The focus of this paper is to study the performance of the quantize-and-forward (QF) scheme over a half-duplex relay channel that is slowly fading, with the assumption that the channel state information (CSI) is available only at the receiver side. In order to do so, three steps are taken. The first step is to characterize the achievable rate of the QF scheme over a discrete memoryless half-duplex relay channel. Then, the achievable rate over a corresponding additive white Gaussian noise channel is obtained (the specific assumption regarding the CSI in this paper makes this step nontrivial). With the results from the first two steps, performance measures such as outage probability, expected rate, and diversity-multiplexing tradeoff (DMT) over slow fading channels are evaluated. It is shown that the QF scheme can significantly outperform the compress-and-forward scheme at finite signal-to-noise ratio (SNR) and it can achieve the optimal DMT at asymptotically high SNR. Moreover, it is shown that simple feedback from the destination node to the relay node can further improve the performance of the QF scheme.

The original compress-and-forward relaying scheme uses the technique of random binning at the relay node and successive decoding at the destination node. Recently, a scheme (termed the quantize-and-forward scheme in this paper) without binning and using joint decoding at the destination node has been proposed, which has been shown to achieve the same rate as the original compress-and-forward scheme. Since the previous work focuses on the so-called full duplex relay network, in this paper, an adaption of it for relay networks with a half-duplex relay is provided. Coding schemes and achievable rate results are presented for discrete memoryless half-duplex relay channels and half-duplex additive white Gaussian noise (AWGN) relay channels. Moreover, slow fading channels are considered, for which outage-related performance measures are evaluated. Specifically, the outage probability and the expected rate of the quantize-and-forward scheme are derived and compared with other well-known schemes. Furthermore, the diversity-multiplexing tradeoff is derived. It is shown that the quantize-and-forward scheme is a more suitable scheme than the compress-and-forward scheme over slow fading channels and it achieves the optimal diversity-multiplexing trade-off of a half-duplex relay channel.

Secure communication protocols over a single-relay system in the presence of a multiple-antenna eavesdropper are investigated. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol that allows both the destination and the source to jam the eavesdropper is shown to achieve secrecy rates that grow linearly with the transmit power in dB, even if all the legitimate nodes have strictly fewer antennas than the eavesdropper. The number of achievable secure degrees of freedom is quantified and shown to match an upper bound when the number of antennas at the destination is sufficiently large. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of another AF scheme and a novel compress-and-forward protocol that can achieve a positive number of secure degrees of freedom using an insecure feedback link.

Resource allocation for symmetric half-duplex bidirectional relaying networks is considered. Various decode-and-forward (DF) based relaying strategies that efficiently exploit quantized channel state information (CSI) at the transmitters (CSIT) are investigated. Adapting the number of channel uses for each relaying phase and allocating transmit power based on limited CSIT is shown to result in a significant improvement in the diversity-multiplexing trade-off (DMT). Without a direct link between the sources, power control is instrumental to efficiently exploit CSI feedback from sources to relay, resulting in superior performance that matches corresponding upper bounds in certain cases. With direct links between the sources, it is shown that DF two-way relaying does not suffer from a diversity loss when the multiplexing gain is high, a significant improvement over the dynamic DF protocol for one-way relaying. The best DMT is achieved when each source broadcasts partial CSI to the other nodes in the network, allowing them to adapt their transmit powers.

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.

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with logSNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.

The optimality of nondynamic DF relaying over a general three-node Nakagami fading channel in terms of the diversity-multiplexing tradeoff (DMT) is established. In particular, when the fading of the relay-source link is less severe than that of the relay-destination link, both orthogonal and nonorthogonal DF protocols are shown to be DMT-optimal over certain ranges of the multiplexing gains. It is also shown that when the multiplexing gains are sufficiently high, the DMT of the DF protocols is completely independent of the statistical properties of the relay-destination link.

The problem of bidirectionally transmitting two analog sources over a fading channel with the help of a relay is studied. In the regime of high signal-to-noise ratios, upper and lower bounds on the exponent of the end-to-end expected distortion are derived. It is shown that simple two-way relaying protocols based on the separation of source and channel coding can provide significant improvements in the distortion exponent over their one-way counterparts. In particular, in the regime of low channel bandwidth to source bandwidth ratios, an amplify-and-forward scheme is shown to achieve good distortion performance, albeit at the cost of large feedback overhead. In the regime of high bandwidth ratio, even better performance is achieved by a novel adaptive decode-and-forward scheme that successfully exploits low-rate feedback from the relay to the source nodes.

Communication over delay-constrained block-fading channels with discrete inputs and imperfect channel state information at the transmitter (CSIT) is studied. The CSIT mismatch is modeled as a Gaussian random variable, whose variance decays as a power of the signal-to-noise ratio (SNR). We focus on the large-SNR behavior of the outage probability when transmit power control is used. 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 significant gains in terms of exponents. It is also shown that when precoders are used at the transmitter, further exponent gains can be attained at the expense of higher decoding complexity.

