On the Achievable Rate for Wideband Channels with Estimated CSI

We consider the achievable rate for frequency-selective fading channels when the channel state information (CSI) is to be estimated at the receiver. Since the estimated CSI is not perfect, the achievable rate must be degraded from that with perfect CSI. Using the rate-distortion theory, we study an upper bound on the achievable rate and investigate how the achievable rate can be maximized through an optimization problem by allocating the resources such as degrees of freedom (the transmission time in our work or transmission power) for the exploration of CSI (i.e., the channel estimation) using pilot symbols, and the exploitation of channels to transmit data symbols. Although our study is based on some ideal assumptions, the results could help develop flexible communication systems such as software defined radio (SDR) to achieve a best performance by optimizing radio resources for unknown channels.     

Optimum Power Allocation for Single-User MIMO and Multi-User MIMO-MAC with Partial CSI

We consider both the single-user and the multi-user power allocation problems in MIMO systems, where the receiver side has the perfect channel state information (CSI), and the transmitter side has partial CSI, which is in the form of covariance feedback. In a single-user MIMO system, we consider an iterative algorithm that solves for the eigenvalues of the optimum transmit covariance matrix that maximizes the rate. The algorithm is based on enforcing the Karush-Kuhn-Tucker (KKT) optimality conditions of the optimization problem at each iteration. We prove that this algorithm converges to the unique global optimum power allocation when initiated at an arbitrary point. We, then, consider the multi-user generalization of the problem, which is to find the eigenvalues of the optimum transmit covariance matrices of all users that maximize the sum rate of the MIMO multiple access channel (MIMO-MAC). For this problem, we propose an algorithm that finds the unique optimum power allocation policies of all users. At a given iteration, the multi-user algorithm updates the power allocation of one user, given the power allocations of the rest of the users, and iterates over all users in a round-robin fashion. Finally, we make several suggestions that significantly improve the convergence rate of the proposed algorithms.     

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.     

Optimal bandwidth allocation for the data and feedback channels in MISO-FDD systems

In frequency-division duplex (FDD) systems, channel-state information (CSI) is estimated by the receiver and then fed back to the transmitter through a feedback link, which inevitably requires additional bandwidth and power. In this letter, we jointly study optimal bandwidth allocation between the data channel, modeled as a flat-fading multiple-input single-output (MISO) channel, and the feedback channel for maximum average throughput in the data channel using a beamforming scheme. We consider two models of the partial CSI at the transmitter (CSIT): the noisy CSIT, modeled as jointly Gaussian with the actual channel state, and the quantized CSIT. In the first model, we use distortion-rate theory to relate the CSIT accuracy to the feedback-link bandwidth. In the second model, we derive a lower bound on the achievable rate of the data channel based on the ensemble of a set of random quantization codebooks. We show that in the MISO flat-fading channel case, beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions.     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

Capacity maximization in eigen‐MIMO with channel estimation and CSI feedback‐link throughput constraint

Water‐filled eigenchannels offer the highest multi‐input multi‐output (MIMO) information‐theoretic capacity, but digital techniques such as quadrature amplitude modulation and finite block lengths will degrade the capacity from the Shannon limit to the capacity of a digital link. Furthermore, eigen‐MIMO requires channel overheads, such as estimating the channel state information (CSI) and feeding it back to the transmitter, which further compromise the capacity. In this paper, the joint influence of channel estimation and imperfect feedback on the information‐theoretic capacity and the practicable capacity is analyzed. The channel is modeled as static over a MIMO channel block. In each block, the forward channel is used for CSI estimation and for the payload data transmission. In the back direction, the channel is used to feed back a quantized form of the CSI to the transmitter with a throughput constraint. These three channel usages are combined into an effective simplex channel simplifying the capacity analysis. The capacities are formulated as functions of the link parameters, enabling optimization of the number of training symbols, the feedback duration, and the power allocation for training and data transfer, with the criterion of maximum capacity. The results presented are subject to the usual approximations used in communications theory. Copyright © 2012 John Wiley & Sons, Ltd.     

On the Secrecy Capacity of Fading Channels

We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels.      

