Channel and capacity estimation errors

Systems with multiple element transmitter and receiver arrays have been shown to achieve very high spectral efficiencies. The theoretically achievable Shannon capacity is a function of the channel between the transmitters and the receivers. On the simulation level, one assumes certain statistical characteristics for the channel, but on a practical level, the actual channel is measured. We show that the accuracy of the measurements affects the accuracy of the capacity estimation when using the Shannon formula. We study analytically how the channel estimation error appears in the capacity formula, and we derive mathematical expressions for the first- and second-order approximations of the error. We also present simulation results that show the effect of the system size, the measurement accuracy, the system signal-to-noise ratio and the nature of the channel itself on the accuracy of the estimation of the channel capacity.     

Symmetric capacity and signal design for L-out-of-Ksymbol-synchronous CDMA Gaussian channels

We consider the symbol-synchronous Gaussian L-out-of-K code-division multiaccess channel, and obtain the capacity region and the upper and lower bounds to the symmetric capacity. The capacity region is found to be the same with or without frame synchronism. The lower bound depends on the signature waveforms through the eigenvalues of the SNR-weighted crosscorrelation matrix. We find a sufficient condition for the signature waveform set to maximize this lower bound and give an algorithm to construct a set of signature waveforms satisfying the sufficient condition     

Channel capacity of fading channels for differentially encodedtransmission

The capacity of flat fading channels when applying differential encoding with noncoherent reception and no channel state information available at the receiver is considered. Numerical results indicate the gains achievable by multiple symbol detection in the case of slowly time-varying channels and provide a comparison between schemes with different potential bandwidth efficiencies     

CHANNEL ESTIMATION FOR ITERATIVE DECODING OVER FADING CHANNELS

A method of coherent detection and channel estimation for punctured convolutional coded binary Quadrature Amplitude Modulation (QAM) signals transmitted over a frequency-flat Rayleigh fading channels used for a digital radio broadcasting transmission is presented.Some known symbols are inserted in the encoded data stream to enhance the channel estimation process.The puilot symbols are used to replace the existing parity symbols so no bandwidth expansion is required.An iterative algorithm that uses decoding information as well as the information contained in the known symbols is used to improve the channel parameter estimate.The scheme complexity grows exponentially with the channel estimation filter length,The performance of the system is compared for a normalized fading rate with both perfect coherent detection(Corresponding to a perfect knowledge of the fading process and noise variance)and differential detection of Differential Amplitude Phase Shift Keying (DAPSK).The tradeoff between simplicity of implementation and bit-error-rate performance of different techniques is also compared.     

Sum capacity of Gaussian vector broadcast channels

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

Channel capacity and non-uniform signalling for free-space optical intensity channels

This work considers the design of capacityapproaching, non-uniform optical intensity signalling in the presence of average and peak amplitude constraints. Although it is known that the capacity-achieving input distribution is discrete with a finite number of mass points, finding it requires complex non-linear optimization at every SNR. In this work, a simple expression for a capacity-approaching distribution is derived via source entropy maximization. The resulting mutual information using the derived discrete non-uniform input distribution is negligibly far away from the channel capacity. The computation of this distribution is substantially less complex than previous optimization approaches and can be easily computed at different SNRs. A practical algorithm for non-uniform optical intensity signalling is presented using multi-level coding followed by a mapper and multi-stage decoding at the receiver. The proposed signalling is simulated on free-space optical channels and outage capacity is analyzed. A significant gain in both rate and probability of outage is achieved compared to uniform signalling, especially in the case of channels corrupted by fog.     

