transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

a deterministic equivalent for the analysis of correlated mimo multiple access channels in this article novel deterministic equivalents for the stieltjes transform and the shannon transform of a class of large dimensional random matrices are provided these results are used to characterize the ergodic rate region of multiple antenna multiple access channels when each point to point propagation channel is modelled according to the kronecker model specifically an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water filling algorithm to obtain these precoders are provided an original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides the above results are validated by monte carlo simulations

the structure of general interference functions and applications this paper provides a theoretical framework for the analysis of interference coupled multiuser systems the fundamental behavior of such a system is modeled by interference functions defined by axioms ldquononnegativity rdquoscale invariance rdquo and ldquomonotonicity rdquo it is shown that every interference function has an interpretation as the optimum of a min max problem where the optimization is over a closed comprehensive positive coefficient set this provides new insight into the structure of general interference functions and its elementary building blocks conversely it is shown that every closed comprehensive positive set can be expressed as a level set of an interference function this shows a close connection between the analysis of interference functions and multiuser performance regions which are typically closed comprehensive the generality of this framework allows for a wide range of potential applications as an example we analyze the problem of interference balancing

on gaussian mimo bc mac duality with multiple transmit covariance constraints owing to the special structure of the gaussian multiple input multiple output mimo broadcast channel bc the associated capacity region computation and beamforming optimization problems are typically non convex and thus cannot be solved directly one feasible approach is to consider the respective dual multiple access channel mac problems which are easier to deal with due to their convexity properties the conventional bc mac duality has been established via bc mac signal transformation and is applicable only for the case in which the mimo bc is subject to a single transmit sum power constraint an alternative approach is based on minimax duality which can be applied to the case of the sum power constraint or per antenna power constraint in this paper the conventional bc mac duality is extended to the general linear transmit covariance constraint ltcc case which includes sum power and per antenna power constraints as special cases the obtained general bc mac duality is applied to solve the capacity region computation for the mimo bc and beamforming optimization for the multiple input single output miso bc respectively with multiple ltccs the relationship between this new general bc mac duality and the minimax duality is also discussed and it is shown that the general bc mac duality leads to simpler problem formulations moreover the general bc mac duality is extended to deal with the case of nonlinear transmit covariance constraints in the mimo bc

universal space time codes from demultiplexed trellis codes in broadcast scenarios or in the absence of accurate channel probability distribution information code design for consistent channel by channel performance rather than average performance over a channel distribution may be desirable root and varaiya s compound channel theorem for linear gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information mi is above the transmitted rate this paper presents two dimensional trellis codes that provide such universal performance over the compound linear vector gaussian channel when demultiplexed over two three and four transmit antennas the presented trellis codes found by exhaustive search guarantee consistent performance on every matrix channel that supports the information transmission rate with an mi gap that is similar to the capacity gap of a well designed additive white gaussian noise awgn specific code on the awgn channel as a result of their channel by channel consistency the universal trellis codes presented here also deliver comparable or in some cases superior frame error rate and bit error rate performance under quasi static rayleigh fading as compared with trellis codes of similar complexity that are designed specifically for the quasi static rayleigh fading scenario

downlink mmse transceiver optimization for multiuser mimo systems duality and sum mse minimization we address the problem of minimum mean square error mmse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on the problem of minimizing the downlink sum mse under a sum power constraint it is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink mse feasible regions we propose two different optimization frameworks for downlink mmse transceiver design the first one solves an equivalent uplink problem then the result is transferred to the original downlink problem duality ensures that any uplink mmse scheme e g linear mmse reception or mmse decision feedback equalization dfe has a downlink counterpart we propose two globally optimum algorithms based on convex optimization the basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels this strategy exploits that the same mse can be achieved in both links for a given choice of transmit and receive filters this iteration is proven to be convergent

