on the existence of strong nash equilibria this paper investigates the existence of strong nash equilibria sne in continuous and convex games we show that the concavity and an additional condition on payoff functions together with the compactness of strategy space permit the existence of strong nash equilibria these conditions are satisfied in many economic games and are quite simple to check we also characterize the existence of sne by providing a necessary and sufficient condition moreover we suggest a procedure that can be used to efficiently compute strong nash equilibrium the result is illustrated with an application to an economy with multilateral environmental externalities and to the simple oligopoly static model

optimal selective feedback policies for opportunistic beamforming this paper studies the structure of downlink sum rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back first it is shown that any sum rate maximizing selective decentralized feedback policy must be a threshold feedback policy this result holds for all fading channel models with continuous distribution functions second the resulting optimum threshold selection problem is analyzed in detail this is a nonconvex optimization problem over finite dimensional euclidean spaces by utilizing the theory of majorization an underlying schur concave structure in the sum rate function is identified and the sufficient conditions for the optimality of homogenous threshold feedback policies are obtained applications of these results are illustrated for well known fading channel models such as rayleigh nakagami and rician fading channels rather surprisingly it is shown that using the same threshold value at all mobile users is not always a rate wise optimal feedback strategy even for a network in which mobile users experience statistically the same channel conditions for the rayleigh fading channel model on the other hand homogenous threshold feedback policies are proven to be rate wise optimal if multiple orthonormal data carrying beams are used to communicate with multiple mobile users simultaneously

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

randomized resource allocation in decentralized wireless networks in this paper we consider a decentralized wireless communication network with a fixed number u of frequency subbands to be shared among n transmitter receiver pairs it is assumed that the number of active users is a realization of a random variable with a given probability mass function moreover users are unaware of each other s codebooks and hence no multiuser detection is possible we propose a randomized frequency hopping fh scheme in which each transmitter randomly hops over a subset of u subbands from transmission slot to transmission slot assuming all users transmit gaussian signals the distribution of the noise plus interference is mixed gaussian which makes calculation of the mutual information between the transmitted and received signals of each user intractable we derive lower and upper bounds on the mutual information of each user and demonstrate that for large signal to noise ratio snr values the two bounds coincide this observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity we compare the performance of the fh system to that of the frequency division fd system in terms of the following performance measures average sum multiplexing gain 1 and average minimum multiplexing gain per user 2 we show that depending on the probability mass function of the number of active users the fh system can offer a significant improvement in terms of 1 and 2 implying a more efficient usage of the spectrum in the sequel we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains developing a new upper bound on the differential entropy of a mixed gaussian random vector and using entropy power inequality we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given snr level we demonstrate that the so called outage capacity can be considerably higher in the fh scheme than in the fd scenario for reasonable distributions on the number of active users this guarantees a higher spectral efficiency in fh compared to fd

virtual implementation in nash equilibrium the two person case needs to be considered separately we provide a complete characterization of virtually implementable two person social choice functions while not all two person social choice functions are virtually implementable our necessary and sufficient condition is simple this contrasts with the rather complex necessary and sufficient conditions for exact implementation we show how our results can be extended to implementation in strict nash equilibrium and coalition proof nash equilibrium to social choice correspondences which map from cardinal preference profiles to lotteries and to environments with a continuum of pure alternatives

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

asymptotic analysis of reduced feedback strategies for mimo gaussian broadcast channels achieving the sum capacity of a multiple input multiple output mimo gaussian broadcast channel is known to require full channel state information csi at the base station which implies the need of a large amount of feedback information from the users different asymptotics of the sum capacity such as its scaling law with respect to the number of users n or the multiplexing gain are conventionally used to assess the performance of suboptimal schemes with reduced feedback or equivalently with partial channel state information at the transmitter in this correspondence the optimal scaling law of the sum rate with respect to n for fixed signal to noise ratio snr fixed number of transmit antennas m and any number of receiving antennas n i e m log log nn is proved to be achievable with a deterministic feedback of only one bit per user moreover the amount of feedback is shown to be further reduced with no asymptotic optimality loss by applying the selective feedback principle leading to an average feedback rate that scales as log n finally the asymptotic performance with respect to snr is studied by assessing how fast the number of users needs to increase with the snr in order to guarantee a noninterference limited behavior

on the user selection for mimo broadcast channels in this paper a downlink communication system in which a base station bs equipped with antennas communicates with users each equipped with receive antennas is considered an efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum rate throughput of the system in a rayleigh fading environment for the asymptotic case when tends to infinity the necessary and sufficient conditions in order to achieve the maximum sum rate throughput such that the difference between the achievable sum rate and the maximum value approaches zero is derived the complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the bs as well as the number of searches required for selecting the users it is shown that the proposed method is capable of achieving a large portion of the sum rate capacity with a very low complexity

