Bandwidth-constrained signature waveforms for maximizing thenetwork capacity of synchronous CDMA systems

Synchronous code-division multiple-access systems where each receiver is a minimum mean-squared-error receiver and each user has the same received power, signaling rate, and required signal-to-interference ratio are considered. Based on the results Viswanath, Anantharam and Tse (see IEEE Trans. Inform. Theory, vol.45, p.1968-83, 1999), the optimal signature waveforms under both fractional out-of-band energy and root-mean-square bandwidth constraints that maximize the network capacity are determined. Comparison to various suboptimal signature waveforms, including the ones constructed from rectangular pulses, is also made to quantify the gain achieved by the optimal signature waveforms     

Bandwidth-constrained signature waveforms and Walsh signal space receivers for synchronous CDMA systems

Synchronous CDMA systems whose transmission bandwidth is quantified through the fractional out-of-band energy (FOBE) constraint are considered. Either a conventional matched filter (MF) receiver or a minimum mean-square error (MMSE) receiver is employed for users' data detection. The total squared correlation (TSC) and the total mean-square error (TMSE) are proposed as the performance parameters for the MF and MMSE receivers respectively. These parameters need to be minimized in order to maximize the signal-to-interference ratios (SIRs) at the receivers' outputs. For a given FOBE bandwidth constraint, the sets of signature waveforms that minimize either TSC or TMSE are obtained from the prolate spheroidal wave functions (PSWFs). Furthermore, if the number of users is the size of a Hadamard matrix, then optimal signature waveforms can be obtained to maximize the individual SIR for every user. Due to the complicated nature of the PSWFs, simplified MF and MMSE receivers based on the Walsh signal space are developed.     

User-capacity maximization in synchronous CDMA subject to RMS-bandlimited signature waveforms

We consider the symbol-synchronous code-division multiple-access (CDMA) channel equipped with either a multiuser linear receiver or a multiuser decision-feedback receiver. The network, or user, capacity is defined to be the number of users that can be supported with available resources, such that every user achieves a certain quality of service (QoS). In this paper, the QoS threshold is given as a signal-to-interference ratio and the bandwidth is given as the root mean squared bandwidth of the received power spectral density of the users' transmitted waveforms. Given the QoS threshold and constraints on bandwidth and the sum of the users' received powers, we maximize user capacity for both the linear and decision-feedback receivers by optimally and jointly designing the users' signature waveforms and power-control polices.     

Iterative construction of optimum signature sequence sets insynchronous CDMA systems

Optimum signature sequence sets that maximize the capacity of single-cell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number of users is less than or equal to the processing gain, and a set of Welch (1994) bound equality (WBE) sequences, otherwise. We present an algorithm where users update their transmitter signature sequences sequentially, in a distributed fashion, by using available receiver measurements. We show that each update decreases the TSC of the set, and produces better signature sequence sets progressively. We prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain. We observe and conjecture that the algorithm converges to a WBE set when the number of users is greater than the processing gain. At each step, the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error (MMSE) receiver corresponding to that signature sequence. Since the MMSE filter can be obtained by a distributed algorithm for each user, the proposed algorithm is amenable to distributed implementation     

A new multistage detector for synchronous CDMA communications

In this paper, we develop a new multistage detector to approach the optimal solution of the detection problem in a synchronous code division multiple access (CDMA) system. The transformation modifies the diagonal elements of the Hessian matrix of the quadratic likelihood function and brings the continuous minimum of the transformed function as close to the optimal solution as possible. The computational complexity is essentially linear with the number of users, except that a few computations of a quadratic function are needed     

Dynamic signature assignment for direct sequence CDMA systems

Multiple access interference (MAI) is one of the major impediments in the reverse link of wide band CDMA systems, due to the synergy of the users' spreading codes, transmission delays and the channel characteristics. We propose to dynamically assign the users' spreading codes and transmission delays, i.e., to assign the user signature, in order to minimize mutual cross-correlations at the receiver. This dynamic signature assignment (DSA) approach helps to avoid (as opposed to combating) MAI at the base station. In assigning the signatures, we present a low-complexity iterative algorithm which utilizes channel information and is able to minimize signal-to-interference-plus-noise (SINR) ratio at receivers. Computer simulation results are presented which show a potential 2-3 fold capacity increase over conventional systems     

