In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for small noise power, the number of users can be much more than the spreading gain without any significant loss of information (overloaded CDMA). A conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution. As the noise level increases, and/or, the ratio of the number of users and the spreading gain increases, the conjectured upper bound approaches the lower bound. We have also derived asymptotic limits of our bounds that can be compared to a formula that Tanaka obtained using techniques from statistical physics; his bound is close to that of our conjectured upper bound for large scale systems.
In this paper, we propose a fast decoder algorithm for uniquely decodable (errorless) code sets for overloaded synchronous optical code-division multiple-access (O-CDMA) systems. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code lengths, the proposed decoder has much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that th…
The sum capacity on a symbol-synchronous CDMA system having processing gain $N$ and supporting $K$ power constrained users is achieved by employing at most $2N-1$ sequences. Analogously, the minimum received power (energy-per-chip) on the symbol-synchronous CDMA system supporting $K$ users that demand specified data rates is attained by employing at most $2N-1$ sequences. If there are $L$ oversized users in the system, at most $2N-L-1$ sequences are needed. $2N-1$ is the minimum number of sequences needed to guarantee optimal allocation for single dimensional signaling. $N$ orthogonal sequence…
The everlasting bandwidth limitations in wireless communication networks has directed the researchers' thrust toward analyzing the prospect of overloaded Code Division Multiple Access (CDMA). In this paper, we have proposed a Genetic Algorithm in search of optimum signature matrices for binary-input synchronous CDMA. The main measure of optimality considered in this paper, is the per-user channel capacity of the overall multiple access system. Our resulting matrices differ from the renowned Welch Bound Equality (WBE) codes, regarding the fact that our attention is specifically aimed at binary,…
In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multiple-access (CDMA) systems. The proposed code set achieves larger number of users $K < K_{max}^t$ than any other known state-of-the-art ternary codes that offer low-complexity decoders in the noisy transmission. Moreover, we propose a simple decoder that uses only a few comparisons and can allow the user to uniquely recover the information bits. Compared to maximum likelihood (ML) decoder, which has a high computational complexity for even mod…
In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA receivers consist of two stages. The first stage is the power estimator and the second one is a Multi-User Detector (MUD). Conventional methods for estimating the user powers are suitable for underor fully-loaded cases (when the number of users is less than or equal to the spreading gain). These methods fail to work for overloaded CDMA systems because of high interference among the users. Since the bandwidth is becoming more and more valuable, it is worth considering overloaded CDMA systems. In this …
In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary over-loaded CDMA are derived that can predict the existence of such over-loaded codes. We also propose…
Code Division Multiple Access (CDMA) is the most promising candidate for wideband data access. This is due to the advantage of soft limit on the number of active mobile devices. Many wireless mesh systems impose an upper bound on the BER performance which restricts the increase in number of mobile users. Capacity is further reduced in Multipath Fading Environment (MFE). This paper presents an effective method of improving the capacity of a CDMA based mesh network by managing the transmitted powers of the mobile devices and using MMSE based Multiuser Detection (MUD). The proposed scheme improve…
In Fixed Wireless Applications (FWA), the Code Division Multiple Access (CDMA) is the most promising candidate for wideband data access. The reason is the soft limit on the number of active mobile devices. Many Fixed Wireless Applications impose an upper bound on the BER performance which restricts the increase in number of mobile users. The number of active mobile users or Capacity is further reduced in Multipath Fading Environment (MFE). This paper presents an effective method of improving the capacity of CDMA based Fixed Wireless Networks by using a hybrid power control algorithm. The propo…
In this paper we are going to estimate the sum capacity of a binary CDMA system in presence of the near-far effect. We model the near-far effect as a random variable that is multiplied by the users binary data before entering the noisy channel. We will find a lower bound and a conjectured upper bound for the sum capacity in this situation. All the derivations are in the asymptotic case. Simulations show that especially the lower bound is very tight for typical values Eb/N0 and near-far effect. Also, we exploit our idea in conjunction with the Tanaka's formula [6] which also estimates the sum c…
An interference-limited noise-free CDMA downlink channel operating under a complexity constraint on the receiver is introduced. According to this paradigm, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. We prove, by adopting statistical mechanics notion, that in the large-system limit such a complexity-constrained CDMA channel gives rise to a …
This paper deals with fading and/or near-far effects with or without power control on the evaluation of the sum capacity of finite dimensional Code Division Multiple Access (CDMA) systems for binary and finite nonbinary inputs and signature matrices. Important results of this paper are that the knowledge of the received power variations due to input power differences, fading and/or near-far effects can significantly improve the sum capacity. Also traditional power controls can not improve the sum capacity; for the asymptotic case, any type of power control on the near-far effects is equivalent…
This paper examines the effect of soft handoff on the uplink user capacity of a CDMA system consisting of a single macrocell in which a single hotspot microcell is embedded. The users of these two base stations operate over the same frequency band. In the soft handoff scenario studied here, both macrocell and microcell base stations serve each system user and the two received copies of a desired user's signal are summed using maximal ratio combining. Exact and approximate analytical methods are developed to compute uplink user capacity. Simulation results demonstrate a 20% increase in user cap…
We consider multiple access communication on a binary input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number of users, we prove an upper bound on the capacity, which matches a formula that Tanaka obtained by using the replica method. We also show concentration of various relevant quantities including mutual information, capacity and free energy. The mathematical methods are quite general and allow us to discuss extensions to other multiuser scenarios.
