space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

finite model approximations and asymptotic optimality of quantized policies in decentralized stochastic control we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents the strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions in particular quantized team policies are asymptotically optimal this result is then applied to witsenhausen s celebrated counterexample and the gaussian relay channel problem for witsenhausen s counterexample our approximation approach provides to our knowledge the first rigorously established result that one can construct an varepsilon optimal strategy for any varepsilon 0 through a solution of a simpler problem

stochastic teams with nonclassical information revisited when is an affine law optimal in this note we consider a parameterized family of two stage stochastic control problems with nonclassical information patterns which includes the well known 1968 counterexample of witsenhausen we show that whenever the performance index does not contain a product term between the decision variables the optimal solution is linear in the observation variables the parameter space can be partitioned into two regions in one of which the optimal solution is linear whereas in the other it is inherently nonlinear extensive computations using two point piecewise constant policies and linear plus piecewise constant policies provide numerical evidence that nonlinear policies may indeed outperform linear policies when the product term is present

static team problems part i sufficient conditions and the exponential cost criterion the stationary conditions of radner are shown under relaxed hypotheses to be sufficient to establish the global optimality of candidate control laws for static team problems with convex cost this extension of radner s theorem establishes the optimality of affine laws for the exponential of a quadratic performance index with jointly gaussian state and observation variables the class of performance indexes of team problems for which the optimal solution is known is thereby enlarged

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

a new generic maximum likelihood metric expression for space time block codes with applications to decoding the metric expression for a generic linear space time block code stbc is studied using a different approach to vectorization and a new representation of the metric the new representation lends itself to a simple measure of reliability based on the sum of inner products and provides a quantifiable definition for minimum distance of a stbc this provides the framework for a new family of near maximum likelihood ml and ml decoding algorithms it also has applications in the development of optimality test criteria for stbcs as well as in the design of stbcs with low decoding complexity

brief paper optimal memoryless control in gaussian noise a simple counterexample in this paper we investigate control strategies for a scalar one step delay system in discrete time i e the state of the system is the input delayed by one time unit in contrast with classical approaches here the control action must be a memoryless function of the output of the plant which comprises the current state corrupted by measurement noise we adopt a first order state space representation for the delay system where the initial state is a gaussian random variable in addition we assume that the measurement noise is drawn from a white and gaussian process with zero mean and constant variance performance evaluation is carried out via a finite time quadratic cost that combines the second moment of the control signal and the second moment of the difference between the initial state and the state at the final time we show that if the time horizon is one or two then the optimal control is a linear function of the plant s output while for a sufficiently large horizon a control taking on only two values will outperform the optimal affine solution this paper complements the well known counterexample by hans witsenhausen which showed that the solution to a linear quadratic and gaussian optimal control paradigm might be nonlinear witsenhausen s counterexample considered an optimization horizon with two time steps two stage control in contrast with witsenhausen s work the solution to our counterexample is linear for one and two stages but it becomes nonlinear as the number of stages is increased the fact that our paradigm leads to nonlinear solutions in the multi stage case could not be predicted from prior results in contrast to prior work the validity of our counterexample is based on analytical proof methods our proof technique rests on a simple nonlinear strategy that is useful in its own right since it outperforms any affine solution

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

high rate concatenated space time block code m tcm designs in this paper a new technique to design improved high rate space time st codes is proposed based on the concept of concatenated st block code stbc and outer trellis coded modulation m tcm encoder constructions unlike the conventional rate lossy stbc mtcm schemes the proposed designs produce higher rate st codes by expanding the codebook of the inner orthogonal stbc the classic set partitioning concept is adopted to realize the stbc mtcm designs with large coding gains the proposed expanded stbc mtcm designs for the two three and four transmitter cases are illustrated simulation results show the proposed stbc mtcm designs significantly outperform the traditional st tcm schemes furthermore decoding complexity of the proposed scheme is low because signal orthogonality is exploited to ease data decoding

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

uncoded transmission is exactly optimal for a simple gaussian sensor network a single memoryless gaussian source is observed by many terminals subject to independent gaussian observation noises the terminals are linked to a fusion center via a standard gaussian multiple access channel the fusion center needs to recover the underlying gaussian source with respect to mean squared error in this correspondence a theorem of witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission i e each terminal s channel input is merely a scaled version of its noisy observation

existence of equilibria via ekeland s principle abstract in the literature when dealing with equilibrium problems and the existence of their solutions the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity together with some weak continuity assumptions of the function in this paper we focus on conditions that do not involve any convexity concept neither for the domain nor for the function involved starting from the well known ekeland s theorem for minimization problems we find a suitable set of conditions on the function f that lead to an ekeland s variational principle for equilibrium problems via the existence of e solutions we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