differential feedback in codebook based multiuser mimo systems in slowly varying channels in downlink multiuser multiple input multiple output mimo systems system performance highly depends on the reliability of downlink channel state information csi at the base station bs in frequency division duplexing the most practical solution is to have downlink csi from the users fed back to the bs most work on this feedback design has assumed independent block fading channels however this paper proposes a new differential feedback scheme using the observation that the channel realizations are usually temporally correlated the sum rate loss assuming differential feedback is analyzed for a system with the number of users k equal to the number of transmit antennas m when k m a user selection algorithm based on an approximated signal to interference plus noise ratio sinr estimation is proposed in simulation results the proposed differential feedback scheme increases the sum rate compared to previous differential feedback schemes moreover the proposed user selection algorithm outperforms semi orthogonal user selection in the moderate signal to noise ratio snr region despite requiring less feedback information in low mobility channels utilizing the channels time correlation during quantization is shown to play a bigger role in determining sum rate performance than multiuser diversity for most snr regimes when a practical number of users is considered

eigen based transceivers for the mimo broadcast channel with semi orthogonal user selection this paper studies the sum rate performance of two low complexity eigenmode based transmission techniques for the mimo broadcast channel employing greedy semi orthogonal user selection sus the first approach termed zfdpc sus is based on zero forcing dirty paper coding the second approach termed zfbf sus is based on zero forcing beamforming we first employ new analytical methods to prove that as the number of users k grows large the zfdpc sus approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that the average sum rates of both techniques converge to the average sum capacity of the mimo broadcast channel for large k in addition to the asymptotic analysis we investigate the sum rates achieved by zfdpc sus and zfbf sus for finite k and show that zfdpc sus has significant performance advantages our results also provide key insights into the benefit of multiple receive antennas and the effect of the sus algorithm in particular we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second order behavior of the multi user diversity gain for finite k the benefit can be very significant we also show the interesting result that the semi orthogonality constraint imposed by sus whilst facilitating a very low complexity user selection procedure asymptotically does not reduce the multi user diversity gain in either first k or second order k terms

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

inefficiency of nash equilibria it is shown that nash equilibria of smooth games generally tend to be inefficient in the pareto sense

optimal and successive approaches to signal design for multiple antenna physical layer multicasting in modern wireless communications systems that send a common information stream called multicasting systems are widely needed for distributing content such as television or radio in this paper the multiple antenna physical layer multicasting channel is considered in which a common message is simultaneously transmitted to multiple single antenna users to achieve the capacity of this multicasting set up the covariance matrix of the transmit signal vector needs to be determined to maximize the smallest maximum achievable rate among all the users in this paper we develop a simple successive algorithm to determine the covariance matrix of the signal vector under the assumption that channel state information csi is perfectly available at the transmitter we first characterize properties of the capacity achieving covariance matrix and derive a closed form expression for the matrix in the two user case we then derive a closed form expression for the rate maximizing beamformer in the case of two users and propose a successive beamforming algorithm that generates the beamforming vector with low computational complexity in the proposed precoding design scheme the covariance matrix is successively constructed by orthogonalizing the subspace spanned by each user s channel vector until the maximum number of recursions which is the same as the minimum of the number of transmit antennas and the number of users is reached the achievable rate of the proposed scheme is compared with the capacity of optimal transmission transmit beamforming antenna subset selection and open loop transmission which does not require csi at the transmitter as the number of users and or antennas grows large it is shown that the average achievable rate of the proposed scheme achieves the same average achievable rate scaling as the true capacity while reducing the computational complexity

a comparison of time sharing dpc and beamforming for mimo broadcast channels with many users in this letter we derive the scaling laws of the sum rate for fading multiple input multiple output gaussian broadcast channels using time sharing to the strongest user dirty paper coding dpc and beamforming when the number of users receivers n is large throughout the letter we assume a fix average transmit power and consider a block fading rayleigh channel first we show that for a system with m transmit antennas and users equipped with n antennas the sum rate scales like mloglognn for dpc and beamforming when m is fixed and for any n either growing to infinity or not on the other hand when both m and n are fixed the sum rate of time sharing to the strongest user scales like min m n loglogn therefore the asymptotic gain of dpc over time sharing for the sum rate is m min m n when m and n are fixed it is also shown that if m grows as logn the sum rate of dpc and beamforming will grow linearly in m but with different constant multiplicative factors in this region the sum rate capacity of time sharing scales like nloglogn

asymptotic analysis of the amount of csi feedback in mimo broadcast channels in this paper we consider a downlink communication system in which a base station bs equipped with m antennas and power constraint p communicates with n users each equipped with k receive antennas it is assumed that the users have perfect channel state information csi of their own channels while the bs only knows the partial csi provided by the receivers via a feedback channel we study the fundamental limits on the amount of feedback required at the bs to achieve the sum rate capacity of the system when bs has perfect csi for all users in the asymptotic case of n considering various signal to noise ratio snr regimes the main results of this paper can be expressed as follows 1 in the fixed snr regime where the snr does not scale with n and low snr regime where the snr is much smaller than 1 in n to achieve the 1 e portion of the sum rate capacity the total amount of feedback should scale at least with e 1 in the fixed snr regime to reduce the gap between the achievable sum rate and the sum rate capacity of the system which is defined as the sum rate gap to zero the amount of feedback should scale at least logarithmically with the sum rate capacity which is achievable by using the random beam forming rbf scheme proposed by sharif and hassibi in the low snr regime we propose an opportunistic beam forming obf scheme which is shown to be asymptotically feedback optimal 2 in the high snr regime where the snr grows to infinity as n the total amount of feedback depends on the number of receive antennas in particular to reduce the sum rate gap to zero in the case of k 1 m 1 should scale at least logarithmically with the snr in the case of k m the amount of feedback does not need to scale with the snr moreover we show that rbf is asymptotically feedback optimal in the high snr regime