This paper examines the uplink user capacity in a two-tier code division multiple access (CDMA) system with hotspot microcells when user terminal power is limited and the wireless channel is finitely-dispersive. A finitely-dispersive channel causes variable fading of the signal power at the output of the RAKE receiver. First, a two-cell system composed of one macrocell and one embedded microcell is studied and analytical methods are developed to estimate the user capacity as a function of a dimensionless parameter that depends on the transmit power constraint and cell radius. Next, novel analy…
Balancing efficiency of bandwidth use and complexity of detection involves choosing a suitable load for a multi-access channel. In the case of synchronous CDMA, with random codes, it is possible to demonstrate the existence of a threshold in the load beyond which there is an apparent jump in computational complexity. At small load unit clause propagation can determine a jointly optimal detection of sources on a noiseless channel, but fails at high load. Analysis provides insight into the difference between the standard dense random codes and sparse codes, and the limitations of optimal detecti…
Recently, new spreading sequences have been proposed to increase the capacity of users. In particular, the Weyl spreading sequences have the larger capacity of users than the Gold codes. This paper shows that the Weyl spreading sequences appear in a bit recovering model and they are orthogonal basis vectors. This result shows the reason why they have the large capacity and that any spreading sequence is expressed as the sum of the Weyl spreading sequences.
We consider the problem of adaptive modulation for wideband DS-CDMA Rayleigh fading channels with imperfect channel state information (CSI). We assume a multidimensional signal subspace spanned by a collection of random spreading codes (multicoding) and study the effects of both the subspace dimension and the probability distribution of the transmitted symbols on the mutual information between the channel input and output in the presence of uncertainty regarding the true state of the channel. We develop approximations for the mutual information as well as both upper and lower bounds on the mut…
This paper proposes a unified approach to joint adaptive parameter estimation and interference cancellation (IC) for direct sequence code-division-multiple-access (DS-CDMA) systems in multipath channels. A unified framework is presented in which the IC problem is formulated as an optimization problem with extra degrees of freedom of an IC parameter vector for each stage and user. We propose a joint optimization method for estimating the IC parameter vector, the linear receiver filter front-end, and the channel along with minimum mean squared error (MMSE) expressions for the estimators. Based o…
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether overloaded error free codes exist in the absence of additive noise under these general settings, and if so whether there are any practical optimum decoding algorithms. The second one is about the bounds for the sum channel capacity when user data and signa…
Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is investigated for a random spreading short/long-code asynchronous direct sequence-code division multiple access (DS-CDMA) system. The discrete-time decision statistics are obtained as the output samples of a bank of symbol matched filters of all users. The crosscorrelation matrix is studied when the number of symbols transmitted by each user tends to infinity. Two levels of asynchronism are considered. One is symbol-asynchronous but chip-synchronous, and the other is chip-asynchronous. The existence of a nonrandom ASD is p…
In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust agains…
A noisy CDMA downlink channel operating under a strict complexity constraint on the receiver is introduced. According to this constraint, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. This channel setting, allowing the use of the simplest receiver scheme, seems to be worthless, making reliable communication at any rate impossible. However, recently this communication paradigm was shown to yield valuable information rates in the case of a noiseless channel. This finding calls for the inves…
The objective of this paper is to design optimal signature matrices for binary inputs. For the determination of such optimal codes, we need certain measures as objective functions. The sum-channel capacity and Bit Error Rate (BER) measures are typical methods for the evaluation of signature matrices. In this paper, in addition to these measures, we use distance criteria to evaluate the optimality of signature matrices. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to search the optimum signature matrices based on these three measures (Sum channel capacity, BER and D…
The main objective of this paper is to compare block transmission system performance analytically for Code Divisional Multiple Access (CDMA) modulations in Generalized Multicarrier environment against linear modulation techniques for both single user and multiuser. The effectivity of GMC-CDMA for multiuser will also be judged for different Direct Sequence CDMA (DS-CDMA) such as MC-CDMA, MC-DS-CDMA, MC-SS-CDMA. The analytical comparison will be in terms of computing probability of bit error for frequency selective and slow flat fading channels for different modulation techniques. The Bit Error …