2 generations of the fourth janko groupj4 abstract a group g is said to be 2 generated if it can be generated by two suitable elements in this paper the authors continue the study of two special kinds of 2 generations namely l m n generations and nx complementary generations of the sporadic simple groups the problem is resolved for the group j 4

low complexity user selection algorithms for multiuser mimo systems with block diagonalization block diagonalization bd is a precoding technique that eliminates interuser interference in downlink multiuser multiple input multiple output mimo systems with the assumptions that all users have the same number of receive antennas and utilize all receive antennas when scheduled for transmission the number of simultaneously supportable users with bd is limited by the ratio of the number of base station transmit antennas to the number of user receive antennas in a downlink mimo system with a large number of users the base station may select a subset of users to serve in order to maximize the total throughput the brute force search for the optimal user set however is computationally prohibitive we propose two low complexity suboptimal user selection algorithms for multiuser mimo systems with bd both algorithms aim to select a subset of users such that the total throughput is nearly maximized the first user selection algorithm greedily maximizes the total throughput whereas the criterion of the second algorithm is based on the channel energy we show that both algorithms have linear complexity in the total number of users and achieve around 95 of the total throughput of the complete search method in simulations

mse balancing in the mimo bc unequal targets and probabilistic interference constraints second order cone soc restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form this paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple input multiple output broadcast channel with imperfect channel state information at the transmitter in particular we propose an iterative solution for mean square error mse balancing with such constraints via the lagrangian dual formulation the mse balancing criteria contrary to signal to interference plus noise ratio and rate criteria exhibit an interesting property when considering different targets for the receivers users with low target values are strictly prioritized in comparison to users with large mse targets that can even be switched off therefore only a subset of the receivers is served at the solution with stringent limitations for the precoders an example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system we provide four different approaches to approximate these probabilistic constraints with deterministic soc constraints and compare their accuracy

degrees of freedom for mutually interfering broadcast channels in this paper we study spatial degree of freedom dof for two mutually interfering broadcast channels ibc as the demand for space division multiple access sdma increases the ibc where each link has a single transmit node and multiple receive nodes becomes important this paper presents the results of the lower and upper bounds on the dof of the ibc from the derived results it is shown that for most cases zero forcing zf beamforming can achieve the optimal dof of the ibc except for some special cases also we identify a condition that disabling receive cooperation in the multiple input multiple output interference channels causes no dof loss it is confirmed that we cannot expect a dof improvement by enabling in cell receive cooperation if in at least one of two bss the number of antennas is greater than or equal to that of users per cell furthermore we observe a positive result that as the number of users goes to infinity the total dof of the ibc converges to the interference free dof which is the maximum achievable dof in the absence of the inter cell interference

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

extended pseudo fermions from non commutative bosons we consider some modifications of the two dimensional canonical commutation relations leading to non commutative bosons and we show how biorthogonal bases of the hilbert space of the system can be obtained out of them our construction extends those recently introduced by one of us f b modifying the canonical anticommutation relations we also briefly discuss how bicoherent states producing a resolution of the identity can be defined

high snr analysis for mimo broadcast channels dirty paper coding versus linear precoding in this correspondence we compare the achievable throughput for the optimal strategy of dirty paper coding dpc to that achieved with suboptimal and lower complexity linear precoding techniques zero forcing and block diagonalization both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain but an absolute difference in terms of throughput does exist the sum rate difference between the two strategies is analytically computed at asymptotically high snr furthermore the difference is not affected by asymmetric channel behavior when each user has a different average snr weighted sum rate maximization is also considered in the process it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate

achievable rates of multi antenna downlink channels with peak power constraints this paper considers a gaussian multiple input single output miso broadcast channel with a per antenna peak power constraint or simply peak power constraint it is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier assuming the perfect knowledge of the channel state information csi at the transmitter we propose an achievable scheme using dirty tape coding dtc the ideal dirty paper coding dpc which is a capacity achieving scheme for the gaussian multiple input multiple output mimo broadcast channel cannot be used for our model because its optimal input distribution is gaussian and thus the peak power constraint is violated on the other hand the channel input of dtc is uniformly distributed in a fixed range which helps to control the peak power of the transmit signal easily we also present an algorithm that finds capacity achieving beamforming vectors and power allocation factors under a per antenna average power constraint and use the optimized parameters in the proposed scheme simulation results show that the proposed scheme provides gains of 2 7db over a non dtc scheme based on minimum mean square error mmse beamforming at high signal to noise ratio snr when there are three receivers and the transmitter has three antennas

