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

complex valued matrix differentiation techniques and key results a systematic theory is introduced for finding the derivatives of complex valued matrix functions with respect to a complex valued matrix variable and the complex conjugate of this variable in the framework introduced the differential of the complex valued matrix function is used to identify the derivatives of this function matrix differentiation results are derived and summarized in tables which can be exploited in a wide range of signal processing related situations

a weighted least squares approach to precoding with pilots for mimo ofdm next generation wireless systems are expected to leverage multiple antenna commonly called multiple input multiple output mimo technology transmitting over broadband channels via orthogonal frequency division multiplexing ofdm it is now well known that mimo systems can obtain error rate and capacity improvements by adapting the transmitter to the current channel conditions linear spatial precoding is a popular technique for channel adaptation where the transmitted space time signal for each subcarrier is multiplied by a precoding matrix before transmission spatial precoding is complicated however in ofdm because channel information is often only known for a small number of pilot tones in this correspondence we present a subspace interpolation method for designing spatial precoders for all subcarriers by using the precoders known on pilot tones the nonpilot precoders are solutions to a weighted least squares design on the grassmann manifold simulation results show performance benefits over existing mimo ofdm techniques

blind separation of mutually correlated sources using precoders this paper studies the problem of blind source separation bss from instantaneous mixtures with the assumption that the source signals are mutually correlated we propose a novel approach to bss by using precoders in transmitters we show that if the precoders are properly designed some cross correlation coefficients of the coded signals can be forced to be zero at certain time lags then the unique correlation properties of the coded signals can be exploited in receiver to achieve source separation based on the proposed precoders a subspace based algorithm is derived for the blind separation of mutually correlated sources the effectiveness of the algorithm is illustrated by simulation examples

lattice based linear precoding for mimo channels with transmitter csi herein the design of linear dispersion codes for multiple input multiple output communication systems is investigated the receiver as well as the transmitter are assumed to have perfect knowledge of the channel and the receiver is assumed to employ maximum likelihood detection we propose to use linear precoding and lattice invariant operations to transform the channel matrix into a lattice generator matrix with large minimum distance separation with appropriate approximations it is shown that this corresponds to selecting lattices with good sphere packing properties lattice invariant transformations are then used to minimize the power consumption an algorithm for this power minimization is presented along with a lower bound on the optimization numerical results indicate significant gains by using the proposed method compared to channel diagonalization with adaptive bit loading

a conjectured r matrix a new spectral parameter independent r matrix that depends on all of the dynamical variables is proposed for the elliptic calogero moser models the necessary and sufficient conditions for the existence this r matrix reduces to a determinantal equality involving elliptic functions the required identity appears new and is still unproven in full generality we present it as conjecture

combining beamforming and space time coding using noisy quantized feedback the goal of combining beamforming and spacetime coding is to obtain full diversity order and to provide additional received power array gain compared to conventional space time codes in this work a class of code constellations is proposed called generalized partly orthogonal designs pods and both high rate and low rate feedback information is incorporated with possible feedback errors a binary symmetric channel bsc model characterizes feedback errors two cases are studied first when the bsc bit error probability is known a priori to the transmission ends and second when it is not known exactly based on a minimum pairwise error probability pep design criterion we design a channel optimized vector quantizer covq for feedback information and a precoder matrix codebook to adjust the transmission codewords the attractive property of our combining scheme is that it converges to conventional space time coding with low rate and erroneous feedback and to directional beamforming with high rate and error free feedback this scheme also shows desirable robustness against feedback channel modeling mismatch