computing the strong nash equilibrium for markov chains games present a novel method for finding the strong nash equilibriumintroduce tikhonov s regularization method to guarantee convergence to a single equilibriumprove the existence of a unique strong nash equilibriumpropose the euler method with penalty function for converging to the strong nash equilibriumpresent the convergence conditions of the step size parameter and tikhonov s regularizator in this paper we present a novel method for finding the strong nash equilibrium the approach consists on determining a scalar and the corresponding strategies d fixing specific bounds min and max that belong to the pareto front bounds correspond to restrictions imposed by the player over the pareto front that establish a specific decision area where the strategies can be selected we first exemplify the pareto front of the game in terms of a nonlinear programming problem adding a set of linear constraints for the markov chain game based on the c variable method for solving the strong nash equilibrium problem we propose to employ the euler method and a penalty function with regularization the tikhonov s regularization method is used to guarantee the convergence to a single strong equilibrium point then we established a nonlinear programming method to solve the successive single objective constrained problems that arise from taking the regularized functional of the game to achieve the goal we implement the gradient method to solve the first order optimality conditions starting from an utopia point pareto optimal point given an initial of the individual objectives the method solves an optimization problem adding linear constraints required to find the optimal strong strategy d we show that in the regularized problem the functional of the game decrease and finally converges proving the existence and uniqueness of strong nash equilibrium pareto optimal nash equilibrium in addition we present the convergence conditions and compute the estimated rate of convergence of variables and corresponding to the step size parameter of the gradient method and the tikhonov s regularization respectively moreover we provide all the details needed to implement the method in an efficient and numerically stable way the usefulness of the method is successfully demonstrated by a numerical example

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

iterative precoder design and user scheduling for block diagonalized systems the block diagonalization bd scheme is a low complexity suboptimal precoding technique for multiuser multiple input multiple output mimo downlink channels which completely precancels the multiuser interference accordingly the precoder of each user lies in the null space of other users channel matrices in this paper we propose an iterative algorithm using qr decompositions qrds to compute the precoders specifically to avoid dealing with a large concatenated matrix we apply the qrd to a sequence of matrices of lower dimensions one problem of bd schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints when the number of users is large a set of users must be selected and selection algorithms should be designed to exploit the multiuser diversity gain finding the optimal set of users requires an exhaustive search which has too high computational complexity to be practically useful based on the iterative precoder design this paper proposes a low complexity user selection algorithm using a greedy method in which the precoders of selected users are recursively updated after each selection step the selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices which is related to the eigenvalues by the hadamard and schur inequalities an asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the mimo broadcast channel the numerical results show that the proposed algorithm achieves a good trade off between sum rate performance and computational complexity when users suffer different channel conditions providing fairness among users is of critical importance to address this problem we also propose two fair scheduling fs algorithms one imposing fairness in the approximation of the data rate and another directly imposing fairness in the product of the squared row norms of the effective channel matrices

asymptotic analysis of amplify and forward relaying in a parallel mimo relay network this paper studies the setup of a parallel mimo relay network in which k relays each equipped with n antennas assist in transmitting data between a source and a destination each equipped with m antennas m n in the half duplex mode it is assumed that there is no direct source destination link and the communication is performed in two hops an amplify and forward relaying scheme called incremental cooperative beamforming scheme icbs is introduced and shown to achieve the capacity of the network in the asymptotic case of k with a gap scaling of at most log k 4 k this result is shown to hold as long as the power of each relay is significantly larger than log3 k log log k k in addition in the case that the source power is equal to the relays power and both tend to infinity the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays simulation results confirm the validity of analytical arguments

communication over mimo broadcast channels using lattice basis reduction a new viewpoint for adopting the lattice reduction in communication over multiple input multiple output mimo broadcast channels is introduced lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points the new viewpoint helps us to generalize the idea of lattice reduction aided lra preceding for the case of unequal rate transmission and obtain analytic results for the asymptotic behavior signal to noise ratio snr rarr infin of the symbol error rate for the lra precoding and the perturbation technique also the outage probability for both cases of fixed rate users and fixed sum rate is analyzed it is shown that the lra method using the lenstra lenstra lovasz lll algorithm achieves the optimum asymptotic slope of symbol error rate called the precoding diversity

existence of strong equilibrium in discontinuous games abstract in this paper we give necessary and sufficient conditions for the existence of strong equilibria in games with non ordered preferences our result does not require continuous preferences and in the case of normal form games quasi concavity of payoff functions is not needed the result has been obtained by using the ky fan minimax inequality examples illustrate our conditions in some economic situations and compare the result with the previous literature