Polynomial complexity optimal multiuser detection for a wider class of problems

The optimum multiuser detection problem was shown to be NP-hard, i.e., its computational complexity increases exponentially with the number of users (Verdu 1986, 1989). In this letter, we show that the optimum multiuser detection problem for a synchronous code-division multiple access (CDMA) system is equivalent to the minimum capacity cut problem in a related network and propose an optimum multiuser detection algorithm with polynomial computational complexity for a certain class of signature sequences. The minimum cut problem is solvable in polynomial time if the capacities of the links not incident to source and sink are nonnegative. This condition in the optimum detection problem is equivalent to all cross correlations between the signature sequences of the users being negative. One example of such a set of signature sequences is obtained when shifted versions of the maximal length sequences (or m-sequences) are used. In this case the cross correlation between users i and j is given as /spl Gamma//sub ij/=-1/G for all i,j, where G is the processing gain.

Gold functions are well-known for designing sequences with good correlation properties. This paper reveals a fascinating relationship between Gold functions and Golay-Davis-Jedwab (GDJ) Boolean functions to design sequences with low correlation and low PAPR, which is the first of its kind. The bent and semi-bent properties of the Gold functions are utilized to derive the correlation of the resultant binary spreading sequence sets, while the complementary properties of the GDJ Boolean functions are used to derive the low PAPR. Based on this idea we propose three new sets of binary spreading sequences with low PAPR and low correlation. The proposed sequence sets have the potential to be used as spreading sequences in non-orthogonal multiple access (NOMA). They have a very large set size, which in turn results in a high overloading factor as compared to the existing sequence sets with the same length and the same correlation, which are generated through systematic constructions.

Near-far resistance is one of the most important performance measures in a multiuser communication system, especially in a code division multiple access (CDMA) system. The optimum multiuser detector can achieve the optimum near-far resistance. However, due to its high computational complexity, the optimum detector is impractical to implement. Nevertheless, computation of the near-far resistance of the optimum multiuser detector is still important since it is the least upper bound on the near-far resistance of any detector, as well as a benchmark for relative performance of any suboptimum detector. Lupas et al. and Zvonar et al. provided the computation of the optimum near-far resistance in the asynchronous AWGN and unipath channel case. In this paper, we extend the above results to the asynchronous multipath channel case. We derive the optimum near-far resistance under the assumption of a common identifiability condition in the blind multiuser detection/equalization literature. We also derive the ideal near-far resistance of three typical methods in blind multiuser detection/equalization (subspace, linear prediction, and constrained optimization) and compare them with that of the optimum detector. Two methods to enhance near-far resistance of suboptimum detectors are also presented. Furthermore, one possible cause that may affect the near-far resistance in a practical setting is analyzed. The computational complexity of the proposed methods is analyzed and compared. Simulations confirm the theoretical findings.

Near-far resistance is one of the most important performance measures in a CDMA multiuser communication system, especially when power control is difficult to implement, such as in an ad hoc wireless network. The optimum multiuser detector can achieve the optimum near-far resistance. But due to its high computational complexity, the optimum detector is impractical to implement. Cost-effective suboptimum detectors, i.e., linear detectors, are more practical to implement. However, the optimality in near-far resistance is generally lost. We examine the structural differences of the channel matrix between the optimum and the suboptimum detectors. A transmission scheme is then proposed that almost restores the near-far resistance of the suboptimum detectors to that of the optimum one, at least theoretically. Computer simulations are performed to verify the theoretical findings.

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with the method proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

For suppressing multiple access interference (MAI) in a CDMA communication system, complementary sequence sets are employed as spreading sequences in such system. In this paper, we present a method for constructing a family of quaternary periodic complementary sequence sets, which arises from the conversion of the existing binary periodic complementary sequence sets with odd period of sub-sequences. The period of sub-sequences in the proposed sequence sets is twice as long as the one of the binary sequence sets employed, which is a drawback in the proposed method. Finally, some examples are given in order to illuminate the validity of the new method.

