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A Low-Complexity High-Performance Preprocessing Algorithm for Multiuser Detection using Gold Sequences
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-6957-2603
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2008 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 9, 4377-4385 p.Article in journal (Refereed) Published
Abstract [en]

The optimum multiuser detection problem can be formulated as a maximum likelihood problem, which yields a binary quadratic programming problem to be solved. Generally this problem is NP-hard and is therefore hard to solve in real time. In this paper, a preprocessing algorithm is presented which makes it possible to detect some or all users optimally for a low computational cost if signature sequences with low cross correlation, e.g., Gold sequences, are used. The algorithm can be interpreted as, e.g., an adaptive tradeoff between parallel interference cancellation and successive interference cancellation. Simulations show that the preprocessing algorithm is able to optimally compute more than 94,% of the bits in the problem when the users are time-synchronous, even though the system is heavily loaded and affected by noise. Any remaining bits, not computed by the preprocessing algorithm, can either be computed by a suboptimal detector or an optimal detector. Simulations of the time-synchronous case show that if a suboptimal detector is chosen, the bit error rate (BER) rate is significantly reduced compared with using the suboptimal detector alone.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2008. Vol. 56, no 9, 4377-4385 p.
Keyword [en]
Code division multiple access, Computational complexity, Error statistics, Interference suppression, Maximum likelihood detection, Multiuser detection, Quadratic programming, Sequences, CDMA channel models, Gold sequences, NP-hard problem, Binary quadratic programming problem, Bit error rate, Low cross correlation, Low-complexity high-performance preprocessing algorithm, Maximum likelihood problem, Optimal detector, Optimum multiuser detection problem, Parallel interference cancellation, Suboptimal detector, Successive interference cancellation, Time-synchronous users
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-12903DOI: 10.1109/TSP.2008.926190OAI: oai:DiVA.org:liu-12903DiVA: diva2:17353
Available from: 2008-03-18 Created: 2008-03-18 Last updated: 2017-12-13
In thesis
1. Integer Quadratic Programming for Control and Communication
Open this publication in new window or tab >>Integer Quadratic Programming for Control and Communication
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main topic of this thesis is integer quadratic programming with applications to problems arising in the areas of automatic control and communication. One of the most widespread modern control methods is Model Predictive Control (MPC). In each sampling time, MPC requires the solution of a Quadratic Programming (QP) problem. To be able to use MPC for large systems, and at high sampling rates, optimization routines tailored for MPC are used. In recent years, the range of application of MPC has been extended to so-called hybrid systems. Hybrid systems are systems where continuous dynamics interact with logic. When this extension is made, binary variables are introduced in the problem. As a consequence, the QP problem has to be replaced by a far more challenging Mixed Integer Quadratic Programming (MIQP) problem, which is known to have a computational complexity which grows exponentially in the number of binary optimization variables. In modern communication systems, multiple users share a so-called multi-access channel. To estimate the information originally sent, a maximum likelihood problem involving binary variables can be solved. The process of simultaneously estimating the information sent by multiple users is called Multiuser Detection (MUD). In this thesis, the problem to efficiently solve MIQP problems originating from MPC and MUD is addressed. Four different algorithms are presented. First, a polynomial complexity preprocessing algorithm for binary quadratic programming problems is presented. By using the algorithm, some, or all, binary variables can be computed efficiently already in the preprocessing phase. In numerical experiments, the algorithm is applied to unconstrained MPC problems with a mixture of real valued and binary valued control signals, and the result shows that the performance gain can be significant compared to solving the problem using branch and bound. The preprocessing algorithm has also been applied to the MUD problem, where simulations have shown that the bit error rate can be significantly reduced compared to using common suboptimal algorithms. Second, an MIQP algorithm tailored for MPC is presented. The algorithm uses a branch and bound method where the relaxed node problems are solved by a dual active set QP algorithm. In this QP algorithm, the KKT systems are solved using Riccati recursions in order to decrease the computational complexity. Simulation results show that both the proposed QP solver and MIQP solver have lower computational complexity compared to corresponding generic solvers. Third, the dual active set QP algorithm is enhanced using ideas from gradient projection methods. The performance of this enhanced algorithm is shown to be comparable with the existing commercial state-of-the-art QP solver \cplex for some random linear MPC problems. Fourth, an algorithm for efficient computation of the search directions in an SDP solver for a proposed alternative SDP relaxation applicable to MPC problems with binary control signals is presented. The SDP relaxation considered has the potential to give a tighter lower bound on the optimal objective function value compared to the QP relaxation that is traditionally used in branch and bound for these problems, and its computational performance is better than the ordinary SDP relaxation for the problem. Furthermore, the tightness of the different relaxations is investigated both theoretically and in numerical experiments.

Place, publisher, year, edition, pages
Institutionen för systemteknik, 2008. 231 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1158
Keyword
Integer Quadratic Programming, Model Predictive Control, Hybrid Systems, Semidefinite Programming, Code Division Multiple Access, Multiuser Detection, Automatic Control, Communication
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-10642 (URN)978-91-85523-03-0 (ISBN)
Public defence
2008-02-27, Visionen, Hus C, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Note
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the Linköping University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this material, you agree to all provisions of the copyright laws protecting it.Available from: 2008-03-18 Created: 2008-03-18 Last updated: 2016-08-31

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Axehill, DanielHansson, AndersGunnarsson, Fredrik

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