on channels with partial channel state information at the transmitter we consider an independent and identically distributed i i d state dependent channel with partial rate limited channel state information csi at the transmitter csit and full csi at the receiver csir the csit comprises two parts both subject to a rate constraint and communicated over noiseless way side channels the first part is coded csi provided by a third party a genie and the second part is the output of a deterministic scalar quantizer of the state a single letter expression for the capacity of the channel is given in case the csit comprises only the coded part we show that the capacity previously suggested in the literature is too optimistic and suggest a correction as part of our expression for the information capacity for the general setting an optimal coding scheme based upon multiplexing of several codebooks is presented it is proved that the capacity of the channel is the same whether the quantizer s output is observed causally or noncausally by the encoder in the rest of the correspondence we focus on the special case where the system employs a stationary quantizer using a rate distortion approach we bound the alphabet s size of the auxiliary random variable rv of the information capacity next we turn to the additive white gaussian noise awgn channel with fading and show that the determination of the capacity region reduces to finding the optimal genie strategies and the optimal power allocation distribution along the product alphabet of the auxiliary rv and the quantizer s output alphabets the suggested model can be applied for example to an orthogonal frequency division multiplexing ofdm communication system here the fading across frequencies comprises the channel state sequence coded fading information is provided to the channel encoder via a way side rate limited channel in addition since coding operation is expensive a simpler scheme provides the channel encoder with quantized fading information e g whether each coefficient is above below a threshold

transmit beamforming for space frequency coded mimo ofdm systems with spatial correlation feedback this paper addresses the problem of joint optimization of transmit beamforming and space frequency sf coding for mimo ofdm systems with spatial correlation feedback in broadband communications this problem is challenging in the sense that the transmitter should be designed to beamform across multiple eigenspaces associated with the multipath environment simultaneously with arbitrary transmit spatial correlation the performance analysis for sf coded mimo ofdm systems with beamforming is provided and a general optimization problem for the beamforming design is formulated three suboptimal approaches to design the beamformer based on the derived design criteria are proposed i eigenvalue selection scheme ii eigenspace selection scheme and iii per subcarrier approach based on decoding at each subcarrier the proposed schemes take into account the multiple eigenspace information associated with the multipath delay channel improvement in the performance over sf coding without beamforming is shown through simulations in terms of bit error rate the eigenvalue selection scheme provides the best performance among the proposed algorithms this scheme locates the subspace associated with the largest eigenvalues in the eigenspace of the covariance matrices with the eigenvalue selection scheme the performance improvement is about 3 db over the sf coding without beamforming for highly correlated channels as shown in our simulations

adaptive mimo ofdm based on partial channel state information relative to designs assuming no channel knowledge at the transmitter considerably improved communications become possible when adapting the transmitter to the intended propagation channel as perfect knowledge is rarely available transmitter designs based on partial statistical channel state information csi are of paramount importance not only because they are more practical but also because they encompass the perfect and no knowledge paradigms in this paper we first provide a partial csi model for orthogonal frequency division multiplexed ofdm transmissions over multi input multi output mimo frequency selective fading channels we then develop an adaptive mimo ofdm transmitter by applying an adaptive two dimensional 2 d coder beamformer we derived recently on each ofdm subcarrier along with an adaptive power and bit loading scheme across ofdm subcarriers relying on the available partial csi at the transmitter our objective is to maximize the transmission rate while guaranteeing a prescribed error performance under the constraint of fixed transmit power numerical results confirm that the adaptive 2 d space time coder beamformer with two basis beams as the two strongest eigenvectors of the channel s correlation matrix perceived at the transmitter combined with adaptive ofdm power and bit loaded with m ary quadrature amplitude modulated qam constellations improves the transmission rate considerably

adaptive modulation and joint temporal spatial power allocation for ostbc mimo systems with imperfect csi we propose a novel adaptive transmission scheme for space time coded multiple input multiple output beamforming systems with imperfect channel state information at the transmitter of which the signal constellation total transmit power temporal power and power allocation among eigen beams spatial power are jointly adapted to maximize the average spectral efficiency subject to a target bit error rate and an average power constraint the power allocation over the spatial and temporal domains makes the traditional approach of partitioning the received signal to noise ratio snr inapplicable to the above design problem by introducing a new variable called as effective signal to noise to modulation ratio esnmr we derive a rate selection policy by partitioning the range of the esnmr with an optimal set of thresholds a closed form temporal power control policy and a simple spatial power allocation algorithm are also obtained numerical results demonstrate that the new adaptive transmission scheme yields a significant performance gain over existing adaptation systems

