Effective interference and effective bandwidth of linear multiuserreceivers in asynchronous CDMA systems

The performance of linear multiuser receivers in terms of the signal-to-interference ratio (SIR) achieved by the users has been analyzed in a synchronous CDMA system under random spreading sequences. In this paper, we extend these results to a symbol-asynchronous but chip-synchronous system and characterize the SIR for linear receivers-the matched-filter receiver the minimum mean-square error (MMSE) receiver and the decorrelator. For each of the receivers, we characterize the limiting SIR achieved when the processing gain is large and also derive lower bounds on the SIR using the notion of effective interference. Applying the results to a power controlled system, we derive effective bandwidths of the users for these linear receivers and characterize the user capacity region: a set of users is supportable by a system if the sum of the effective bandwidths is less than the processing gain of the system. We show that while the effective bandwidth of the decorrelator and the MMSE receiver is higher in an asynchronous system than that in a synchronous system, it progressively decreases with the increase in the length of the observation window and is asymptotic to that of the synchronous system, when the observation window extends infinitely on both sides of the symbol of interest. Moreover, the performance gap between the MMSE receiver and the decorrelator is significantly wider in the asynchronous setting as compared to the synchronous case     

Optimal sequences, power control, and user capacity of synchronousCDMA systems with linear MMSE multiuser receivers

There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spread-spectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (S-CDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its quality-of-service (QoS) requirement (expressed in terms of its desired signal-to-interference ratio) met. This characterization allows one to describe the user capacity through a simple effective bandwidth characterization: users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity     

Linear multiuser receivers: effective interference, effectivebandwidth and user capacity

Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. We show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison     

Iterative Group-Blind Multiuser Detection and Decoding With Signal Rank Estimation for Coded CDMA Systems

In this paper, a turbo receiver structure is proposed for the uplink of coded code-division multiple-access (CDMA) systems in the presence of unknown users. The proposed receiver consists of two stages following each other. The first stage performs soft interference cancellation and group-blind linear minimum mean square error (MMSE) filtering, and the second stage performs channel decoding. The proposed group-blind linear MMSE filter suppresses the residual multiple-access interference (MAI) from known users based on the spreading sequences and the channel characteristics of these users while suppressing the interference from other unknown users using a subspace-based blind method. The proposed receiver is suitable for suppressing intercell interference in heavily loaded CDMA systems. Since the knowledge of the number of unknown users is crucial for the proposed receiver structure, a novel estimator is also proposed to estimate the number of unknown users in the system by exploiting the statistical properties of the received signal. Simulation results demonstrate that the proposed estimator can provide the number of unknown users with high accuracy; in addition, the proposed group-blind receiver integrated with the new estimator can significantly outperform the conventional turbo multiuser detector in the presence of unknown users.      

Resource pooling and effective bandwidths in CDMA networks withmultiuser receivers and spatial diversity

Much of the performance analysis on multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems is focused on worst case near-far scenarios. The user capacity of power-controlled networks with multiuser receivers are less well-understood. Tse and Hanly (see ibid., vol.45, p.541-657, 1999) have shown that under some conditions, the user capacity of an uplink power-controlled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. We show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signal-to-interference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of “resource pooling” arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas     

An Adaptive MMOE-PIC Detector for Asynchronous DS-CDMA Communications

We propose a modified linear parallel interference cancelation (PIC) structure using the adaptive minimum mean output-energy (MMOE) algorithm for direct-sequence code-division multiple-access (DS-CDMA) systems. The complexity of the proposed receiver structure is shown to be linear in the number of users and hence, lower complexity than the centralized minimum mean-squared error (MMSE) multiuser detector. It is demonstrated that the proposed receiver structure can significantly reduce the long training period required by the standard adaptive MMOE receiver in near-far environments. Both numerical and theoretical results show that the proposed receiver performs close to the optimum MMSE receiver whereas the conventional adaptive MMOE detector suffers from high BER’s due to the imperfect filter coefficients. Also our results show a three fold increase in the number of users when the MMOE-PIC is used relative to the conventional MMOE receiver. Furthermore, the transient behavior of the proposed MMOE-PIC receiver due to abrupt changes in the interference level is examined. It is shown that the proposed adaptive receiver offers much faster self recovery, with less signal-to-interference ratio (SIR) degradation, than the standard MMOE in sever near-far scenarios.     

Linear multiuser receivers in random environments

We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in “random directions.” Such a random environment may arise in a DS-CDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the receiver, the resulting SIR performance is a function of the directions and therefore also random. We study the asymptotic distribution of this random performance in the regime where both the number of users K and the number of degrees of freedom N in the system are large, but keeping their ratio fixed. Our results show that for both the decorrelator and the minimum mean-square error (MMSE) receiver, the variance of the SIR distribution decreases like 1/N, and the SIR distribution is asymptotically Gaussian. We compute closed-form expressions for the asymptotic means and variances for both receivers. Simulation results are presented to verify the accuracy of the asymptotic results for finite-sized systems     

MMSE detection in asynchronous CDMA systems: an equivalence result

The analysis of linear minimum mean-square error (MMSE) detection in a band-limited code-division multiple-access (CDMA) system that employs random spreading sequences is considered. The key features of the analysis are that the users are allowed to be completely asynchronous, and that the chip waveform is assumed to be the ideal Nyquist sinc function. It is shown that the asymptotic signal-to-interference ratio (SIR) at the detector output is the same as that in an equivalent chip-synchronous system. It is hence been established that synchronous analyses of linear MMSE detection can provide useful guidelines for the performance in asynchronous band-limited systems.     