optimal estimation over the collision channel consider a distributed sensing system that comprises two sensors each observing a random variable and a remote estimator the goal of the remote estimator is to produce estimates of the random variables based on information transmitted to it by the sensors the random variables are independent and information is transferred from the sensors to the estimator via a collision channel which can only convey a single packet each sensor has the authority to decide what and when to transmit and simultaneous transmissions result in a collision event to be detected at the estimator in our formulation there is no communication between the sensors which precludes the use of coordinated strategies our results characterize the structure of policies at the sensors and the remote estimator that are optimal with respect to a mean squared error criterion more specifically we show that there exist optimal policies at the sensors that use deterministic threshold strategies to decide when to transmit this structural result is independent of the distributions of the observed random variables in our analysis we prove that the computation of a person by person optimal threshold policy can be recast as a one bit optimal quantization problem for which the cost is nonuniform across representation symbols based on that observation we provide an iterative procedure akin to the lloyd max algorithm that can be used to compute locally optimal solutions in the gaussian case our iterative method converged to an optimal solution in all numerical examples we have tried we provide several examples that show the optimality of asymmetric threshold policies even when the overall framework is symmetric such as when both random variables are gaussian with zero mean and the same variance

an efficient zj based decoding algorithm for space time trellis codes in slow rayleigh fading channels in this paper we propose a computationally efficient decoding algorithm for space time trellis codes in slow rayleigh fading channels the proposed scheme is based on a stack algorithm with two key ideas i a variable stack size depending upon the signal to noise ratio to avoid the exhaustive search of paths and ii a normalized metric which is defined as each cumulative path metric divided by its own length in the stack to provide an appropriate comparison of the paths with different lengths simulation results demonstrate that the proposed algorithm achieves near ml performance with significant reduction in complexity compared with the conventional viterbi algorithm

super orthogonal space time trellis codes we introduce a new class of space time codes called super orthogonal space time trellis codes these codes combine set partitioning and a super set of orthogonal space time block codes in a systematic way to provide full diversity and improved coding gain over earlier space time trellis code constructions we also study the optimality of our set partitioning and provide coding gain analysis codes operating at different rates up to the highest theoretically possible rate for different number of states can be designed by using our optimal set partitioning super orthogonal space time trellis codes can provide a tradeoff between rate and coding gain simulation results show more than 2 db improvements over the codes presented in the literature while providing a systematic design methodology

space time codes from structured lattices we present constructions of space time st codes based on lattice coset coding first we focus on st code constructions for the short block length case i e when the block length is equal to or slightly larger than the number of transmit antennas we present constructions based on dense lattice packings and nested lattice voronoi shaping our codes achieve the optimal diversity multiplexing tradeoff dmt of quasi static multiple input multiple output mimo fading channels for any fading statistics and perform very well also at practical moderate values of signal to noise ratios snr then we extend the construction to the case of large block lengths by using trellis coset coding we provide constructions of trellis coded modulation tcm schemes that are endowed with good packing and shaping properties both short block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer mmse gdfe lattice decoding and a combination of this with a viterbi tcm decoder for the tcm case beyond the interesting algebraic structure we exhibit codes whose performance is among the state of the art considering codes with similar encoding decoding complexity

white noise representations in stochastic realization theory it is proved that any random sequence can be exhibited as the output of a stochastic dynamical system driven by white noise further refinements are obtained for markov stationary and ergodic sequences this settles some open problems in stochastic realization theory posed by willems and van schuppen nato asi ams seminar on algebraic and geometric methods in linear system theory harvard university cambridge ma 1979

improved quasi orthogonal codes through constellation rotation in this letter we show that the performance of recently proposed quasi orthogonal space time codes can be improved by phase shifting the constellations of the symbols constituting the code the optimal rotation of the symbols increases the minimum distance of the corresponding space time codewords leading to substantially improved performance

semiorthogonal space time block codes in this paper a new class of full diversity rate one space time block codes stbcs called semiorthogonal algebraic space time block codes sast codes is proposed sast codes are delay optimal when the number of transmit antennas is even the sast codeword matrix has a generalized alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols sast codes with maximal coding gain are constructed by using rate one linear threaded algebraic space time ltast codes compared with ltsat codes sast codes not only reduce the complexity of maximum likelihood detection but also provide remarkable performance gain they also outperform other stbc with rate one or less sast codes also perform well with suboptimal detectors such as the vertical bell laboratories layered space time v blast nulling and cancellation receiver finally sast codes attain nearly 100 of the shannon capacity of open loop multiple input single output miso channels

proximal methods for cohypomonotone operators conditions are given for the viability and the weak convergence of an inexact relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a hilbert space in turn new convergence results are obtained for an extended version of the proximal method of multipliers in nonlinear programming

multivalued mixed variational inequalities with locally lipschitzian and locally cocoercive multivalued mappings abstract in this paper we study the problem of solving multivalued mixed variational inequalities by using some sequential approximation techniques of fixed point theory we solve the multivalued mixed variational inequalities involving locally lipschitzian or locally cocoercive multivalued mappings we establish that the convexity of the multivalued mapping values is not needed and construct by using the banach contraction principle converging sequences to the solutions also we show how to choose regularization parameters to compute these solutions

