The core component of a cognitive radio is its detector. When a device is equipped with multiple antennas, the detection method is usually based on an eigenvalue analysis. This paper explores the performance of the most common largest eigenvalue detector, for the case of a narrowband temporally white signal and calibrated receiver noise. In contrast to popular Gaussian assumption, our performance bounds are valid for any signal and noise that belong to the wide class of sub-Gaussian random processes. Moreover, the results are given in closed-form for any finite number of observations and antennas, in contrary to the widespread asymptotic analysis approach.

We present a novel upper bound on the Ergodic Rate Density (ERD) of ALOHA wireless ad-hoc networks. Our analysis uses a proper model of the physical layer together with an abstraction of higher communication layers. The novel bound is very general and supports various system models including for example, beamforming, spatial multiplexing, different fading models and different power control schemes. We also derive a closed form expression for the maximal gap between the novel bound and a known lower bound on the ERD. This maximal gap holds for any network that operates below the optimal density. This expression is simple to evaluate and only depends on the path loss factor. For example, for a path loss factor of α = 3 the novel upper bound is proved to be at most 31% higher than the lower bound (and hence also from the actual ERD). The usefulness and the generality of the novel bound is demonstrated by applications in multiple-antenna schemes. In particular, we study the optimization of the number of transmitted spatial streams in a MIMO network and derive the scaling of the ERD as the number of antennas grows. The results are further demonstrated using extensive simulations.

In this paper, a new analog error correcting code with an iterative decoder is presented for real-valued signals corrupted by impulsive noises. In the proposed algorithm, a redundancy coding matrix is used as an analog version of the cyclic redundancy check (CRC) that is commonly used for data verification in digital communication. Using this analog CRC enables an alternate decoding scheme in which iterative decoding is possible without transferring new errors between consecutive iterations. In each iteration of the algorithm, the problem of decoding the long block code is decoupled into two sets of parallel small linear programming problems. Simulation results show that this leads to a reduction in decoding complexity as compared to one-step linear programming decoding.

The performance of Wireless Ad hoc Networks (WANETs) depends on the availability of Channel State Information (CSI) on all channels in the network. In this work we study the performance when each receiver has CSI only on the channel from its desired transmitter. We present a novel lower bound on the Ergodic Rate Density of a WANET with partial CSI. The novel bound is compared to a previously known bound and its superiority is demonstrated. We also use the novel bound to study the effect of CSI availability on the WANETs' performance. We show that for Rayleigh fading the CSI-gain of the bound can be up to 78%. But, if each network is optimized with respect to the active transmitter density, then the CSI gain of the bound is at most 13%. Simulation results show the practicality of the novel bound and the accuracy of the CSI-gain expressions.

This paper examines the problem of rate allocation for multicasting over slow Rayleigh fading channels using network coding. In the proposed model, the network is treated as a collection of Rayleigh fading multiple access channels. In this model, rate allocation schemes that are based solely on the statistics of the channels are presented. The schemes are aimed to minimize the outage probability. An upper bound is presented for the probability of outage in the fading MAC. A suboptimal solution based on this bound is given for the MAC network model. We also consider outage probability minimization for TDMA schemes for the multiple access channels.

In this paper we consider the problem of distributed throughput maximization of cognitive radio networks with the multi-channel ALOHA medium access protocol. First, we characterize the Nash Equilibrium Points (NEPs) of the network when users solve an unconstrained rate maximization (i.e., the total transmission probability equals one). Then, we focus on constrained rate maximization, where user rates are subject to a total transmission probability constraint. We propose a simple best-response algorithm that solves the constrained rate maximization, where each user updates its strategy using its local channel state information (CSI) and by monitoring the channel utilization. We prove the convergence of the proposed algorithm using the theory of potential games. Furthermore, we show that the network approaches a unique equilibrium as the number of users increases. Then, we formulate the problem of choosing the access probability as a leader-followers Stackelberg game, where a single user is chosen to be the leader to manage the network. We show that a fully distributed setup can be applied to approximately optimize the network throughput for a large number of users. Finally, we extend the model to the case where primary and secondary users co-exist in the same frequency band.