New suboptimal multiuser detectors for synchronous CDMA systems

In code-division multiple access (CDMA) systems, the optimal multiuser detection is equivalent to an unconstrained quadratic bivalent optimization problem, and its computational complexity increases exponentially with the number of users. In this paper, we propose several new suboptimal detectors with a greatly reduced computational complexity based on a local minimization algorithm for a synchronous CDMA system. The performances of these detectors are compared with those of the conventional, optimal, and several other suboptimal detectors     

Antenna-diversity-assisted genetic-algorithm-based multiuser detection schemes for synchronous CDMA systems

A spatial diversity reception assisted multiuser code-division multiple-access detector based on genetic algorithms (GAs) is proposed. Two different GA-based individual-selection strategies are considered. In our first approach, the so-called individuals of the GA are selected for further exploitation, based purely on the sum of their corresponding figures of merit evaluated for the individual antennas. According to our second strategy, the GA's individuals are selected based on the concept of the so-called Pareto optimality, which uses the information from the individual antennas independently. Computer simulations showed that the GAs employing the latter strategy achieve a lower bit-error rate as compared to the former strategy. For a 15-user GA-assisted system employing a spreading factor of 31, a complexity reduction factor of 81 was achieved at a performance identical to that of the optimum multiuser detector using a full search.     

RMS bandwidth constrained signature waveforms that maximize thetotal capacity of PAM-synchronous CDMA channels

Optimum time-limited signal sets of equal and unequal energies are obtained under root mean square (RMS) bandwidth constraints. The total capacity and the total asymptotic efficiency of the PAM synchronous Gaussian CDMA (PSG-CDMA) channel are considered as the optimality criteria. The latter measure is monotonic with the determinant of the correlation matrix, R, and the former is monotonic with det(I+σ ^-2R), where σ² represents the noise level. Average as well as maximum RMS bandwidth constraints are considered in the equal-energy case, and the energy-weighted RMS bandwidth constraint is considered for unequal energy signals. For the equal-energy problem, signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum RMS bandwidth constraints. For the total capacity measure, such simultaneously optimal signal sets are also obtained, albeit under the restriction that the number of signals n be a Hadamard matrix dimension. When the Hadamard dimension is in particular a power of two, we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded PSG-CDMA channel. Unequal energy signal sets are also found under an energy-weighted RMS bandwidth constraint for both optimality criteria     

The design and performance analysis for several new classes ofcodes for optical synchronous CDMA and for arbitrary-medium time-hoppingsynchronous CDMA communication systems

New families of spread-spectrum codes are constructed, that are applicable to optical synchronous code-division multiple-access (CDMA) communications as well as to arbitrary-medium time-hopping synchronous CDMA communications. Proposed constructions are based on the mappings from integer sequences into binary sequences. The authors use the concept of number theoretic quadratic congruences and a subset of Reed-Solomon codes similar to the one utilized in the Welch-Costas frequency-hop (FH) patterns. The properties of the codes are as good as or better than the properties of existing codes for synchronous CDMA communications: both the number of code-sequences within a single code family and the number of code families with good properties are significantly increased when compared to the known code designs. Possible applications are presented. To evaluate the performance of the proposed codes, a new class of hit arrays called cyclical hit arrays is recalled, which give insight into the previously unknown properties of the few classes of number theoretic FH patterns. Cyclical hit arrays and the proposed mappings are used to determine the exact probability distribution functions of random variables that represent interference between users of a time-hopping or optical CDMA system. Expressions for the bit error probability in multi-user CDMA systems are derived as a function of the number of simultaneous CDMA system users, the length of signature sequences and the threshold of a matched filter detector. The performance results are compared with the results for some previously known codes     

二维同步OCDMA系统的性能分析

构造了一种用于二维同步光码分多址(OCDMA)系统的修正素数跳频码(MPC/PC),分析了码字的自相关和互相关性能,研究了二维同步OCDMA系统的误码率和吞吐量性能.结果表明,与一维同步OCDMA系统相比,二维同步OCDMA系统的可接入用户数大大增加,误码率大大降低,吞吐量明显提高.     