Channel capacity limits for multiple-access channels with slowRayleigh fading

The complex-valued collaborative coding multiple-access (CVCCMA) technique has been shown to offer efficient simultaneous transmission by multiple users over a common radio channel, without the use of orthorgonal codes nor subdivisions in time or frequency. The authors describe the capacity calculation for a T user CVCCMA system in a slow Rayleigh fading environment with additive white Gaussian noise (AWGN). The capacity, in terms of bits per channel use has also been derived by simulation for different values of T with MPSK modulation     

Channel estimation and interference suppression infrequency-selective fading channels

The issue of interference suppression is considered for wireless time-division multiple-access (TDMA) systems equipped with multiple receive antennas in frequency-selective fading channels. A novel scheme is presented to estimate the multipath channel, coherently demodulate information symbols, and meanwhile suppress radio interference. The proposed scheme is simple to implement and able to mitigate interference of various origins, including intersymbol interference, co-channel interference and others. Numerical examples are presented to illustrate the performance of the proposed scheme     

FDMA capacity of Gaussian multiple-access channels with ISI

This paper proposes a numerical method for characterizing the rate region achievable with frequency-division multiple access (FDMA) for a Gaussian multiple-access channel with intersymbol interference. The frequency spectrum is divided into discrete frequency bins and the discrete bin-assignment problem is shown to have a convex relaxation, making it tractable to numerical optimization algorithms. A practical low-complexity algorithm for the two-user case is also proposed. The algorithm is based on the observation that the optimal frequency partition has a two-band structure when the two channels are identical or when the signal-to-noise ratio is high. The simulation result shows that the algorithm performs well in other cases as well. The FDMA-capacity algorithm is used to devise the optimal frequency-division duplex plan for very-high-speed digital subscriber lines     

On the capacity of binary and Gaussian channels withrun-length-limited inputs

Bounds on the capacity of binary symmetric channels and additive Gaussian channels with run-length-limited two-level (binary, bipolar) inputs are presented, and their tightness is demonstrated for some cases. Stationary input sequences, which do not degrade capacity, are considered when deriving the bounds. Lower bounds on the magnetic recording density for a simple continuous-time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions. A superiority of about 1.5 dB in signal-to-noise ratio is observed for the soft-decision scheme     

Outer bounds on the capacity of Gaussian interference channels

Two outer bounds on the capacity region of the two-user Gaussian interference channel (IFC) are derived. The idea of the first bound is to let a genie give each receiver just enough information to decode both messages. This bound unifies and improves the best known outer bounds of Sato and Carleial. Furthermore, the bound extends to discrete memoryless IFCs and is shown to be equivalent to another bound of Carleial. The second bound follows directly from existing results of Costa and Sato and possesses certain optimality properties for weak interference.     

On the asymptotic capacity of stationary Gaussian fading channels

We consider a peak-power-limited single-antenna flat complex-Gaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with special emphasis on tightness in the high signal-to-noise ratio (SNR) regime. Necessary and sufficient conditions (in terms of the autocorrelation of the fading process) are derived for capacity to grow double-logarithmically in the SNR. For cases in which capacity increases logarithmically in the SNR, we provide an expression for the "pre-log", i.e., for the asymptotic ratio between channel capacity and the logarithm of the SNR. This ratio is given by the Lebesgue measure of the set of harmonics where the spectral density of the fading process is zero. We finally demonstrate that the asymptotic dependence of channel capacity on the SNR need not be limited to logarithmic or double-logarithmic behaviors. We exhibit power spectra for which capacity grows as a fractional power of the logarithm of the SNR     

Channel estimation for OFDM systems with transmitter diversity inmobile wireless channels

Transmitter diversity is an effective technique to improve wireless communication performance. In this paper, we investigate transmitter diversity using space-time coding for orthogonal frequency division multiplexing (OFDM) systems in high-speed wireless data applications. We develop channel parameter estimation approaches, which are crucial for the decoding of the space-time codes, and we derive the MSE bounds of the estimators. The overall receiver performance using such a transmitter diversity scheme is demonstrated by extensive computer simulations. For an OFDM system with two transmitter antennas and two receiver antennas with transmission efficiency as high as 1.475 bits/s/Hz, the required signal-to-noise ratio is only about 7 dB for a 1% bit error rate and 9 dB for a 10% word error rate assuming channels with two-ray, typical urban, and hilly terrain delay profiles, and a 40-Hz Doppler frequency. In summary, with the proposed channel estimator, combining OPDM with transmitter diversity using space-time coding is a promising technique for highly efficient data transmission over mobile wireless channels     