resource allocation in multiantenna systems achieving max min fairness by optimizing a sum of inverse sir we address the problem of jointly optimizing transmit powers and linear preequalizers e g beamformers for a multiuser downlink channel all results can be transferred to the dual uplink channel the link quality of each user is determined by the signal to interference ratio sir two common strategies for distributing the system resources by joint optimization of transmit powers and beamformers are 1 maximize the minimum sir to which we refer as max min fairness and 2 minimize the sum of weighted inverse sir both strategies are generally not equivalent in this paper it is shown how the weighting factors should be chosen so that the sum optimization approach achieves optimal max min fairness an efficient iterative algorithm is proposed for solving this nonlinear optimization problem monotonicity and convergence are proved

degrees of freedom of interference channels with comp transmission and reception we study the degrees of freedom dof of the k user interference channel with coordinated multipoint comp transmission and reception each message is jointly transmitted by m t successive transmitters and is jointly received by m r successive receivers we refer to this channel as the comp channel with a transmit cooperation order of m t and receive cooperation order of m r since the channel has a total of k transmit antennas and k receive antennas the maximum possible dof is equal to k we show that the comp channel has k dof if and only if m t m r geq k 1 the key idea is that the zero forcing of the interference corresponding to the i rm th message at the decoder of the j rm th message where j ne i can be viewed as a shared responsibility between the m t transmitters carrying the i rm th message and the m r receivers decoding the j rm th message for the general case we derive an outer bound that states that the dof is bounded above by left lceil k m t m r 2 2 right rceil for the special case with only comp transmission i e m r 1 we propose a scheme that can achieve k m t 1 2 dof for all k and conjecture that the result holds true for all k in the proposed coding scheme the m t transmitters carrying each message are used to cancel the interference introduced by this message at the first m t 1 receivers thereby allowing each of these receivers to enjoy 1 dof and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space the achievability proofs are based on the notion of algebraic independence from algebraic geometry

modulo loss reduction for vector perturbation systems in this letter we present an improved precoding technique which reduces a modulo loss in vector perturbation with low complexity instead of searching perturbation vectors in the infinite lattice the proposed scheme restricts the search range by utilizing the distribution of the perturbation vector depending on transmitted data as a result we can achieve significant complexity savings at the transmitter while providing better performance compared to the original vector perturbation

precoding for the multiantenna downlink multiuser snr gap and optimal user ordering this paper develops a practical design method for implementing tomlinson harashima precoding thp in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver a two step design process is proposed for minimizing the total transmit power while satisfying every user s minimum data rate and maximum bit error rate ber requirements first the ber and rate requirements are converted to virtual rate requirements which account for the gap to capacity introduced by practical quadrature amplitude modulation qam and thp the second step is to determine the transmit covariance matrices which specify the entire thp system that will provide these virtual rates at the minimum total transmit power as one of the main features in the proposed scheme an algorithm for finding the optimal user encoding or presubtraction order in polynomial time is proposed in addition we also propose an algorithm that finds a near optimal order but which is much less complex the proposed method outperforms existing zero forcing based thp systems in term of power efficiency

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

low complexity non iterative coordinated beamforming in 2 user broadcast channels we propose a new non iterative coordinated beamforming scheme to obtain full multiplexing gain in 2 user mimo systems in order to find the beamforming and combining matrices we solve a generalized eigenvector problem and describe how to find generalized eigenvectors according to the gaussian broadcast channels selected simulation results show that the proposed method yields the same sum rate performance as the iterative coordinated beamforming method while maintaining lower complexity by non iterative computation of the beamforming and combining matrices we also show that the proposed method can easily exploit selective gain by choosing the best combination of generalized eigenvectors