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

optimization and convergence of observation channels in stochastic control this paper studies the optimization of observation channels stochastic kernels in partially observed stochastic control problems in particular existence and continuity properties are investigated mostly but not exclusively concentrating on the single stage case continuity properties of the optimal cost in channels are explored under total variation setwise convergence and weak convergence sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored

high rate multisymbol decodable stbcs from clifford algebras it is well known that space time block codes stbcs obtained from orthogonal designs ods are single symbol decodable ssd and from quasi orthogonal designs qods are double symbol decodable dsd however there are ssd codes that are not obtainable from ods and dsd codes that are not obtainable from qods in this paper a method of constructing g symbol decodable g sd stbcs using representations of clifford algebras are presented which when specialized to g 1 2 gives ssd and dsd codes respectively for the number of transmit antennas 2a the rate in complex symbols per channel use of the g sd codes presented in this paper is a 1 g 2a g the maximum rate of the dsd stbcs from qods reported in the literature is a 2a 1 which is smaller than the rate a 1 2a 2 of the dsd codes of this paper for 2a transmit antennas in particular the reported dsd codes for 8 and 16 transmit antennas offer rates 1 and 3 4 respectively whereas the known stbcs from qods offer only 3 4 and 1 2 respectively the construction of this paper is applicable for any number of transmit antennas the diversity sum and diversity product of the new dsd codes are studied it is shown that the diversity sum is larger than that of all known qods and hence the new codes perform better than the comparable qods at low signal to noise ratios snrs for identical spectral efficiency simulation results for dsd codes at various spectral efficiencies are provided

design of fully diverse multiple antenna codes based on sp 2 fully diverse constellations i e sets of unitary matrices whose pairwise differences are nonsingular are useful in multiple antenna communications especially in multiple antenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we construct four transmit antenna constellations appropriate for differential modulation based on the symplectic group sp 2 they can be regarded as extensions of alamouti s celebrated two transmit antenna orthogonal design which can be constructed from the group sp 1 we further show that the structure of sp 2 codes lends itself to efficient maximum likelihood ml decoding via the sphere decoding algorithm finally the performance of sp 2 codes is compared with that of other existing codes including alamouti s orthogonal design a 4 spl times 4 complex orthogonal design cayley differential unitary space time codes and group based codes

golden space time trellis coded modulation in this paper we present a multidimensional trellis coded modulation scheme for a high rate 2times2 multiple input multiple output mimo system over slow fading channels set partitioning of the golden code is designed specifically to increase the minimum determinant the branches of the outer trellis code are labeled with these partitions and viterbi algorithm is applied for trellis decoding in order to compute the branch metrics a sphere decoder is used the general framework for code design and optimization is given performance of the proposed scheme is evaluated by simulation and it is shown that it achieves significant performance gains over the uncoded golden code

on the existence of optimal policies for a class of static and sequential dynamic teams in this paper we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team optimal solutions we first investigate the existence of optimal solutions in static teams where the observations of the decision makers are conditionally independent given the state and satisfy certain regularity conditions building on these findings and the static reduction method of witsenhausen we then extend the analysis to sequential dynamic teams in particular we show that a large class of dynamic linear quadratic gaussian lqg teams including the vector version of the well known witsenhausen s counterexample and the gaussian relay channel problem viewed as a dynamic team admit team optimal solutions results in this paper substantially broaden the class of stochastic control problems with nonclassical information known to have optimal solutions

a bundle method for solving variational inequalities in this paper we present a bundle method for solving a generalized variational inequality problem this problem consists of finding a zero of the sum of two multivalued operators defined on a real hilbert space the first one f is monotone and the second is the subdifferential of a lower semicontinuous proper convex function our method is based on the auxiliary problem principle due to cohen and our strategy is to approximate in the subproblems the nonsmooth convex function by a sequence of convex piecewise linear functions as in the bundle method for nonsmooth optimization this makes the subproblems more tractable first we explain how to build step by step suitable piecewise linear approximations by means of a bundle strategy and we present a new stopping criterion to determine whether the current approximation is good enough this criterion is the same as that commonly used in the special case of nonsmooth optimization second we study the convergence of the algorithm for the case when the stepsizes are chosen going to zero and for the case bounded away from zero in the first case the convergence can be proved under rather mild assumptions the operator f is paramonotone and possibly multivalued in the second case the convergence needs a stronger assumption f is single valued and satisfies a dunn property finally we illustrate the behavior of the proposed algorithm by some numerical tests