On the transport capacity of Gaussian multiple access and broadcast channels

We study the transport capacity of the Gaussian multiple access channel (MAC), which consists of multiple transmitters and a single receiver, and the Gaussian broadcast channel (BC), which consists of a single transmitter and multiple receivers. The transport capacity is defined as the sum, over all transmitters (for the MAC) or receivers (for the BC), of the product of the data rate with a reward r(x) which is a function of the distance x that the data travels. In the case of the MAC, assuming that the sum of the transmit powers is upper bounded, we calculate in closed form the optimal power allocation among the transmitters, that maximizes the transport capacity, using Karush-Kuhn-Tucker (KKT) conditions. We also derive asymptotic expressions for the optimal power allocation, that hold as the number of transmitters approaches infinity, using the most-rapid-approach method of the calculus of variations. In the case of the BC, we calculate in closed form the optimal allocation of the transmit power among the signals to the different receivers, both for a finite number of receivers and for the case of asymptotically many receivers, using our results for the MAC together with duality arguments. Our results can be used to gain intuition and develop good design principles in a variety of settings. For example, they apply to the uplink and downlink channel of cellular networks, and also to sensor networks which consist of multiple sensors that communicate with a single central station. Work was carried out while all authors were with the Telecommunications Research Center Vienna (ftw.), and supported by K plus funding for the ftw. project I0 “Signal and Information Processing.” Parts of this work have appeared, in preliminary form, in [1,2,3], Gautam A. Gupta holds a joint B.S./M.S. degree in mathematics and computing at the Department of Mathematics of the Indian Institute of Technology at New Delhi. During the summer of 2003, he attended a summer course on Probability and Statistical Mechanics organized by the Scoula Normale Superiore, in Pisa, Italy. During the summers of 2004 and 2005 he worked at the Telecommunications Research Center Vienna (ftw.) as a summer intern. During the spring of 2006, he was a visitor at the Norwegian University of Science and Technology, working toward his M. S. Thesis. Stavros Toumpis received the Diploma in electrical and computer engineering from the National Technical University of Athens, Greece, in 1997, the M.S. degrees in electrical engineering and mathematics from Stanford University, CA, in 1999 and 2002, respectively, and the Ph.D. degree in electrical engineering, also from Stanford, in 2003. From 1998 to 1999, he worked as a Research Assistant for the Mars Global Surveyor Radio Science Team, providing operational support. From 2000 to 2003, he was a Member of the Wireless Systems Laboratory, at Stanford University. From 2003 to 2005, he was a Senior Researcher with the Telecommunications Research Center Vienna (ftw.), in Vienna, Austria. Since 2005, he is a Lecturer at the Department of Electrical and Computer Engineering of the University of Cyprus. His research is on wireless ad hoc networks, with emphasis on their capacity, the effects of mobility on their performance, medium access control, and information theoretic issues. Jossy Sayir received his Dipl. El.-Ing. degree from the ETH Zurich in 1991. From 1991 to 1993, he worked as a development engineer for Motorola Communications in Tel Aviv, Israel, contributing to the design of the first digital mobile radio system ever produced by Motorola. He returned to ETH from 1993 to 1999, getting his PhD in 1999 under the supervision of Prof. J.L. Massey. The title of his thesis is “On Coding by Probability Transformation.” Since 2000, he has been employed at the Telecommunications Research Center (ftw) in Vienna, Austria, as a senior researcher. His research interests include iterative decoding methods, joint source and channel coding, numerical capacity computation algorithms, Markov sources, and wireless ad hoc and sensor networks. Since July 2002, he manages part of the strategic research activities at Ftw and supervises a group of researchers. He has taught courses on Turbo and related codes at Vienna University of Technology and at the University of Aalborg, Denmark. He has served on the organization committees of several international conferences and workshops. Ralf R. Müller was born in Schwabach, Germany, 1970. He received the Dipl.-Ing. and Dr.Ing. degree with distinction from University of Erlangen-Nuremberg in 1996 and 1999, respectively. From 2000 to 2004, he was with Forschungszentrum Telekommunikation Wien (Vienna Telecommunications Research Center) in Vienna, Austria. Since 2005 he has been a full professor at the Department of Electronics and Telecommunications at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. He held visiting appointments at Princeton University, U.S.A., Institute Eurecom, France, The University of Melbourne, Australia, and The National University of Singapore and was an adjunct professor at Vienna University of Technology. Dr. Müller received the Leonard G. Abraham Prize (jointly with Sergio S. Verdú) from the IEEE Communications Society and the Johann-Philipp-Reis Prize (jointly with Robert Fischer). He was also presented an award by the Vodafone Foundation for Mobile Communications and two more awards from the German Information Technology Society (ITG). Dr. Müller is currently serving as an associate editor for the IEEE Transactions on Information Theory.     