quantized feedback information in orthogonal space time block coding this work considers how the presence of quantized channel information obtained from a feedback link may be utilized for determining a transmit weighting matrix that improves the performance of a predetermined orthogonal space time block ostb code to reduce the effects of feedback delay quantization errors and feedback channel bit errors methods based on vector quantization for noisy channels are used in the design of the feedback link the resulting transmission scheme and feedback link take the imperfect nature of the channel information into account while combining the benefits of conventional beamforming with those provided by ostb coding

coded modulation with mismatched csit over mimo block fading channels reliable communication over delay constrained multiple input multiple output mimo block fading channels with discrete inputs and mismatched imperfect channel state information at the transmitter csit is studied the csit mismatch is modeled as gaussian random variables whose variances decay as a power of the signal to noise ratio snr a special focus is placed on the large snr decay of the error and outage probabilities when power control with long term power constraints is used without explicitly characterizing the corresponding power allocation algorithms we derive the outage exponent as a function of the system parameters including the csit noise variance exponent and the exponent of the peak power constraint it is shown that csit even if noisy is always beneficial and leads to important gains in terms of exponents

robust power allocation algorithms for mimo ofdm systems with imperfect csi this paper presents a bayesian approach to the design of transmit prefiltering matrices in closed loop schemes robust to channel estimation errors the algorithms are derived for a multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system two different optimization criteria are analyzed the minimization of the mean square error and the minimization of the bit error rate in both cases the transmitter design is based on the singular value decomposition svd of the conditional mean of the channel response given the channel estimate the performance of the proposed algorithms is analyzed and their relationship with existing algorithms is indicated as with other previously proposed solutions the minimum bit error rate algorithm converges to the open loop transmission scheme for very poor csi estimates

performance and optimized design of space time codes for mimo wireless systems with imperfect channel estimates multiple antennas constitute an effective mean to achieve spatial diversity in emerging bandwidth efficient multiple input multiple output mimo wireless systems until now most contributions in this area are focused on the two limit cases of fully coherent and fully incoherent decoding which in turn occur when perfect channel estimates and no channel estimates are available at the receiver however very accurate channel estimates typically demand long training sequences that reduces spectral efficiency therefore testing capabilities of multiple antenna systems with partially coherent decoding may be appealing for improving power versus bandwidth tradeoff in this contribution we focus on the optimized design and performance evaluations of multiple antenna block coded systems with partially coherent maximum likelihood ml decoding after considering emerging fourth generation wlans 4gwlans as a possible application scenario we present new performance bounds and optimized design criteria together with a new family of robust space time unitary block codes that self match to channel estimation errors we name these codes self matching

general rank multiuser downlink beamforming with shaping constraints using real valued ostbc in this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints we combine beamforming with full rate high dimensional real valued orthogonal space time block coding ostbc to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design the original multi constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation sdr which can be solved efficiently in contrast to conventional rank one beamforming approaches in which an optimal beamforming solution can be obtained only when the sdr solution after rank reduction exhibits the rank one property in our approach optimality is guaranteed when a rank of eight is not exceeded we show that our approach can incorporate up to 79 additional shaping constraints for which an optimal beamforming solution is guaranteed as compared to a maximum of two additional constraints that bound the conventional rank one downlink beamforming designs simulation results demonstrate the flexibility of our proposed beamformer design

multicell optimization for diversity and interference mitigation we study diversity and interference mitigation with an emphasis on the interaction between the transmitter receiver tx rx pairs in a two user two cell system in which the performance at each rx depends on the actions of the both desired and the interfering txs we will propose two techniques the first scheme is a greedy or competitive algorithm in which each tx rx pair employs an orthogonal space time st block code combined with a multimode beamformer a generalized st code to minimize the error probability to its own rx till an equilibrium is reached the second scheme is a cooperative algorithm also based on a generalized st code in which each tx rx pair minimizes its error probability at its desired rx but cooperates by limiting the amount of interference to the second pair s rx we will model and characterize the equilibrium of the competitive scheme called the nash equlibrium we will then show that by using the cooperative algorithm it is possible to find pareto dominant actions where both tx rx pairs either equal or improve their performance when compared with the ne actions we will analyze the conditions for pareto dominance of the cooperative scheme and finally demonstrate the performance improvements of both schemes over the single tx rx pair generalized st code

