Peng Hui Tan

Linear interference cancellation in CDMA based on iterative techniques for linear equation systems

It has previously been shown that well known iterations for solving a set of linear equations correspond to linear interference cancellation structures. Here, we suggest applying a block-wise iteration that consists of an outer and an inner iteration. The outer iteration used is the Gauss-Seidel (GS) method, while for the inner iteration, we study direct matrix inversion, the Jacobi over-relaxation iteration, and the conjugate gradient iteration. When a true inner iteration is used, this approach allows for a timely derivation of the acceleration parameters required by advanced iterations. The block iteration is based on a symbol-level implementation which leads to the same detection delay profile for both parallel and serial structures at the expense of differences in the amount of serial processing required. This is discussed in some detail and quantified for comparison. The performance of the detectors is studied via computer simulations where it is found that the block approach can provide significantly faster convergence, leading to improved detection delay over the simpler GS iteration. The improvements are obtained at the expense of an increase in the required serial processing speed.

Constrained maximum-likelihood detection in CDMA

The detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a (0, 1)-constrained maximum-likelihood (ML) problem, a problem which is known to be NP-hard. In contrast, the unconstrained ML problem can be solved quite easily and is known as the decorrelating detector. In this paper, we consider the constrained ML problem where the solution vector is restricted to lie within a closed convex set (CCS). Such a design criterion leads to detector structures which are ML under the constraint assumption. A close relationship between a sphere-constrained ML detector and the well-known minimum mean square error detector is found and verified. An iterative algorithm for solving a CCS constraint problem is derived based on results in linear variational inequality theory. Special cases of this algorithm, subject to a box-constraint, are found to correspond to known, nonlinear successive and parallel interference cancellation structures, using a clipped soft decision for making tentative decisions, while a weighted linear parallel interference canceler with signal-dependent weights arises from the sphere constraint. Convergence issues are investigated and an efficient implementation is suggested. The bit-error rate performance is studied via computer simulations and the expected performance improvements over unconstrained ML are verified.

Multiuser detection in CDMA - a comparison of relaxations, exact, and heuristic search methods

In this paper, we compare several optimization methods for solving the optimal multiuser detection problem exactly or approximately. The purpose of using these algorithms is to provide complexity constraint alternatives to solving this nondeterministic polynomial-time (NP)-hard problem. An approximate solution is found either by relaxation or by heuristic search methods, while the branch and bound algorithm is used to provide an exact solution. Simulations show that these approaches can have bit-error rate (BER) performance which is indistinguishable from the maximum likelihood performance. A tabu search method is shown to be an effective (in terms of BER performance) and efficient (in terms of computational complexity) heuristic when compared to other heuristics like local search and iterative local search algorithms. When the number of users increases, the tabu search method is more effective and efficient than the semidefinite relaxation approach.

The application of semidefinite programming for detection in CDMA

In this paper, a detection strategy based on a semidefinite relaxation of the optimal maximum-likelihood problem is investigated. Cutting planes are also used to strengthen the approximation. The semidefinite program arising from the relaxation can be solved efficiently by interior point methods with polynomial complexity in the number of users. The simulated bit error rate performance shows that this approach provides a good approximation to the ML detector.

Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation

In this paper, a class of nonlinear minimum mean-squared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multiple-access interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference-cancellation scheme. Corresponding multiuser soft-input, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Finally, a large-system performance analysis is conducted for the simplified PDA, showing that the bit-error rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large-system prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance

Box-constrained maximum-likelihood detection in CDMA

The detection strategy usually denoted optimal multiuser detection is equivalent to the solution of a (0,1)-constrained maximum-likelihood (ML) problem, a problem which is known to be NP-complete. In contrast, the unconstrained ML problem can be solved quite easily and is known as the decorrelating detector. In this paper, we consider the box-constrained ML problem and suggest a general iterative solution algorithm. Special cases of this algorithm correspond to known, nonlinear successive and parallel interference cancellation structures, using a clipped soft decision function for making tentative decisions. These structures are therefore maximum-likelihood under the assumption that the detected data vector is constrained to lie within a hypercube. Convergence issues are investigated and an efficient implementation is suggested. The BER performance is studied via computer simulations and the expected performance improvements over unconstrained ML is verified.

A reactive tabu search heuristic for multiuser detection in CDMA

In this paper, a heuristic detection strategy for approximating the solution the optimal maximum-likelihood (ML) problem is investigated. The heuristic detector is based on a reactive tabu search, where a local descent algorithm is complemented by a list of forbidden moves in order to diversify the search. It adheres to the symbol constraints and performs local moves in the space of feasible solutions. The simulated bit error rate performance shows that this approach provides a good approximation to the ML detector.

Iterative multiuser decoding based on probabilistic data association

We propose a low complexity soft-input/soft-output multiuser detector based on probabilistic data association. This new scheme has a total computational complexity of O(K2) + O(2ν) per user, which is the same as the complexity of linear soft-input/soft-output multiuser detectors. Numerical results demonstrate that the proposed detector, together with rate 1/2 error control coding, outperforms linear alternatives and achieves single-user performance at loads beyond 2N users, where N is the processing gain.

Belief Propagation for Coded Multiuser Detection

In this paper a simplified parallel belief propagation (BP) algorithm is suggested as a suboptimal soft-input soft-output multiuser detector in an iterative multiuser decoding scheme. The iterative decoding scheme itself is based on applying an outer BP algorithm for message passing between the BP multiuser detector and the single-user decoders. The performance of the iterative decoding process is investigated based on parallel scheduling of the outer BP algorithm. In addition, we analyze the large system BER performance of the corresponding multiuser decoding algorithms. By making Gaussian assumptions on the output of the single-user decoders and the BP multiuser detector, we derive expressions which describe approximately the BER performance of the algorithms. Finally, numerical examples are presented, demonstrating the accuracy of this approximation

Linear interference cancellation in CDMA based on block iterations

It has previously been shown that well-known iterations for solving a set of linear equations correspond to linear interference cancellation structures for short-code CDMA. Here, we suggest applying a block-wise iteration which consists of an outer and an inner iteration. This approach makes it possible to extend the equivalence to include long-code asynchronous CDMA. The outer iteration used is the Gauss-Seidel method while for the inner iteration, we study the Jacobi and the Gauss-Seidel iterations, their over-relaxation extensions as well as the conjugate gradient iteration. It is then possible to relate all the iterations to cancellation structures directly in the time domain and to determine relaxation factors in a timely manner. The performance of the detectors is studied via computer simulations.