On the effect of receiver estimation error upon channel mutual information

Our goal in this paper is to study the effect of the receiver structure upon the achievable data rates. We consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output (MIMO) wireless channel. To encompass a number of transmission schemes, we study this problem utilizing affine precoding, which is a unified model of linearly precoded data symbols with superimposed training. We focus on Bayesian receivers that estimate both the unknown fading coefficients and the data symbols. The receiver may adopt either of the following strategies to retrieve the data symbols: strategy (i) the receiver obtains joint Bayesian channel and symbol estimates, strategy, (ii) the receiver obtains a Bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols. For both strategies, we provide lower bounds on the mutual information between the data symbols and their corresponding estimates, and we relate these bounds to the symbol Cramer-Rao bound (CRB) matrices. In contrast to strategy (ii), for strategy (i) the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error. For strategy (ii) we show that asymptotically (as the size of the transmission block grows) there is no loss of information after the maximum a posteriori (MAP) estimate of Gaussian symbols. We also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Performance analysis of a deterministic channel estimator for blocktransmission systems with null guard intervals

A deterministic algorithm was proposed for channel identification in block communication systems. The method assumed that the channel has a finite impulse response (FIR) and that null guard intervals of length greater than the channel order are inserted between successive blocks to prevent interblock interference and allow block synchronization. In the absence of noise, the algorithm provides error-free channel estimates, using a finite number of received data, without requiring training sequences and without imposing a restriction neither on the channel, except for finite order and time invariance, nor on the symbol constellation. Using small perturbation analysis, we derive approximate expressions of the estimated channel covariance matrix, which are used to quantify the resilience of the estimation algorithm to additive noise and channel fluctuations. Specifically, we consider channel fluctuations induced by transmitter/receiver relative motion, asynchronism, and oscillators' phase noise. We also compare the channel estimation accuracy with the Cramer-Rao bound (CRB) and prove that our estimation method is statistically efficient at practical SNR values for any data block length. Finally, we validate our theoretical analysis with simulations and compare our transmission scheme with an alternative system using training sequences for channel estimation     

Power control for delay constrained multi‐channel communications using outdated CSI

In this paper, we study the power allocation scheme for a single user, multi‐channel system, e.g., orthogonal frequency‐division multiplexing (OFDM) systems, under time‐variant wireless fading channels. We assume the receiver feeds back perfectly estimated channel state information (CSI) to the transmitter after a processing delay. The objective of the power allocation is to maximize throughput subject to quality‐of‐service (QoS) constraint. The QoS measure of our consideration is a triplet of data rate, delay, and delay bound violation probability. A two‐step sub‐optimal power allocation scheme is proposed to address the impact of outdated CSI. In the first step, the total transmission power that can be used within one block is determined according to the summation of the channel gains of all the channels. In the second step, the total transmission power is allocated among all the channels. The proposed power control scheme is less sensitive to the feedback delay. Compared to the optimal power allocation scheme designed for the perfect CSI scenario, it has lower computational complexity while achieving comparable capacity. Copyright © 2010 John Wiley & Sons, Ltd.     

Design Guidelines for Training-Based MIMO Systems With Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit that takes channel estimation errors into account, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for nonfeedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.     

Feedback gain in multiple antenna systems

Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel assumptions is large and most practical systems lie in between. Therefore, it is important to analyze multiple antenna systems in the presence of partial channel information. We upper bound the outage probability performance of multiple antenna systems with preamble-based channel estimation and quantized feedback. We design causal feedback and power control schemes to minimize this upper bound on outage probability. We consider the following practical issues in our analysis and design: (1) the channel information is imperfect both at the receiver and at the transmitter and (2) part of the total available resources for the system need to be used for estimation and feedback. Our results demonstrate that for block fading channels, sending a periodic preamble and causally receiving channel state information via a feedback channel can lead to substantial gains in the outage performance over any nonfeedback scheme. Most of the gains achieved by perfect feedback can be achieved by very few bits of feedback. Furthermore, it is demonstrated that these outage probability gains can be translated into improvements in frame error rate performance of systems using space-time codes. Thus, implementing a power control, even at the cost of reduced spectral resources for the forward channel is beneficial for block fading channels     

Random coding error exponents for flat fading channels withrealistic channel estimation

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied     

Simultaneous Information and Power Transfer Using Magnetic Resonance

To deal with the major challenges of embedded sensor networks, we consider the use of magnetic fields as a means of reliably transferring both information and power to embedded sensors. We focus on a power allocation strategy for an orthogonal frequency‐division multiplexing system to maximize the transferred power under the required information capacity and total available power constraints. First, we consider the case of a co‐receiver, where information and power can be extracted from the same signal. In this case, we find an optimal power allocation (OPA) and provide the upper bound of achievable transferred power and capacity pairs. However, the exact calculation of the OPA is computationally complex. Thus, we propose a low‐complexity power reallocation algorithm. For practical consideration, we consider the case of a separated receiver (where information and power are transferred separately through different resources) and propose two heuristic power allocation algorithms. Through simulations using the Agilent Advanced Design System and Ansoft High Frequency Structure Simulator, we validate the magnetic‐inductive channel characteristic. In addition, we show the performances of the proposed algorithms by providing achievable ?‐C regions.     