In this paper, new upper and lower bounds are proposed for the capacity of discrete-time Laguerre channel. Laguerre behavior is used to model various types of optical systems and networks such as optical amplifiers, short distance visible light communication systems with direct detection and coherent code division multiple access (CDMA) networks. Bounds are derived for short distance visible light communication systems and coherent CDMA networks. These bounds are separated in three main cases: when both average and peak power constraints are imposed, when peak power constraint is inactive and …
We study the problem of transmission of binary input non-linear functions over a network of mobiles based on CDMA. Motivation for this study comes from the application of using cheap measurement devices installed on personal cell-phones to monitor environmental parameters such as air pollution, temperature and noise level. Our model resembles the MAC model of Nazer and Gastpar except that the encoders are restricted to be CDMA encoders. Unlike the work of Nazer and Gastpar whose main attention is transmission of linear functions, we deal with non-linear functions with binary inputs. A main con…
A new subcarrier combining technique is proposed for MC -CDMA receiver in mobile Rayleigh fading channel. It exploits the structure formed by repeating spreading sequences of users on different subcarriers to simultaneously suppress multiple access interference (MAI) and provide implicit channel tracking without any knowledge of the channel amplitudes or training sequences. This is achieved by adaptively weighting each subcarrier in each symbol period by employing a simple gradient descent algorithm to meet the constant modulus (CM) criterion with judicious selection of step-size. Improved BER…
In this paper, we present a multi-user resource allocation framework using fragmented-spectrum synchronous OFDM-CDMA modulation over a frequency-selective fading channel. In particular, given pre-existing communications in the spectrum where the system is operating, a channel sensing and estimation method is used to obtain information of subcarrier availability. Given this information, some real-valued multi-level orthogonal codes, which are orthogonal codes with values of $\{\pm1,\pm2,\pm3,\pm4, ... \}$, are provided for emerging new users, i.e., cognitive radio users. Additionally, we have o…
We analyze a MIMO DS-CDMA channel with a general multiuser detector including a nonlinear multiuser detector, using the replica method. In the many-user, limit the MIMO DS-CDMA channel with the multiuser detector is decoupled into a bank of single-user SIMO Gaussian channels if a spatial spreading scheme is employed. On the other hand, it is decoupled into a bank of single-user MIMO Gaussian channels if a spatial spreading scheme is not employed. The spectral efficiency of the MIMO DS-CDMA channel with the spatial spreading scheme is comparable with that of the MIMO DS-CDMA channel using an op…
Communications in dispersive direct-sequence code-division multiple-access (DS-CDMA) channels suffer from intersymbol and multiple-access interference, which can significantly impair performance. Joint maximum \textit{a posteriori} probability (MAP) equalization and multiuser detection with error control decoding can be used to mitigate this interference and to achieve the optimal bit error rate. Unfortunately, such optimal detection typically requires prohibitive computational complexity. This problem is addressed in this paper through the development of a reduced state trellis search detecti…
We consider asynchronous CDMA systems in no-fading environments with a particular focus on a certain user. This certain user is called a desired user in this paper. In such a situation, an optimal sequence, maximum Signal-to-Interference plus Noise Ratio (SINR) and the maximum capacity for a desired user are derived with other spreading sequences being given and fixed. In addition, the maximum SINR and the optimal sequence for a desired user are written in terms of the minimum eigenvalue and the corresponding eigenvector of a matrix, respectively. Since it is not straightforward to obtain an e…
We consider the CDMA (code-division multiple-access) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse signatures, and a detection algorithm based on belief propagation (BP) with linear time complexity. In the new scheme, each user conveys its power onto a finite number of chips l, in the large system limit. We analyze the performances of BP detection and prove that they coincide with the ones of optimal (symbol MAP) detection in the l->\infty limit. In the same limit, we prove that the information …
This paper is focused on the cross-layer design problem of joint multiuser detection and power control for energy-efficiency optimization in a wireless data network through a game-theoretic approach. Building on work of Meshkati, et al., wherein the tools of game-theory are used in order to achieve energy-efficiency in a simple synchronous code division multiple access system, system asynchronism, the use of bandlimited chip-pulses, and the multipath distortion induced by the wireless channel are explicitly incorporated into the analysis. Several non-cooperative games are proposed wherein user…