In recent years, much attention has been paid to the analysis of random wireless ad hoc networks (WANETs) that combine the effect of the physical layer and the medium access layer. However, most works have concentrated on an outage rate model which does not accurately describe the performance of modern communication systems. In this work we consider the ergodic rate density (ERD) of a random ALOHA WANET with a homogenous Poisson point process node distribution. We present two novel lower bounds on the ERD, one for general transmission and reception strategies and the other for receivers with a spatial interference cancellation capability. The bounds are simpler than previously published results for ALOHA WANETs (that have primarily considered the outage rate density). In addition, the bounds and the bounding technique are quite general and enable the derivation of closed form expressions of the ERD for various network models. The efficiency and simplicity of the bounds are demonstrated through several applications, and insights are drawn on the behavior of the network performance as function of the path-loss factor, transmission strategies and number of antennas. Simulation results demonstrate that these simple lower bounds predict the performance of ALOHA WANETs with high accuracy.

In this paper we propose to use the well known game theoretic Gale-Shapley stable marriage theorem from game theory as a basis for spectrum allocation in cognitive radio networks. We analyze the performance of the proposed solution and provide tight lower and upper bounds on both the stable allocation and the optimal allocation performance. Then we present a novel opportunistic multichannel medium access control technique that achieves stable allocation within a single CSMA contention window. We discuss practical implementation issues and put forward two other varieties of the algorithm which have lower implementation complexity. Finally, we provide simulated examples.

In this paper, we present a new analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This product code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the Donoho matrices by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.

In this paper we discuss rate control for multiuser multi carrier systems, where the transmitter has a single antenna and is subject to a PSD mask limitation while the receiver has multiple receive antennas. This case is typical in many systems, where each mobile unit has a single transmit stream, and its transmit PSD is limited by regulatory constraints. This scenario is also typical DSL upstream transmission with a vector receiver. In both scenarios we are given a vector of target rates determined by the network operator and we want to set up a transmission strategy for each user at each tone. We show that in this case the problem can be solved using linear programming, rather than general convex optimization. The proposed rate allocation technique has two important applications. First, it provides a computationally simple tool to evaluate the optimal performance of multiple access systems under various operator utility functions. Second, it can serve as a practical tool for rate control of multiple access OFDM systems.

In a wireless OFDM communication system multiple players share the same spectrum while experiencing different channel realizations. Allocation algorithms exploit this feature and optimize the allocation of frequency bins according to various optimization criteria (e.g., weighted Max-Min, Nash Bargaining Solution (NBS), etc). These allocations do not allow players to transmit on the same frequency bin simultaneously. Thus, the communication channel is not fully utilized when the mutual interferences are weak. Here we propose a more general allocation scheme, called Partial Orthogonal Allocation (POA), where players can transmit simultaneously on some of the frequency bins, and maintain orthogonality of transmission on the other frequency bins. For this schema, the Nash Bargaining Solution is proposed and analyzed.

In this paper we derive performance bounds for tracking time-varying OFDM multiple-input multiple-output (MIMO) communication channel in the presence of additive white Gaussian noise (AWGN). We discuss two channel tracking schemes. The first tracks the filter coefficients directly in time-domain, while the second separately tracks each tone in the frequency-domain. The Kalman filter, with known channel statistics, is utilized for evaluating the performance bounds. It is shown that the time-domain tracking scheme, which exploits the sparseness of the channel impulse response, outperforms the computationally more efficient, frequency-domain tracking scheme, which does not exploit the smooth frequency response of the channel.

In this paper we discuss the use of cooperative game theory for analyzing interference channels. We extend our previous work, to games with N players as well as frequency selective channels and joint TDM/FDM strategies. We show that the Nash bargaining solution can be computed using convex optimization techniques. We also show that the same results are applicable to interference channels where only statistical knowledge of the channel is available. Moreover, for the special case of two player 2 times K frequency selective channel (with K frequency bins) we provide an O(K log2K) complexity algorithm for computing the Nash bargaining solution under mask constraint and using joint FDM/TDM strategies. Simulation results are also provided.