Upper bounds on the capacity of Gaussian channels with feedback

The capacity of the discrete-time additive Gaussian channel without feedback is known. A class of upper bounds on the capacity with noiseless feedback that are quite good for some exemplary channels is obtained     

The coding capacity of mismatched Gaussian channels (Corresp.)

Bounds on the coding capacity of Gaussian channels are obtained when the power constraint on the signal is mismatched to the channel noise. In the case of some feedback channels in which the noise has a Cramér-Hida representation of finite multiplicity, an exact expression for the coding capacity is given.     

Gaussian multiaccess channels with ISI: capacity region andmultiuser water-filling

The capacity region of a two-user Gaussian multiaccess channel with intersymbol interference (ISI) in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive Gaussian noise process is discussed. A geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented. This method can be viewed as a nontrivial generalization of the single-user water-filling argument. It is shown that, as in the traditional memoryless multiaccess channel, frequency-division multiaccess (FDMA) with optimally selected frequency bands for each user achieves the total capacity of the multiuser Gaussian multiaccess channel with ISI. However, the capacity region of the two-user channel with memory is, in general, not a pentagon unless the channel transfer functions for both users are identical     

Channel estimation and long-range prediction of fast fading channels for adaptive OFDM system

This correspondence presents the channel estimation and long-range prediction technique for adaptive-orthogonal-frequency-division-multiplexing (AOFDM) system. The efficient channel loading is accomplished by feeding the accurately predicted channel-state-information (CSI) back to transmitter. The frequency-selective wireless fading channel is modelled as a tapped-delay-line-filter governed by a first-order autoregressive (AR1) process; and an adaptive channel estimator based on the generalised-variable-step-size least-mean-square (GVSS-LMS) algorithm tracks AR1 correlation coefficient. To compensate for the signal fading due to channel state variations, a modified-Kalman-filter (MKF)-based channel estimator is utilised. In addition, channel tracking is also performed for predicting future CSI at receiver, based on the numeric-variable-forgetting-factor recursive-least-squares (NVFF-RLS) algorithm. Subsequently, adaptive bit allocation for AOFDM system is employed by using predicted CSI at transmitter. Here, the proposed combination of GVSS-LMS and MKF algorithms for robust channel estimation and the NVFF-RLS algorithm for efficient channel prediction is incorporated. The performance validation of presented method is carried out by using different channel realisations through simulation, and also by comparing it with fixed step-size LMS, MKF and fixed forgetting-factor RLS algorithm based conventional techniques. Eventually, the reliable performance of underlying AOFDM system can be achieved in terms of the lower mean squared estimation/prediction errors and alleviated symbol error rate.     

Channel estimation and channel tracking for correlated block-fading channels in massive MIMO systems

This paper presents a channel estimation and tracking method for correlated block-fading channels in massive MIMO wireless cellular systems. In order to conserve resources, the proposed algorithm requires the uplink pilot signal only once, at the start of communication. By utilizing the temporal correlation between consecutive Resource Blocks (RBs) and the error correction capability of turbo codes, the channel matrix in subsequent RBs is estimated at the Base Station (BS) itself using the uplink data of current the RB and the estimated channel matrix of previous the RB. Compared to existing blind estimation methods, the proposed method places fewer limitations on the system settings such as the number of BS antennas, the number of users, and the number of coherent channel usage compared to existing blind estimation methods. Simulation results show that the proposed algorithm provides better performance for a moderate RB size, a high-order of QAM scheme, and a smaller ratio of the number of BS antennas and mobile terminals (N/K). For a reasonably small N/K (order of 10), the proposed scheme achieves a lower symbol error probability than the conventional pilot-based estimation approach.