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

optimizing zero forcing precoders for mimo broadcast systems in this paper we develop optimization techniques for linear zero forcing zf multiple input multiple output mimo broadcast bc precoders a computationally efficient technique based on qr update algorithms for implementing this optimization is then proposed the application of the proposed zf precoders and decoders to systems with both large and small numbers of users is considered the proposed optimization technique is also shown to perform very well in conjunction with nonlinear tomlinson harashima precoding both coded and uncoded performances are considered

joint spatial division and multiplexing the large scale array regime we propose joint spatial division and multiplexing jsdm an approach to multiuser mimo downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced dimensional channel state information at the transmitter csit jsdm achieves significant savings both in the downlink training and in the csit uplink feedback thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing fdd systems for which uplink downlink channel reciprocity cannot be exploited in the proposed scheme the multiuser mimo downlink precoder is obtained by concatenating a prebeamforming matrix which depends only on the channel second order statistics with a classical multiuser precoder based on the instantaneous knowledge of the resulting reduced dimensional effective channel matrix we prove a simple condition under which jsdm incurs no loss of optimality with respect to the full csit case for linear uniformly spaced arrays we show that such condition is approached in the large number of antennas limit for this case we use szego s asymptotic theory of toeplitz matrices to show that a dft based prebeamforming matrix is near optimal requiring only coarse information about the users angles of arrival and angular spread finally we extend these ideas to the case of a 2 d base station antenna array with 3 d beamforming including multiple beams in the elevation angle direction we provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max min fairness criteria showing extremely attractive performance our numerical results are obtained via asymptotic random matrix theory avoiding lengthy monte carlo simulations and providing accurate results for realistic finite number of antennas and users

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

degrees of freedom region of the mimo x channel we provide achievability as well as converse results for the degrees of freedom region of a multiple input multiple output mimo x channel i e a system with two transmitters two receivers each equipped with multiple antennas where independent messages need to be conveyed over fixed channels from each transmitter to each receiver the inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message with m 1 antennas at each node we find that the total sum rate degrees of freedom are bounded above and below as 1 les eta x les 4 3 if m 1 and channel matrices are nondegenerate then the precise degrees of freedom eta x 4 3 m thus the mimo x channel has noninteger degrees of freedom when m is not a multiple of 3 simple zero forcing without dirty paper encoding or successive decoding suffices to achieve the 4 3 m degrees of freedom if the channels vary with time frequency then the channel with single antennas m 1 at all nodes has exactly 4 3 degrees of freedom the key idea for the achievability of the degrees of freedom is interference alignment i e signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired we also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio

on mmse vector perturbation precoding for mimo broadcast channels with per antenna group power constraints recently studies on suboptimal precoding techniques for multiple input multiple output broadcast channels mimo bc which achieve performance near to that of the dirty paper coding dpc have drawn attention to vector perturbation vp precoding in practice each antenna or more generally each antenna group has its own limit on the transmitted power which makes per antenna group power constraints more meaningful than the sum power constraint in this paper we introduce an optimization technique for vp precoding employing the minimum mean square error mmse criterion with per antenna group power constraints this technique is inspired by the p sphere encoding in a sense that it involves finding the node with the lowest mean square error mse over a lattice we demonstrate that the mse metric as well as the p norm one can be enclosed in a proper frobenius norm ball this frobenius norm ball shrinks until it captures the perturbing vector minimizing the mse numerical results show that the proposed algorithm outperforms conventional vp precoding and the p sphere encoding but at higher complexity consequently we investigate a couple of simplified techniques employing the mmse criterion which perform almost as well as the proposed precoding technique but are less complex