The problem of blind despreading of short-code direct sequence spread-spectrum signal in asynchronous or synchronous system is considered. A novel blind estimation algorithm for time offset, spreading and information sequences is presented in this paper. Firstly, the received signal is divided into two-information-period-length temporal vectors overlapped by one-information-period and accumulates these vectors one by one to form the accumulated matrix. The algorithm exploits an unbiased estimation of user’s time offset to realize synchronization blindly, and an operation of singular value decomposition is applied to the intercepted matrix, which is intercepted from the accumulated matrix according to user’s time offset. Lastly, the spreading sequence is recovered from a right singular vector blindly; therefore, the shortcomings of traditional algorithms, such as phase ambiguity when make use of two vectors to form the spreading sequence, are avoided. And the information sequence is then recovered blindly from the left singular vector. Simulation results show that the new method is capable of retrieving time offset, the spreading and information sequences with higher accuracy than previous methods.

In multiuser detection for a direct-sequence code division multiple access system, the genetic algorithm based multiuser detector (GA-MUD) is regarded as a feasible scheme that exhibits the near optimum performance yet requires less computational complexity than the optimum multiuser detector does. Through a new measurement called the computational efficiency, this paper indicates that the improper configuration of the fixed generation number makes most computations in the GA-MUD redundant. To overcome this problem, we propose a novel redundancy-saving genetic algorithm (RSGA) in this paper. The simulation result shows that the RSGA can effectively remove the unnecessary iterations with slight performance degradation and exploit the real potential of the GA-MUD. Hence, the computational complexity of the GA-MUD can be significantly reduced by eliminating the redundancy. Due to its simplicity, the proposed scheme can be applied to all varieties of GA-MUD and does not cause additional computation burden.

This paper presents a generation method of an orthogonal set of real-valued periodic orthogonal sequences which has fast correlation algorithm. The periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and its orthogonal set is the set of the sequences whose periodic crosscorrelation function of the zero shift is zero. The real-valued periodic orthogonal sequence of period N = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> with positive integer n is derived from a real-valued Huffman sequences of length M = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sup> + 1 with positive integer v and v ≥ n which has the aperiodic autocorrelation function with zero sidelobes except at left and right shift-ends. The set of real-valued periodic orthogonal sequences can be sufficiently applied to various systems, such as synchronous CDMA systems and digital watermarkings.

The receiver in a wireless communication system has the task of computing good estimates for the data symbols that have been transmitted. The best (optimum) detector is the Maximum Likelihood (ML) detector. However, it requires a high computational complexity. This work aims to efficiently detect the transmitted symbols with a reduced complexity. In order to produce a near optimum receiver, two methods are presented. These methods are obtained by convex optimization relaxations which yield global optimum solutions. The relaxations are combined with the idea of using the structure of the channel matrix to reduce the computational complexity. The channel matrix exhibits a banded Toeplitz structure. In each case, the dual problem of the convex optimization relaxation is solved to estimate the noise power. Gradient descent algorithm is used to solve the dual problem in the first relaxation while the bisection method is applied for the second relaxation. In both cases, the result is a Generalized Minimum Mean Squared Error (GMMSE) detector which has a form similar to the Minimum Mean Square Error (MMSE) detector and a performance almost the same as the MMSE detector, but it is not require the knowledge of the noise power. The GMMSE detectors can be used in scenarios where adapted or blind adaptive detection is not suitable, for instance when the channel is rapidly changing. Using a circular approximation of banded Toeplitz matrix the Fast Fourier Transform (FFT) can be applied to reduce the computational complexity of the detectors. Finally, the local search method is applied to enhance the performance of the proposed GMMSE detector. The proposed detector is a near optimum detector with low computational complexity.