On optimum transmission power strategy in MIMO systems with covariance feedback

We study the optimum transmission power strategy in a multiple-input multiple-output (MIMO) system with perfect channel state information (CSI) at the receiver and channel covariance matrix at the transmitter. A necessary and sufficient condition is derived for the optimum power allocation at the transmitter to maximize the average mutual information. Furthermore, we apply this result to extend the discussion on optimality of beamforming to general cases of transmitting in m directions for achieving capacity.     

Simplified Semi-Blind Channel Estimation for Space–Time Coded MIMO-OFDM Systems

The combination of Space–Time Coded Multiple Input Multiple Output systems (STC-MIMO) with Orthogonal Frequency Division Multiplexing (OFDM) is recently being investigated as an effective means of providing high-speed data transmission over dispersive wireless channels. The strengths of the two techniques coalesce and render MIMO-OFDM systems robust to ISI and IBI. However, the decoding and demodulation of STC-OFDM needs reliable channel knowledge at the receiver, unless differential modulation techniques are used. Semi-blind methods for channel estimation are seen to provide the best trade-off in terms of bandwidth overhead, computational complexity and latency. The conventional Expectation-Maximization (EM) algorithm for semi-blind channel estimation improves a pilot-based estimate with a two step process; however, it is computationally complex to implement. In this paper, we propose a variant of the EM method, referred to as ML-EM, for semi-blind estimation of doubly dispersive channels in space–time coded MIMO-OFDM systems. Here, the conventional EM algorithm is coupled with the ML decoder for space time block codes (STBCs). The technique shows good performance, even in highly correlated antenna arrays, and is computationally simpler than conventional EM. The method incurs a training overhead of less than 1%, and performs close to exact CSI through iterative processing at the receiver.     

Doubly-Selective Channel Estimation Using Data-Dependent Superimposed Training and Exponential Basis Models

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.     

Doubly iterative receiver for block transmissions with EM-based channel estimation

Cyclic-prefix code division multiple access (CP-CDMA), multicarrier CDMA (MC-CDMA) and single carrier cyclic-prefix (SCCP) transmission are some schemes that could support the increasing demand of future high data rate applications. The linear and nonlinear equalizers used to detect the transmitted signal are always far from the Maximum-Likelihood (ML) detection bound. The block iterative generalized decision feedback equalizer (BI-GDFE) is an iterative and effective interference cancelation scheme which could provide near-ML performance yet with very low complexity. In order to deploy this scheme, the channel state information (CSI) must be available at the receiver. In practice, this information has to be estimated by using pilot and data symbols. This paper investigates the problem of channel estimation using the Expectation Maximization (EM) algorithm. The BI-GDFE provides the soft information of the transmitted signals to the EM-based algorithm in the form a combination of hard decision and a coefficient so-called the input-decision correlation (IDC). The resultant receiver becomes a doubly iterative scheme. To evaluate the performance of the proposed estimation algorithm, the Cramér-Rao Lower Bound (CRLB) is also derived. Computer simulations show that the bit error rate (BER) performance of the proposed receiver for joint channel estimation and signal detection can reach the performance of the BI-GDFE with perfect CSI.     

Unquantized and uncoded channel state information feedback in multiple-antenna multiuser systems

We propose a channel state information (CSI) feedback scheme based on unquantized and uncoded (UQ-UC) transmission. We consider a system where a mobile terminal obtains the downlink CSI and feeds it back to the base station using an uplink feedback channel. If the downlink channel is an independent Rayleigh fading channel, then the CSI may be viewed as an output of a complex independent identically distributed Gaussian source. Further, if the uplink feedback channel is an additive white Gaussian noise channel, and the downlink CSI is perfectly known at the mobile terminal, it can be shown that UQ-UC CSI transmission (that incurs zero delay) is optimal in that it achieves the same minimum mean-squared error distortion as a scheme that optimally (in the Shannon sense) quantizes and encodes the CSI, while theoretically incurring infinite delay. Since the UQ-UC transmission is suboptimal on correlated wireless channels, we propose a simple linear CSI feedback receiver that can be used to improve the performance of UQ-UC transmission while still retaining the attractive zero-delay feature. We provide bounds on the performance of such UQ-UC CSI feedback and study its impact on the achievable information rates. Furthermore, we explore its application and performance in multiple-antenna multiuser wireless systems, and also propose a corresponding pilot-assisted channel-state estimation scheme.