We investigate the detection dynamics of a soft parallel interference canceller (soft-PIC), which includes a hard-PIC as a special case, for code-division multiple-access (CDMA) multiuser detection, applied to a randomly spread, fully synchronous base-band uncoded CDMA channel model with additive white Gaussian noise under perfect power control in the large-system limit. We analyze the detection dynamics of some iterative detectors, namely soft-PIC, the Onsager-reaction-cancelling parallel interference canceller (ORC-PIC) and the belief-propagation-based detector (BP-based detector), by the ge…
Two-tier femtocell networks-- comprising a conventional macrocellular network plus embedded femtocell hotspots-- offer an economically viable solution to achieving high cellular user capacity and improved coverage. With universal frequency reuse and DS-CDMA transmission however, the ensuing cross-tier cochannel interference (CCI) causes unacceptable outage probability. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network. We evaluate a network-wide area spectral efficiency metric called the \emph{operating contour (OC)} defined as …
A general formalization is given for asynchronous multiple access channels which admits different assumptions on delays. This general framework allows the analysis of so far unexplored models leading to new interesting capacity regions. In particular, a single letter characterization is given for the capacity region in case of 3 senders, 2 synchronous with each other and the third not synchronous with them.
Reliable estimation of users' channels and data in rapidly time varying fading environments is a very challenging task of multiuser detection (MUD) techniques that promise impressive capacity gains for interference limited systems such as non-orthogonal CDMA and spatial multiplexing MIMO based LTE. This paper analyzes relative channel estimation error performances of conventional single user and multiuser receivers for an uplink of DS-CDMA and shows their impact on output signal to interference and noise ratio (SINR) performances. Mean squared error (MSE) of channel estimation and achievable s…
In ALOHA-type packetized network, the transmission times of packets follow a stochastic process. In this paper, we advocate a deterministic approach for channel multiple-access. Each user is statically assigned a periodic protocol signal, which takes value either zero or one, and transmit packets whenever the value of the protocol signal is equal to one. On top of this multiple-access protocol, efficient channel coding and network coding schemes are devised. We illustrate the idea by constructing a transmission scheme for the tandem collision network, for both slot-synchronous and slot-asynchr…
Molecular communication is set to play an important role in the design of complex biological and chemical systems. An important class of molecular communication systems is based on the timing channel, where information is encoded in the delay of the transmitted molecule---a synchronous approach. At present, a widely used modeling assumption is the perfect synchronization between the transmitter and the receiver. Unfortunately, this assumption is unlikely to hold in most practical molecular systems. To remedy this, we introduce a clock into the model---leading to the molecular timing channel wi…
Non-orthogonal communications play an important role in future communication architectures. In such scenarios, the received signal is corrupted by an interfering signal which is typically cyclostationary in continuous-time. If the period of interference is synchronized with the sampling period, the sampled interference is a discrete-time (DT) cyclostationary process. However, in the common interference scenario, the period of the interference is not necessarily synchronized with the sampling period. In such cases, the DT interference is an almost cyclostationary process. In this work we charac…
The collision channel without feedback (CCw/oFB) model introduced by Massey and Mathys, depicts a scenario in which M users share a thermal noise-free communication channel with random relative time offsets among their clocks. This paper considers an extension of this model, which allows the receiver to use successive interference cancellation (SIC) to iteratively cancel the interference caused by those collided packets that have been decoded by the receiver. As the main result of this paper, we derive the zero-error capacity region of this channel in the slot-synchronous case, and present a z…
A nonlinear detector derived within a maximum likelihood estimation framework is shown to be effective in retrieving the channel coefficients and data of users on the uplink channel of a noncooperative wireless system without the access point having any prior channel state information (no CSI or noncoherent setup). Rather than relying on pilot-assisted transmissions, it is shown that a maximum likelihood-based detector emerges naturally from an information-theoretic argument. The assumptions under which the detector is designed are as follows: 1) the uplink data from different users are indepe…
The theory of multiple-input multiple-output (MIMO) technology has been well-developed to increase fading channel capacity over single-input single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. Th…
Multi-user multiple-input multiple-output (MU-MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information (CSI). In particular, we consider two distinct operation modes, namely when the phase noise processes at the $M$ …