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

automatic design of orthogonal or near orthogonal linear dispersive space time block codes this paper considers a wireless multiple input multiple output mimo communication system in a frequency nonselective scenario with spatially uncorrelated rayleigh fading channel coefficients and investigates the design of linear dispersive ld space time block codes efficient ld codes are obtained by optimizing the constituent weight matrices so that an upper bound on the union bound of the codeword error probability is minimized interestingly the proposed design procedure automatically generates ld codes that either correspond to or are close to the well known class of orthogonal space time block ostb codes a theoretical analysis confirms this by proving that ostb codes are indeed optimal when the setup under study permits their existence simulation results demonstrate the excellent performance of the designed codes in particular the importance of the codes near orthogonal property is illustrated by showing that low complexity linear equalizer techniques can be used for decoding purposes while incurring a relatively moderate performance loss compared with optimal maximum likelihood ml decoding

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

how to find g admissible abelian regular coverings of a graph abstract given a finite connected simple graph and a subgroup g of its automorphism group a general method for finding all finite abelian regular coverings of that admit a lift of each element of g is developed as an application all connected arc transitive abelian regular coverings of the petersen graph are classified up to isomorphism

root mean square decomposition for est based spatial multiplexing systems we consider the transceiver design for multiple input multiple output mimo systems when the channel state information csi is available at the transmitter as well as the receiver first we propose an open loop low complexity mimo spatial multiplexing scheme based on the energy spreading transform est sm the est sm can spatially multiplex multiple data streams and iteratively detect the data streams with almost negligible interstream interference at sufficiently high snr then we propose a closed loop precoding scheme suitable for the est sm called root mean square decomposition rmsd scheme the rmsd precoding scheme combined with the est sm decomposes a mimo channel into multiple subchannels with identical snrs this desired property minimizes bit error rate ber when different bit allocations on different subchannels which cause a significant increase in system complexity are not used we show that when the est sm is used the rmsd scheme is optimal in ber performance and it achieves full diversity simulation results show that the rmsd scheme outperforms other existing techniques such as the geometric mean decomposition gmd scheme jiang ieee trans signal process vol 53 no 10 pp 3791 3803 and the uniform channel decomposition ucd scheme1 jiang ieee trans signal process vol 53 no 11 pp 4283 4294 in ber performance

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

on the relation of ostbc and code rate one qstbc average rate ber and coding gain recently the statistical properties of the equivalent channel representation of a multiple input multiple output mimo system employing code rate one quasi orthogonal space time block codes qstbc which are constructed by using orthogonal space time block codes ostbc as building elements was characterized based on these characterizations we analyze the average rate or mean mutual information the bit error rate performance and the coding gain achieved with qstbc for any number of receive and nt 2n n ges 2 transmit antennas first we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity qstbc moreover we present an upper bound on the coding gain we derive a lower and upper bound on the ber performance for qstbc furthermore we analyze the average rate achievable with qstbc in case of an uninformed transmitter and also the case in which the transmitter knows the mean channel matrix whereas the receiver has perfect csi along with the analysis we compare all the results of these performance measures with the results achieved with ostbc revealing important connections between ostbc and qstbc for example the coding gain of a qstbc is upper bounded by the coding gain of the underlying ostbc also the ber of a qstbc for nt transmit and nr receive antennas is tightly lower bounded by the ber of a full diversity providing intersymbol interference free system in addition to that we show that gains in terms of average rate by using a qstbc and thus with higher nt instead of the underlying ostbc are only attainable if the available channel state information at the transmitter csit is utilized finally we illustrate our theoretical results using numerical simulations

gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

robust transceiver optimization in downlink multiuser mimo systems we study robust transceiver optimization in a downlink multiuser wireless system where the transmitter and the receivers are equipped with antenna arrays the robustness is defined with respect to imperfect knowledge of the channel at the transmitter the errors in the channel state information are assumed to be bounded and certain quality of service targets in terms of mean square errors mses are guaranteed for all channels from the uncertainty regions iterative algorithms are proposed for the transceiver design the iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions the framework supports robust counterparts of several mse optimization problems including transmit power minimization with per user or per stream mse constraints sum mse minimization min max fairness etc although the convergence to the global optimum cannot be claimed due to the intricacy of the problems numerical examples show good practical performance of the presented methods we also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure the uncertainty modeling and a multicellular setup

on the expected rate of slowly fading channels with quantized side information we study a multiple layer variable rate system employing quantized feedback to maximize the expected rate over a single input single output slowly fading gaussian channel the transmitter uses partial channel state information which is obtained via an optimized resolution constrained feedback link to adapt the power and to assign code layer rates subject to different power constraints to systematically design the system parameters we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels we present the necessary and sufficient conditions for single layer coding to be optimal irrespective of the number of code layers that the system can afford unlike in the ergodic case even coarsely quantized feedback is shown to improve the expected rate considerably our results also indicate that with as little as one bit of feedback information the role of multilayer coding reduces significantly

space time spreading and block coding for correlated fading channels in the presence of interference we consider point to point wireless links with multiple antennas in the presence of interference and exploit channel s spatial correlation and the temporal covariance of the interference to design multiantenna transmitters we develop a space time spreading scheme that maximizes average signal to interference and noise ratio and an optimally power loaded space time beamforming stbf scheme which improves error probability performance in order to increase transmission rates we combine orthogonal space time block coding with stbf optimize power loading across beams and develop low complexity receivers optimal training for least squares error channel estimation and stbf for minimum mean square error channel estimation are also studied our analytical and simulated results corroborate that stbf with optimal power loading can considerably reduce error probability and channel estimation errors

on the structure of limited feedback beamforming codebooks for amplify and forward relay networks we determine necessary conditions on the structure of symbol error rate ser optimal compact quantizer codebooks for limited feedback beamforming in wireless networks with one transmitter receiver pair and r parallel amplify and forward relays we call a codebook small if its cardinality is less than r and large otherwise a d codebook depends on the power constraints and can be optimized accordingly while an i codebook remains fixed it was previously shown that any i codebook that contains the single relay selection srs codebook achieves the full diversity order r we prove the following every full diversity i codebook contains the srs codebook and thus is necessarily large in general as the power constraints grow to infinity the limit of an ser optimal large d codebook contains an srs codebook provided that it exists for small codebooks the maximal diversity is equal to the codebook cardinality every diversity optimal small i codebook is an orthogonal multiple relay selection omrs codebook moreover the limit of an ser optimal small d codebook is an omrs codebook we observe that srs is nothing but a special case of omrs for codebooks with cardinality equal to r as a result we call omrs as the universal necessary condition for codebook optimality finally we confirm our analytical findings through simulations

application of quasi orthogonal space time block codes in beamforming it is well known that when channel information is available at the transmitter transmit beamforming scheme can be employed to enhance the performance of a multiple antenna system recently jongren et al and zhou giannakis proposed a new performance criterion based on partial channel side information at the transmitter with this criterion an optimal beamforming matrix was constructed for the orthogonal space time block codes however the same method has not been applied to the recently proposed quasi orthogonal space time block codes qstbcs due to the nonorthogonal nature of the quasi orthogonal designs in this paper the issue of combining beamforming with qstbcs is addressed based on our asymptotic analysis we extend the beamforming scheme from jongren et al and construct the beamforming matrices for the quasi orthogonal designs the proposed beamforming scheme accomplishes high transmission rate as well as high order spatial diversity the new qstbc beamformer can be presented as a novel four directional or eight directional eigen beamformer that works for systems with four or more transmit antennas simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various snrs and for channels with different quality of feedback

