) receiver. However, to find the optimum is an NP-hard problem as the number of users grows. Many authors proposed sub-optimal linear and nonlinear solu- tions such as Decorrelating Detector, MMSE (Minimum Mean Square Error) detector, Multistage Detector, Hoppfield neural network or Stochastic Hoppfield neural network [1], [2], [3], [4], and the refer- ences therein. One can find a comparison of the performance of the above mentioned algorithms in [5]. Nonlinear sub-optimal solutions provide quite good performance, however, only asymptotically. Quantum computation based algorithms seem to be able to fill this long-felt gap. Beside the classical de- scription, which we recently use, researchers in the early century raised the idea of quantum theory, which nowadays becomes remark- able in coding theory, information theory and for signal processing [6]. Nowadays, every scientist applies classical computation, using se- quential computers. Taking into account that Moore’s law can not be held for the next ten years because silicon chip transistors reach atomic scale, therefore new technology is required. Intel, IBM, AT&T and other companies invest large amount of research to develop de- vices based on quantum principle. Successful experiments share up that within 3-4 years quantum computation (QC) assisted devices will be available on the market as enabling technology for 3G and 4G sys- tems. This paper is organized as follows: in Section II. we shortly review the necessity of multi-user detection, as well as the applied quantum computation principles are shown. In Section III. Grover’s quantum search algorithm is introduced. In Section IV. we discuss the applied system model and the proposed novel multi-user detection algorithm, respectively. Finally we conclude our paper in Section V. II. THEORETICAL BACKGROUNDS A. Multi-User Detection One of the major attributes of CDMA systems is the multiple usage of a common frequency and time slot. Despite the interference caused by the multiple access property, the users can be distinguished by their codes. Let us investigate an uplink DS-DCDMA system, where the symbol of the user is denoted by , . In DS-CDMA systems an information bearing bit is encoded by means of a user specific code of length of the processing gain (PG)[1]. In case of uplink communication we assume perfect power control. In the receiver side it is not required synchronization between input signals and user specific codes, however we make our decision on symbols. Applying BPSK modulation, the output signal of the user, denoted by , is given as where and are the energy associated to the user’s bit and the user continuous signature waveform, respectively denotes, the time duration of one chip, is the chip of the code word of subscriber and refers to the chip elementary waveform, which could be otherwise We investigate a one path uplink wideband CDMA propagation chan- nel, however, an extension to multi-path model could be done, effort- lessly. The channel distortion for the user is modelled by a simple impulse response function , where and are the path gain and the delay of the user, respectively. They are assumed to be constant during a symbol period of . We con- sider uplink scenario because downlink can be regarded as a special, simplified case of uplink. This model contains almost all elements of a typical WCDMA channel except multipath propagation, which was omitted to simplify the explanation of the new quantum computation 0-7803-7400-2/02/$17.00 (C) 2002 IEEE