In this paper, we consider a system with K single-antenna client users, n/sub B/ base stations (each base station has n/sub B/ antennas) as well as a centralized controller. All the base stations operate at the same frequency and have optimal multi-user detection per base-station. A client user could be associated with a single base station at any time. We consider a general problem of uplink macroscopic scheduling where the centralized controller dynamically determines an appropriate association mapping of the K users with respect to the n/sub B/ base stations over a macroscopic time scale. We propose a novel analytical framework for the above macroscopic scheduling problems. A simple rule is to associate a user with the strongest base station (camp-on-the-strongest-cell) and this has been widely employed in conventional cellular systems. However, based on the optimization framework, we found that this conventional approach is in fact not optimal when multi-user detection is employed at the base station. We show that the optimal macroscopic scheduling algorithm is of exponential complexity and we propose a simple greedy algorithm as a feasible solution. It is shown that the macroscopic scheduling gain relative to the conventional approach increases with increasing n/sub B/ (due to the extra degree of freedom introduced by multiple antennas) and decreasing path loss exponent (due to large area of overlapping).

In this letter, new sets of non-orthogonal spreading sequences are constructed for uplink grant-free access of devices. Based on Golay complementary sequences and sets, the spreading sequences have theoretically bounded low peak-to-average power ratio (PAPR) for multicarrier transmission. Also, the corresponding spreading matrix has theoretically bounded low coherence, which guarantees the reliable performance of compressed sensing (CS) based joint channel estimation (CE) and multiuser detection (MUD). While the spreading sequence set accommodates up to 300% overloaded devices, a large number of distinct sequence sets can also be constructed for future applications. Simulation results demonstrate that the Golay-based sequences exhibit the PAPR of at most 4, which is lower than those for random bipolar, Gaussian, and Zadoff-Chu (ZC) sequences. We also observe that the Golay-based sequences provide the reliable performance for CS-based joint CE and MUD. Finally, the Golay-based sequences have fewer phases than ZC sequences, which can be more suitable for low cost devices in machine-type communications (MTC).

We consider decentralized diagnosis in discrete event systems that are modeled as non-deterministic finite automata and are observed, through distinct natural projection maps, at multiple observation sites. Specifically, we consider a scenario where two or more observers (each with its own map) are allowed to communicate their assessments (state estimates and matching normal/failure conditions) to a centralized location which then makes an overall decision based on the intersection of the local state estimates and their matching conditions. This intersection based decentralized diagnosis (IBDD) scheme can be implemented with polynomial complexity, both at the observation sites and at the centralized location. It is shown that IBDD can be verified with an algorithm of polynomial complexity that constructs verifiers for the observation sites, and analyzes properties of their parallel composition and product with the system.

Optimum multiuser detection (OMD) in direct-sequence code-division multiple access (DS-CDMA) communication systems is a combinatorial optimization problem and has been proven NP-complete. Many heuristics have been presented to solve this problem, but few of them consider the fitness landscape of OMD carefully. In this paper, we analyze the fitness landscape of OMD, including the neighborhood structure and the distribution of local optima. Numerical results give hints on how to design efficient heuristic algorithms for the problem. A meta-heuristic algorithm considering the analysis results is proposed With a proper local search and a well-chosen perturbation strategy, the proposed algorithm can find the (near) optimal solution rapidly with lower computational complexity. Simulation results show it outperforms other heuristic multiuser detection algorithms when the number of users is large. In the condition of small number of users, it can achieve the bit error rate (BER) bound of OMD.

In this paper, we propose a new multiuser detector that is based on the explicit estimation of Lagrange multipliers. The optimum multiuser detector, proposed by S. Verdu in 1986, is a binary quadratic problem. It belongs to NP hard problems and can not be used currently. In this paper, the binary quadratic problem is changed into a quadratic optimization problem with equation constraints, and then written in Lagrange form, the relationship between the Lagrange multipliers, user information codes and channel noise is derived. According to different methods of estimating Lagrange multipliers, two existing multiuser detectors are given: decorrelation and minimum mean-squared error (MMSE) detectors. According to the special features of the multiuser detection problem, a new method of estimating Lagrange multipliers is given in this paper and then a new multiuser detector is obtained. The numerical results showed that the bit-error-ratio (BER) of the new detector is close to that of the optimum multiuser detector and less than that of sub-optimum multiuser detection.