limited feedback unitary precoding for orthogonal space time block codes orthogonal space time block codes ostbcs are a class of easily decoded space time codes that achieve full diversity order in rayleigh fading channels ostbcs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information when channel state information is available at the transmitter though precoding the space time codeword can be used to support different numbers of transmit antennas and to improve array gain unfortunately transmitters in many wireless systems have no knowledge about current channel conditions this motivates limited feedback precoding methods such as channel quantization or antenna subset selection this paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver the receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error free zero delay feedback channel a criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system low average distortion codebooks are derived based on the optimal codeword selection criterion the resulting design is found to relate to the famous applied mathematics problem of subspace packing in the grassmann manifold codebooks designed by this method are proven to provide full diversity order in rayleigh fading channels monte carlo simulations show that limited feedback precoding performs better than antenna subset selection

capacity of a multiple antenna fading channel with a quantized precoding matrix given a multiple input multiple output mimo channel feedback from the receiver can be used to specify a transmit precoding matrix which selectively activates the strongest channel modes here we analyze the performance of random vector quantization rvq in which the precoding matrix is selected from a random codebook containing independent isotropically distributed entries we assume that channel elements are independent and identically distributed i i d and known to the receiver which relays the optimal rate maximizing precoder codebook index to the transmitter using b bits we first derive the large system capacity of beamforming rank one precoding matrix as a function of b where large system refers to the limit as b and the number of transmit and receive antennas all go to infinity with fixed ratios rvq for beamforming is asymptotically optimal i e no other quantization scheme can achieve a larger asymptotic rate we subsequently consider a precoding matrix with arbitrary rank and approximate the asymptotic rvq performance with optimal and linear receivers matched filter and minimum mean squared error mmse numerical examples show that these approximations accurately predict the performance of finite size systems of interest given a target spectral efficiency numerical examples show that the amount of feedback required by the linear mmse receiver is only slightly more than that required by the optimal receiver whereas the matched filter can require significantly more feedback

on channel orthogonalization using space time block coding with partial feedback orthogonal space time block codes ostbcs yield full diversity gain even while requiring only a linear receiver such full rate rate one orthogonal designs are available for complex symbol constellations only for n 2 transmit antennas in this paper we propose a new family of full rate space time block codes stbcs using a single parameter feedback for communication over rayleigh fading channels for n 3 4 transmit antennas and m receive antennas the proposed rate one codes achieve full diversity and the performance is similar to maximum receiver ratio combining the decoding complexity of these codes are only linear even while performing maximum likelihood decoding the partial channel information is a real phase parameter that is a function of all the channel gains and has a simple closed form expression for n 3 4 this feedback information enables us to derive channel orthogonal designs starting from quasi orthogonal stbcs the feedback complexity is significantly lower than conventional closed loop transmit beamforming we compare the proposed codes with the open loop ostbcs and also with the closed loop equal gain transmission egt scheme which uses equal power loading on all antennas simulated error rate performances indicate that the proposed channel orthogonalized stbcs significantly outperform the open loop orthogonal designs for the same spectral efficiency moreover even with significantly lower feedback and computational complexity the proposed scheme outperforms the egt technique for m n

worst case mse precoder design for imperfectly known mimo communications channels this paper considers a worst case precoder design problem for multiple input multiple output mimo wireless communication systems with imperfect channel knowledge at the transmitter when the mimo channel is a full row rank matrix which arises generically when the number n sub t of transmit antennas is greater or equal to the number n sub r of receive antennas and when channel state information is known perfectly at the transmitter the channel can be equalized exactly by employing a precoder equal to the channel pseudo inverse however in actual systems it is necessary to take into account the channel estimation error we consider here a worst case precoder design problem where the goal is to find the precoder minimizing the equalization mean square error for the least favorable channel located in a ball centered about the estimated channel lagrangian optimization is used to convert this min max problem into a min min convex minimization problem over a convex domain which can be solved in closed form the robust precoder and associated least favorable channel have an intuitive interpretation since the least favorable channel zeroes out the weakest subchannels and the robust precoder implements a pseudo inverse only for the remaining subchannels