Performances of acquisition schemes for CDMA systems with complex signature sequences

This paper investigates the acquisition performance of code-division multiple-access communication systems using deterministic complex signature sequences. Unlike most earlier studies, performances are obtained in the presence of multiple user interference, and the results can be applied to complex as well as binary signature sequences. Two serial search acquisition schemes are considered. The first scheme assumes that there is no data in the reference user's signal until the acquisition is achieved. The second scheme allows data modulation in the reference user's signal during the acquisition process. Probability of detection and probability of false alarm of both schemes are obtained without using the Gaussian approximation. Instead, a discrete approximation of the probability density function of the MUI is used in performance evaluations. Numerical results are presented for example sets of Gold, 4-phase, and FZC sequences. They show that complex and binary sequences have comparable acquisition performances. Results also show significant degradation of acquisition performances as the number of users increases.     

Variable-length code construction for incoherent optical CDMA systems

The purpose of this study is to investigate the multirate transmission in fiber-optic code-division multiple-access (CDMA) networks. In this article, we propose a variable-length code construction for any existing optical orthogonal code to implement a multirate optical CDMA system (called as the multirate code system). For comparison, a multirate system where the lower-rate user sends each symbol twice is implemented and is called as the repeat code system. The repetition as an error-detection code in an ARQ scheme in the repeat code system is also investigated. Moreover, a parallel approach for the optical CDMA systems, which is proposed by Marić et al., is also compared with other systems proposed in this study. Theoretical analysis shows that the bit error probability of the proposed multirate code system is smaller than other systems, especially when the number of lower-rate users is large. Moreover, if there is at least one lower-rate user in the system, the multirate code system accommodates more users than other systems when the error probability of system is set below 10⁻⁹.     

Optimal sequences and sum capacity of synchronous CDMA systems

The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints-this solves the open problem posed by Rupf and Massey (see ibid., vol.40, p.1261-6, 1994) which had solved the equal power constraint case. We identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them     

Multilevel trellis-coded modulations for mobile multimedia satellite systems using synchronous CDMA

In this paper the performance of multilevel trellis-coded modulations (MTCMs) for satellite mobile multimedia systems using synchronous CDMA is investigated. A model for the multiple-access interference arising from the non-orthogonality of the spreading waveforms is developed for different modulation and spreading schemes and transmission over the mobile satellite channel. Using this model, the performance of MTCMs for synchronous CDMA is analysed and compared with the Ungerboeck and Schegel–Costello trellis-coded modulation (TCM) designs. The impact on the transmission of synchronization errors between the different users is presented and the power control requirements are derived. © 1998 John Wiley & Sons, Ltd.     

User capacity for synchronous multirate CDMA systems with linear MMSE receivers

The performance of linear minimum mean-square error (MMSE) multiuser receivers in a dual-rate synchronous direct-sequence code-division multiple-access (DS-CDMA) system is investigated using the random spreading sequence analysis. Multicode (MC) systems and different variants of variable spreading length (VSL) systems are studied. User capacity regions are obtained for these systems.     