transmit selection diversity for unitary precoded multiuser spatial multiplexing systems with linear receivers multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference in such a system the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain this paper proposes two precoding methods that use extra transmit antennas beyond the minimum required to provide additional degrees of diversity the approach taken is to solve for a unitary transmit precoder under a zero interuser interference constraint that minimizes an upper bound on the symbol error rate ser for each user solutions where all transmit antennas are employed as well as subsets of antennas to reduce analog components are described numerical results confirm a dramatic improvement in terms of ser and mutual information over single user multiple input multiple output mimo methods and static allocation methods for example the proposed techniques achieve a signal to noise ratio snr improvement of 6 10 db at an uncoded ser of 10 3 with only one extra transmit antenna

on vector perturbation precoding for the mimo gaussian broadcast channel precoding schemes in the framework of vector perturbation vp for the multiple input multiple output mimo gaussian broadcast channel gbc are investigated the vp scheme originally a one shot technique is generalized to encompass processing over multiple time instances using lattice based extended alphabets perturbations and considering the infinite time span extension limit a lower bound on the achievable sum rate using the generalized vp scheme is analytically obtained the lower bound is shown to asymptotically achieve the optimum sum rate in the high signal to noise ratio snr regime both in terms of degrees of freedom and power offset for any number of users and transmit antennas for the two user cases it is shown that the lower bound coincides with the sum capacity for low snr the above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm which exhibits a polynomial complexity in the number of users the proposed precoding scheme demonstrates that the shaping gain is achievable for vp schemes when employing good multidimensional lattices it is also shown that the suboptimum algorithm has its merits even when processing over multiple time instances is not employed for the 2 times 2 mimo gbc the vp scheme is generalized further and an inner bound for the entire achievable rate region is obtained by which an interesting correspondence is identified with the ultimate capacity region as obtained by dirty paper coding

exact sum rate analysis of mimo broadcast channels with random unitary beamforming random unitary beamforming rub is an attractive transmission scheme for mimo broadcast channels because of its ability to achieve high sum rate capacity with limited feedback in this letter we derive the exact analytical expressions for the ergodic sum rate of mimo broadcast channels with rub the analysis is facilitated by the development of the complete statistical characterization of ordered beam sinrs for a user which can find their application in many related problems

a vector perturbation with user selection for multiuser mimo downlink recent works on multiuser mimo study have shown that the linear growth of capacity in single user mimo system can be translated to the multiuser mimo scenario as well in this paper we propose a method pursuing performance gain of vector perturbation in multiuser downlink systems instead of employing the maximum number of mobile users for communication we use small part of them as virtual users for improving reliability of users participating communication by controlling parameters of the virtual users including information and perturbation vector we obtain considerable improvement in the effective snr simulation results on the realistic multiuser miso and mimo downlink systems show that the proposed method brings substantial performance gain over the standard vector perturbation with marginal overhead in computations

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

weighted sum rate optimization for downlink multiuser mimo coordinated base station systems centralized and distributed algorithms this paper considers the joint linear transceiver design problem for the downlink multiuser multiple input multiple output mimo systems with coordinated base stations bss we consider maximization of the weighted sum rate with per bs antenna power constraint problem we propose novel centralized and computationally efficient distributed iterative algorithms that achieve local optimum to the latter problem these algorithms are described as follows first by introducing additional optimization variables we reformulate the original problem into a new problem second for the given precoder matrices of all users the optimal receivers are computed using minimum mean square error mmse method and the optimal introduced variables are obtained in closed form expressions third by keeping the introduced variables and receivers constant the precoder matrices of all users are optimized by using second order cone programming socp and matrix fractional minimization approaches for the centralized and distributed algorithms respectively finally the second and third steps are repeated until these algorithms converge we have shown that the proposed algorithms are guaranteed to converge we also show that the proposed algorithms require less computational cost than that of the existing linear algorithm all simulation results demonstrate that our distributed algorithm achieves the same performance as that of the centralized algorithm moreover the proposed algorithms outperform the existing linear algorithm in particular when each of the users has single antenna we have observed that the proposed algorithms achieve the global optimum