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

a differential space time modulation scheme for correlated rayleigh fading channels performance analysis and design differential space time modulation dstm is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels it can be viewed as an extension of the differential phase shift keying scheme in single antenna systems in this paper we investigate the performance of multiantenna systems employing dstm under spatially correlated rayleigh fading channels we present three expressions for calculating the pairwise error probability pep of the dstm scheme the first expression allows us to numerically calculate the exact pep the remaining two are closed form expressions of the exact pep at asymptotically high signal to noise ratios and the pep upper bound it is found that when the distance matrix is proportional to the identity matrix the error probability is determined by the channel correlation matrix and the initial transmitted code matrix based on the new pep upper bound we derive a criterion for optimizing the initial code matrix for this special case simulation results show that the performance of the differential space time coded systems can be significantly improved by designing the initial transmitted code matrix according to the proposed design criterion

a novel weighted multilevel space time trellis coding scheme it has been shown that when perfect or partial channel state information csi is available at the transmitter the performance and capacity of a space time coded system can be further improved multilevel space time trellis codes mlsttc s are capable of simultaneously providing bandwidth efficiency diversity improvement and coding gain with significantly reduced decoding complexity especially for larger constellations and higher throughputs in this paper we present a design of combined multilevel space time trellis codes and beam forming based on feedback from receiver henceforth referred to as weighted multilevel space time trellis codes wmlsttcs the channel profile is used to provide a beam forming scheme that achieves the better performance by properly weighting transmitted signals weights are selected that matches best with a channel profile feedback from the receiver indicative of long term characteristics of the wireless channel wmlsttcs provide improvement in performance of mlsttcs

differential space time modulation with eigen beamforming for correlated mimo fading channels in this paper joint differential space time modulation dstm and eigen beamforming for correlated multiple input multiple output mimo fading channels while dstm does not require knowledge of each channel realization the channel s spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance a transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space time block coding error probability is analyzed for both spatially correlated and independent rayleigh fading channels based on the error probability analysis power loading coefficients are derived to improve performance the analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to dstm without beamforming

space time trellis codes based on channel phase feedback space time coding stc has been proposed recently for multiple antenna wireless communication systems most of the proposed stc schemes use the assumption that either no channel state information or the channel mean covariance information is available at the transmitter in this paper we propose a new stc scheme for a closed loop transmission system where quantized channel phase information is available at the transmitter a new performance criterion is derived for the quasi static fading channel this design criterion is then used to construct a new class of space time trellis codes sttcs the proposed code construction is based on the concatenation of a standard multiple trellis coded modulation outer code with an inner code the inner code is selected from a series of inner codes using the channel phase feedback the series of inner codes are constructed based on the systematic set partitioning of several classes of space time signal designs simulation results show significant performance improvement over the other sttcs in the literature in addition the proposed coding scheme enjoys low peak to average power ratio simple decoding and power efficient low cost implementation

optimal transmitter eigen beamforming and space time block coding based on channel correlations optimal transmitter designs obeying the water filling principle are well documented and widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information csi may be costly or impossible to acquire in rapidly varying wireless environments we develop in this paper statistical water filling approaches for stationary random fading channels these approaches require only knowledge of the channel correlations that do not necessitate frequent updates and can be easily acquired applied to a multiple transmit antenna paradigm our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel s correlation matrix and with proper power loading across the beams the optimality pertains to minimizing a tight bound on the symbol error rate the resulting loaded eigen beamforming outperforms not only the equal power allocation across all antennas but also the conventional beamformer that transmits the available power along the strongest direction coupled with orthogonal space time block codes two dimensional 2 d eigen beamforming emerges as a more attractive choice than conventional one dimensional 1 d beamforming with uniformly better performance without rate reduction and without complexity increase