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.     

CDMA systems in fading channels: admissibility, network capacity,and power control

We study the admissibility and network capacity of imperfect power-controlled code-division multiple access (CDMA) systems with linear receivers in fading environments. In a CDMA system, a set of users is admissible if their simultaneous transmission does not result in violation of any of their quality-of-service (QoS) requirements; the network capacity is the maximum number of admissible users. We consider a single-cell imperfect power-controlled CDMA system, assuming known received power distributions. We identify the network capacities of single-class systems with matched-filter (MF) receivers for both the deterministic and random signature cases. We also characterize the network capacity of single-class systems with linear minimum-mean-square-error (MMSE) receivers for the deterministic signature case. The network capacities can be expressed uniquely in terms of the users' signal-to-interference ratio (SIR) requirements and received power distributions. For multiple-class systems equipped with MF receivers, we find a necessary and sufficient condition on the admissibility for the random signature case, but only a sufficient condition for the deterministic signature case. We also introduce the notions of effective target SIR and effective bandwidth, which are useful in determining the admissibility and hence network capacity of an imperfect power-controlled system     

A Unified Approach to Power control in Large Energy-Constrained CDMS Systems

A unified approach to power control is proposed for maximizing utility in terms of energy efficiency in code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) for each user in the large-system limit. Suppose that each user seeks to selfishly maximize its own energy efficiency, a unique Nash equilibrium is shown to exist and be SIR-balanced, thus extending a previous result on linear receivers. A unified power control algorithm for reaching the Nash equilibrium is proposed, which adjusts transmit powers iteratively by computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for linear receivers, and is demonstrated via simulation for the multiuser maximum likelihood detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.     

Large-system performance analysis of blind and group-blindmultiuser receivers

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N, the number of users K, and the number of received signal samples M all go to infinity, while keeping the ratios K/N and M/N fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the Q function     

How fading affects CDMA: an asymptotic analysis with linearreceivers

Using asymptotic analysis, we study the effect of frequency-flat fading on code division multiple access (CDMA) systems with linear receivers and random spreading sequences. Specifically, we let the number of users grow without bound, while the ratio of number of users to spreading sequence length is kept fixed to a value α. We treat separately the cases of slow fading (nonergodic channel) and of fast fading (ergodic channel). For the former channel, we derive the outage probability, while for the latter we compute the channel capacity. In both cases, multiple classes of users with different qualities of service are dealt with. As α→∞, the system throughput tends to the same limit of 1.44 bit/symbol as for the nonfading channel with both single-user matched filter (SUMF) and linear minimum mean-square-error (MMSE) receivers. The outage probability exhibits a floor for all α with the SUMF receivers, while with MMSE receiver the floor is present only for α>1. We also address the tradeoffs involved in the allocation of available bandwidth between spreading and coding     

Asymptotic normality of linear multiuser receiver outputs

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.     

Linear Differentially Coherent Multiuser Detection for Multipath Channels

By combining multipath processing, differential signal detection, and multiuser detection techniques, we develop a class of near-far resistant linear detectors for differentially coherent multipath signals. We derive and establish performance relationships among the following detectors: an optimally near-far resistant detector, a suboptimum detector which does not require knowledge of the signal coordinates, and a minimum mean square error (MMSE) detector which achieves near-optimum asymptotic efficiency. We present an adaptive multiuser detector which converges to the MMSE detector without training sequences and which requires less information than the conventional single user rake receiver.     

Multiuser detection for continuous phase modulation over Rayleigh fading channels

We study multiuser (MU) continuous phase modulation (CPM) over Rayleigh fading channels with a receiver antenna array. An optimum symbol-by-symbol MU detector is derived and its practical implementation with reduced-complexity is considered. According to the numerical results, the MU detector performs very close to a system free of interference by other users, when each user has more than one receiving antenna. For three receiving antennas, this difference is less than 0.25 dB, 0.4 dB, and 0.6 dB for two, three and four users, respectively. Moreover, the proposed system is bandwidth efficient as CPM is a bandwidth efficient modulation scheme, and the MU system only uses the single user CPM bandwidth.     

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     

Blind adaptive multiuser detection

The decorrelating detector and the linear minimum mean-square error (MMSE) detector are known to be effective strategies to counter the presence of multiuser interference in code-division multiple-access channels; in particular, those multiuser detectors provide optimum near-far resistance. When training data sequences are available, the MMSE multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes. This paper introduces an adaptive multiuser detector which converges (for any initialization) to the MMSE detector without requiring training sequences. This blind multiuser detector requires no more knowledge than does the conventional single-user receiver: the desired user's signature waveform and its timing. The proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest     

Blind multiuser detection for code-hopping DS-CDMA signals in asynchronous multipath channels

Blind detection of a desired user's signal in a code-hopping (CH) direct sequence code-division multiple access (CDMA) system is considered. In CH CDMA systems each user switches between a predetermined set of short-code sequences. A user signal in such systems may be treated as the superposition of several virtual short-code signals. A code-constrained inverse filter criterion (IFC)-based blind detector for short-code CDMA signals in asynchronous multipath channels to detect a desired user's signal was recently presented by Tugnait and Li (2001). A novel approach combining the code-constrained IFC and a penalty function is proposed to simultaneously extract all virtual users associated with a given CH user. Global minima of the proposed cost function are analyzed. An extension of an existing subspace-based approach is also investigated. An illustrative simulation example is provided where the proposed algorithm is compared with a clairvoyant matched filter receiver, two linear minimum mean-square error (MMSE) receivers with channels known, and the subspace-based approach.