subchannel allocation in multiuser multiple input multiple output systems assuming perfect channel state information at the transmitter of a gaussian broadcast channel strategies are investigated on how to assign subchannels in frequency and space domain to each receiver aiming at a maximization of the sum rate transmitted over the channel for the general sum capacity maximizing solution which has recently been found a method is proposed that transforms each of the resulting vector channels into a set of scalar channels this makes possible to achieve capacity by simply using scalar coding and detection techniques the high complexity involved in the computation of this optimum solution motivates the introduction of a novel suboptimum zero forcing allocation strategy that directly results in a set of virtually decoupled scalar channels simulation results show that this technique tightly approaches the performance of the optimum solution i e complexity reduction comes at almost no cost in terms of sum capacity as the optimum solution the zero forcing allocation strategy applies to any number of transmit antennas receive antennas and users

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

multiple access channels with memory with and without frame synchronism the capacity region of frame synchronous and frame asynchronous discrete two user multiple access channels with finite memory is obtained frame synchronism refers to the ability of the transmitters to send their code words in unison the absence of frame synchronism in memoryless multiple access channels is known to result in the removal of the convex hull operation from the expression of the capacity region it is shown that when the channel has memory frame asynchronism rules out nonstationary inputs to achieve any point in the capacity region thereby allowing only coding strategies that involve cooperation in the frequency domain but not in the time domain this restriction drastically reduces the capacity region of some multiple access channels with memory and in particular the total capacity of the channel which is invariant to frame asynchronism for memoryless channels

design guidelines for limited feedback in the spatially correlated broadcast channel a linear beamformer design for the broadcast channel where the base station is equipped with n t antennas and signals to m 2 users each with a single antenna and where the vector channels are spatially correlated is considered this problem is of relevance in wireless standardization efforts where two users are simultaneously scheduled instead of the theoretically feasible n t user scheduling to minimize signaling overhead the users are assumed to have perfect channel state information csi whereas the base station has statistical information of the channels in the first part of this work the role of the relevance of feedback is studied via the quantification of the gap in ergodic sum rate between the perfect csi and statistics only extremes in this direction the importance of orthogonality of the dominant eigenmodes of the two users in maximizing the gap is established in the second part of this work in scenarios with a large gap limited feedback beamforming codebooks and a codeword selection metric are designed for the low rate feedback setting the main contribution here is the proposal of a generalized eigenvector codebook and feedback of the codeword index that maximizes an estimate of the signal to interference and noise ratio textsf sinr of each user extensions of this scheme are also proposed for the general n t antenna case with m users where m le n t it is shown via numerical studies that this scheme leads to significant performance improvement across a large family of channels over schemes such as grassmannian random vector quantization single user codebooks with the channel projection metric for codeword selection

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

network mimo with linear zero forcing beamforming large system analysis impact of channel estimation and reduced complexity scheduling we consider the downlink of a multicell system with multiantenna base stations and single antenna user terminals arbitrary base station cooperation clusters distance dependent propagation pathloss and general fairness requirements base stations in the same cooperation cluster employ joint transmission with linear zero forcing beamforming subject to sum or per base station power constraints intercluster interference is treated as noise at the user terminals analytic expressions for the system spectral efficiency are found in the large system limit where both the numbers of users and antennas per base station tend to infinity with a given ratio in particular for the per base station power constraint we find new results in random matrix theory yielding the squared frobenius norm of submatrices of the moore penrose pseudo inverse for the structured non i i d channel matrix resulting from the cooperation cluster user distribution and path loss coefficients the analysis is extended to the case of nonideal channel state information at the transmitters obtained through explicit downlink channel training and uplink feedback specifically our results illuminate the trade off between the benefit of a larger number of cooperating antennas and the cost of estimating higher dimensional channel vectors furthermore our analysis leads to a new simplified downlink scheduling scheme that preselects the users according to probabilities obtained from the large system results depending on the desired fairness criterion the proposed scheme performs close to the optimal finite dimensional opportunistic user selection while requiring significantly less channel state feedback since only a small fraction of preselected users must feed back their channel state information