In this paper we analyze the interference channel as a conflict situation. This viewpoint implies that certain points in the rate region are unreasonable to one of the players. Therefore these points cannot be considered achievable based on game theoretic considerations. We then propose to use Nash bargaining solution as a tool that provides preferred points on the boundary of the game theoretic rate region. We provide analysis for the 2times2 interference channel using the FDM achievable rate region. We also outline how to generalize our results to other achievable rate regions for the interference channel as well as the multiple access channel

A noncoherent coded system, which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection, is presented in this two-part paper, where Part I focuses on the performance analysis of the system and Part II deals with the structural properties of the underlying convolutional codes. These convolutional codes are referred to as nd-convolutional codes. It is shown that nd-convolutional codes provide a general framework for various noncoherent coding systems, including differential systems. Two models of the carrier phase are examined and the relationships between them is established. For the first one, the carrier phase remains constant for L channels signals, whereas for the second one, it unvaries throughout the transmission period. The regular structure of nd-codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities, as well as a simple expression for the generalized cutoff rate. The exponential rate of the error probability, which is the single parameter governing the error performance at large signal-to-noise ratios, is identified via large deviations techniques. This parameter leads to the interesting conclusion that increasing L does not necessarily monotonically improve the error performance of the noncoherent system. The same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples. These examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes, some of which are tabulated in Part II of the paper, is required.

For pt.I see ibid., vol.43, no.2, p.558-75 (1997). The structural properties of a noncoherent coded system, which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection, is presented in this second part of a two-part paper, where the performance analysis was provided in Part I. These convolutional codes are referred to as nd-convolutional codes and they provide a general framework for various noncoherent coding systems, including differential systems, for several practical models of the carrier phase. The exponential rate in which the error probability decays to zero, derived in Part I of the paper, is used here to obtain the free equivalent distance of nd-codes, which is the single parameter dominating the error performance at large signal-to-noise ratios. The free equivalent distance is upper-bounded by the free nd-distance, which constitutes a more convenient and practical parameter to work with, and it is the basis for a computer search for optimal nd-codes. The resultant codes of the computer search are compared to codes which are optimal for coherent detection, and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd-distance. The ambiguity problem, inherent to noncoherent systems, is also treated in this paper in the general framework of nd-catastrophic codes, and necessary and sufficient conditions for catastrophic error propagation are identified.

We investigate the problem of decoding digital data when soft decisions are constrained to take on values from a finite set. We propose a physically reasonable objective function for selecting the desired assignment of metrics to the received analog signals. We develop a search algorithm for designing a table-look-up that is used by the decoder to select the appropriate intermediate metrics and show that an optimum solution exists. We provide a number of illuminating examples to elucidate our ideas and work out in detail some practical cases.>

A tapped delay line (TDL) model is proposed for capturing the essence of indoor and outdoor propagation modes in 1800 MHz PCS band. The TDL models are used for system evaluation and verification of various PCS common air interface proposals by simulations and tests. For bandlimited inputs the TDL model is equivalent to a wider channel followed by a bandlimiting filter. Each tap is weighted by a complex random process with parameters derived from the statistical properties of the wideband channel.>

The effect of handoff techniques on cell coverage and reverse link capacity is investigated for a spread spectrum CDMA system. It is shown that soft handoff increases both parameters significantly relative to conventional hard handoff.>

A modified version of the multilevel coded modulation scheme of Imai and Hirakawa (1977) is presented and analyzed. In the transmitter, the outputs of the component codes are bit interleaved prior to mapping into 8-PSK channel signals. A multistage receiver is considered, in which the output amplitudes of the Gaussian channel are soft limited before entering the second and third stage decoders. Upper bounds and Gaussian approximations for the bit error probability of every component code, which take into account errors in previously decoded stages, are presented. Aided by a comprehensive computer simulation, it is demonstrated in a specific example that the addition of the interleaver and soft limiter in the third stage improves its performance by 1.1 dB at a bit error probability of 10/sup /spl minus/5/, and that the multilevel scheme improves on an Ungerboeck's code with the same decoding complexity. The rate selection of the component codes is also considered and a simple selection rule, based on information theoretic arguments, is provided.>