optimal joint spatial and temporal power adaptation for space time coded systems with imperfect csi in this correspondence a joint optimization of spatio temporal s t power allocation to minimize the average bit error rate ber subject to an average power constraint is developed for beamforming orthogonal space time block coded multiantenna systems over flat rayleigh fading channels in the presence of imperfect channel state information at the transmitter csit compared to the spatial only s o power allocation methods the optimal s t strategy reduces ber significantly it can be used as a benchmark to evaluate the existing suboptimal s t schemes a necessary and sufficient condition which can determine the number of eigenbeams being used for optimal s t power allocation without computing power allocation is derived this result can greatly simplify the power allocation algorithm numerical results show that the proposed optimal s t algorithm has not only the best ber performance but also the lowest computational complexity in comparison with the existing s t strategies

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

precoder design for space time coded systems over correlated rayleigh fading channels using convex optimization a class of computationally efficient linear precoders for space time block coded multiple input multiple output wireless systems is derived based on the minimization of the exact symbol error rate ser and its upper bound both correlations at the transmitter and receiver are assumed to be present and only statistical channel state information in the form of the transmit and receive correlation matrices is assumed to be available at the transmitter the convexity of the design based on ser minimization is established and exploited the advantage of the developed technique is its low complexity we also find various relationships of the proposed designs to the existing precoding techniques and derive very simple closed form precoders for special cases such as two or three receive antennas and constant receive correlation the numerical simulations illustrate the excellent ser performance of the proposed precoders

transmit precoding in a noncoherent relay channel with channel mean feedback this paper investigates the optimal source transmit precoding to maximize the ergodic mutual information between the input and the output of a noncoherent amplify and forward relay channel with multiple antennas at the source and with a single antenna at both the relay and the destination it is assumed that only the source relay channel mean information is available at the source the challenge here is that relaying introduces a nonconvex structure in the objective function therefore previous methods dealing with channel mean feedback which generally require the concavity of the objective function cannot be applied to circumvent the difficulty at hand a different approach based on stochastic ordering is employed the stochastic optimization problem here is ultimately transformed into the comparison of two nonnegative random variables in the laplace transform order it is shown that the optimal source transmit strategy is to transmit along the known channel mean and its orthogonal eigen channels our result subsumes as an asymptotic case the optimal precoding for multiple input single output miso channels without relaying under mean feedback furthermore the analysis can be partially extended to the case with multiple antennas at the relay numerical examples are provided to complement and corroborate the analysis

optimization of nonlinear signal constellations for real world mimo channels the performance of spatial multiplexing sm multiple input multiple output mimo communication systems is highly dependent on the richness of scattering the presence of dominant components and the interelement spacings in this paper a new interpretation of the impact of transmit correlation on the performance of sm is given based on a so called symbol related array factor nonlinear signal constellations for sm over real world fading channels are then designed by minimizing an estimate of the average symbol error rate under an average transmit power constraint the new transmission scheme exploits the spectral efficiency advantage of sm and the robustness of eigen beamforming through simulations it is shown to be more robust against fading correlations and high ricean k factors than sm using the classical phase shift keying psk and quadrature amplitude modulation qam constellations the symbol error rate performance of this scheme is not affected by a change in the propagation environment or the interelement distance furthermore if the scheme is used on the uplink no explicit rate consuming feedback link from the base station to the mobile station is required

limited feedback design for interference alignment on mimo interference networks with heterogeneous path loss and spatial correlations interference alignment is degree of freedom optimal on k user mimo interference channels and many previous works have studied the transceiver designs however these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology in this paper we consider a limited feedback system with heterogeneous path loss and spatial correlations and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency we propose a novel spatial codebook design and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology we bound the system throughput under the proposed dynamic scheme in terms of the transmit snr feedback bits and the interference topology parameters it is shown that when the number of feedback bits scales with snr as c s cdot log hbox snr cal o 1 the sum degrees of freedom of the network are preserved moreover the value of scaling coefficient c s can be significantly reduced in networks with asymmetric interference topology