Blind code-timing estimation for CDMA systems with bandlimited chip waveforms in multipath fading channels

In this paper, we present a blind code-timing estimator for asynchronous code-division multiple-access (CDMA) systems that use bandlimited chip waveforms. The proposed estimator first converts the received signal to the frequency domain, followed by a frequency deconvolution to remove the convolving chip waveform, and then calculates the code-timing estimate from the output of a narrowband filter with a sweeping center frequency, which is designed to suppress the overall interference in the frequency domain. The proposed estimator is near-far resistant, and can deal with time- and frequency-selective channel fading. It uses only the spreading code of the desired user, and can be adaptively implemented for both code acquisition and tracking. We also derive an unconditional Crame/spl acute/r-Rao bound (CRB) that is not conditioned on the fading coefficients or the information symbols. It is a more suitable lower bound than a conditional CRB for blind code-timing estimators which do not assume knowledge of the channel or information symbols. We present numerical examples to evaluate and compare the proposed and several other code-timing estimators for bandlimited CDMA systems.     

A low complexity multiuser detector for synchronous CDMA system

In a code-division multiple-access (CDMA) system, multiuser detection (MUD) can exploit the information of signals from other interfering users to increase the system capacity. However, the optimum MUD for CDMA systems requires the solution of an NP-hard combinatorial optimization problem. It is well known that the computational complexity of the optimum multiuser detector is exponential with the number of active users in the system. In this paper, we apply a hybrid algorithm to develop a suboptimal MUD strategy. The result of symmetric successive overrelaxation (SSOR) preconditioned conjugate-gradient method is first used to initialize the reduced-complexity recursive (RCR) multiuser detector. Then, RCR algorithm is applied to detect the received data bit by optimizing an objective function in relation with the linear system of decorrelating detector. Simulation results for the synchronous case show that the performance of our proposed SSOR-RCR multiuser detector is promising and outperform the decorrelator and linear minimum mean squared error multiuser detector with lower computational complexity.     

Performances of DPSK and FSK CDMA systems with complex signature sequences

This paper investigates the performance of direct‐sequence code‐division multiple‐access (CDMA) communication systems in Gaussian noise channels using binary and M‐ary noncoherent signaling schemes with complex signature sequences. Differential‐phase‐shift‐keyed (DPSK) signaling with differentially coherent demodulation and frequency‐shift‐keyed (FSK) signaling with noncoherent demodulation are considered. Upper and lower bounds are presented for the probability of bit error (p.b.e.) of binary DPSK and binary FSK systems when the number of users is small. Simulation and Gaussian approximation are used to obtained the p.b.e. when the number of users is large. Two types of complex sequences (FZC and 4‐phase sequences) and one type of binary sequences (Gold sequences) are used for evaluating numerical results. Results show that complex sequences outperform binary sequence when the number of users is small. However, as the number of users gets large, all sequences have similar performances. These suggest that complex sequences should be used when the number of users is small, but binary sequences should be used when the number of users is large, as binary sequences are easier to generate. This revised version was published online in June 2006 with corrections to the Cover Date.     

Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

Overloaded code division multiple access being the only means of the capacity extension for conventional code division multiple access accommodates more number of signatures than the spreading gain. Recently, ternary Signature Matrices with Orthogonal Subsets (SMOS) has been proposed, where the capacity maximization is 200%. The proposed multi‐user detector using matched filter exploits the twin tree hierarchy of correlation among the subsets to guarantee the errorless recovery. In this paper, we feature the non‐ternary version of SMOS (i.e., 2k‐ary SMOS) of same capacity, where the binary alphabets in all the k constituent (orthogonal) subsets are unique. Unlike ternary, the tree hierarchy for 2k‐ary SMOS is non‐uniform. However, the errorless detection of the multi‐user detector remains undeviated. For noisy transmission, simulation results show the error performance of the right child for each subset of 2k‐ary to be significantly improved over the left. The optimality of the right child of the largest (Hadamard) subset is also discovered. At higher loading, for larger and smaller subsets the superiority is reported for the 2k‐ary and ternary, respectively, and the counter‐intuitive deviations observed for the lower loading scenarios are logically explained. For the overall capacity maximization being 150%, superiority is featured by the 2k‐ary, but beyond, it becomes a conditional entity. Copyright © 2016 John Wiley & Sons, Ltd.