An improved series of bounds is presented for the other-cell interference in cellular power-controlled CDMA. The bounds are based on allowing control by one of a limited set of base stations. In particular, it is shown that the choice of cellular base station with least interference among the set of N/sub c/>1 nearest base stations yields much lower total mean interference from the mobile subscribers than the choice of only the single nearest base station.>

Performance of a wideband multipath-fading terrestrial digital coded communication system is treated. The analysis has applications to a cellular system using direct-sequence spread-spectrum code-division multiaccess (CDMA) with M-ary orthogonal modulation on the many-to-one reverse (user-to-base station) link. For these links, power control of each multiple-access user by the cell base station is a critically important feature. This feature is implemented by measuring the power received at the base station for each user and sending a command to either raise or lower reverse link transmitter power by a fixed amount. Assuming perfect interleaving, the effect of the power control accuracy on the system performance is assessed.>

A suboptimal trellis coding approach based on the concept of combining a good convolutional code and bit interleavers is presented. The aim is to improve the reliability of digital radio communication over a fading channel. It is shown that over a Rayleigh channel and for a fixed code complexity the proposed system is superior to the baseline system. Its performance is analyzed using the generalized R/sub o/ and the upper bound on the bit error rate. The results suggest that on a Rayleigh channel, the standard trellis codes may not be the correct approach for improving the reliability of the communication channel. The discussion is restricted to a rate 2/3 coded system with 8-PSK modulation.>

The performance of M-ary phase-shift keying (PSK) coded systems in the presence of added white Gaussian noise (AWGN), with a noisy carrier reference in the receiver, is examined. The results are obtained by combining the Chernoff bound technique with the generating function approach. The bit error probability analysis is carried out for 8- and 16-PSK with code rates of 2/3 and 3/4, respectively. The numerical results obtained demonstrate the error performance degradation due to a Tikhonov phase noise process with parameter alpha .>

A simple statistical channel model is suggested to account for single position bit shifts that have been identified as one of the major impairments in magnetic recording. The authors investigate bounds on the capacity of this channel where the channel inputs are the (d,k) codes commonly used in magnetic recordings. For d>or=2, this channel is conveniently described in terms of phrase lengths where a bit shift causes a phrase either to shrink or to expand. The inherent correlation present in consecutive shift-affected phrases introduces memory into the channel model. Sequences of nondecreasing lower bounds and nonincreasing upper bounds on the capacity are evaluated and investigated for a variety of parameters. Lower bounds on the zero-error capacity are also studied. The channel model is extended to a concatenated scheme of a bit shift channel connected in tandem with the binary symmetric channel, thus capturing both major error generating mechanisms-the bit shifts as well as randomly generated errors. Lower and upper bounds on the capacity of this concatenated channel model with (d,k) input sequences are derived and discussed.>

It is shown that under certain conditions, when convolutional codes with precoding are used in conjunction with a partial response channel, the number of decoder states in a maximum-likelihood decoder matched to both the code and channel is 1/2 of that predicted by J.K. Wolf and G. Ungerboeck (ibid., vol.COM-34, no.7, p.751-72, 1986).>

Several results on binary (d, k) codes are given. First, a novel derivation for the capacity of these codes based on information-theoretic principles is given. Based on this result the spectrum of a (d, k) code is computed. Finally, the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the (d, k) constraint is considered. Lower bounds on the capacity of such a channel are derived.>

Generating function techniques for analyzing the error event and the bit-error probabilities for trellis codes are considered. The conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes, and instead, a state diagram where the number of states is equal to the square of the number of trellis states must be used. It is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states {\em is equal to} the number of trellis states. The class of codes considered includes trellis codes of rateR=(n-1)/nbased upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same "configuration matrix," i.e., the same ordered set of mutual distances. The complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states. Bounds on the performance of some interesting codes are given based upon this method.