Several half-duplex decode-and-forward two-way relaying protocols that efficiently exploit quantized channel state information (CSI) at the transmitters (CSIT) are investigated. Adapting the number of channel uses for each relaying phase and the transmit power based on limited CSIT is shown to result in a significant improvement in the diversity-multiplexing tradeoff (DMT). With CSI feedback from relay to sources, allocating the number of channel uses is sufficient to match the performance of power allocation. However, power control is instrumental to efficiently exploit CSI feedback from sources to relay.

A multi antenna channel with partial channel state information at the transmitter (CSIT) is studied. The partial CSIT takes the form of the channel matrix corrupted by additive white Gaussian noise (AWGN) with a variance that is assumed to decay as a power of the signal-to-noise ratio (SNR). It is shown that under a long-term power constraint and in the regime of asymptotically high SNR, a large diversity gain over the channel can be achieved by using rarely a high power at the transmitter that compensates for bad channel realizations. Examples relating the diversity gain of the systems with the channel Doppler bandwidth are discussed.

The problem of optimizing resource allocation over a half-duplex relay channel with noisy channel state information at the source transmitter (CSIT) is studied, with a focus on the asymptotically high signal-to-noise ratio (SNR) regime. A novel upper bound on the diversity-multiplexing tradeoff (DMT) is derived, taking into account the quality of the CSIT. It is shown that from a DMT perspective, the decode-and-forward (DF) protocol is strictly optimal over a certain range of the multiplexing gains. When the quality of the CSIT is sufficiently high, the DMT performance of the DF protocol with noisy CSIT equals that of the dynamic DF protocol shifted above by a constant diversity gain, which depends only on the quality of the CSIT about the source-destination link. When the quality of the CSIT reduces, DF relaying is still DMT-optimal, but only over a smaller range of the multiplexing gains. In an intermediate range of the multiplexing gains, nonorthogonal schemes provide some additional gains when the CSIT quality is sufficiently low. It is also shown that the DMT of the amplify-and-forward (AF) protocol is offset by a constant term depending on the quality of the CSIT of the source-destination link only.

The compress-and-forward (CF) strategy achieves the optimal diversity-multiplexing tradeoff (DMT) of a three-node half-duplex relay network in slow fading, under the assumption that the relay has perfect knowledge of all three channel coefficients and that the relay makes use of Wyner-Ziv (WZ) source coding with side information. This paper studies the achievable DMT of the same network when the relay is constrained to make use of standard (non-WZ) source coding. Under a short-term power constraint at the relay, using source coding without side information results in a significant loss in terms of the DMT. For multiplexing gainsrles2/3, this loss can be fully compensated for by using power control at the relay. On the contrary, forrisin (2/3,1), the loss with respect to WZ coding remains significant.

The problem of transmitting a Gaussian source over a half-duplex fading relay channel with limited channel state feedback is studied. It is shown that under a short-term power constraint, combining a simple feedback scheme with separate source and channel coding outperforms the best known no-feedback strategies even with only a few bits of feedback information. Partial power control is shown to be instrumental in achieving a very fast decaying average distortion, especially in the regime of high bandwidth ratios. Performance limitation due to the lack of full channel state information at the destination is also investigated, where the degradation in terms of the distortion exponent is shown to be significant. However, even in such restrictive scenarios, using partial feedback still yields distortion exponents superior to any no-feedback schemes.

The problem of resource allocation to maximize the outage exponent over a fading relay channel using the decode-and-forward protocol with quantized channel state feedback (CSF) is studied. Three different scenarios are considered: relay-to-source, destination-to-relay, and destination-to-source-and-relay CSF. In the relay-to-source CSF scenario, it is found that using merely one bit of CSF to control the source transmit power is sufficient to achieve the multiantenna upper bound in a range of multiplexing gains. In the destination-to-relay CSF scenario, the systems slightly outperform dynamic decode-and-forward (DDF) at high multiplexing gains, even with only one bit of feedback. Finally, in the destination-to-source-and-relay CSF scenario, if the source-relay channel gain is unknown to the feedback quantizer at the destination, the diversity gain only grows linearly in the number of feedback levels, in sharp contrast to an exponential growth for multiantenna channels. In this last scenario, a simple scheme is shown to perform close to the corresponding upper bound.

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is combined with a unitary transformation based on the long-term channel statistics. The heavily quantized feedback link is directly optimized to maximize the expected achievable rate under different power constraints, using vector quantization and convex optimization techniques on a sample channel distribution. Robustness against errors in the feedback link is also pursued with tools in channel optimized vector quantization. Simulations indicate the benefits of the proposed scheme.

Low-rate feedback design for multiple-input multiple-output broadcast channels is studied under a vector quantization framework. Iterative algorithms are proposed to design the partial feedback link, the scheduler, and the linear precoding codebook. It is demonstrated that the gain due to multi-user diversity can be significant even with heavily quantized channel state information at the transmitter. Our results highlight the potential of multi-user diversity, even with simple schemes and extremely-low-rate feedback.

The problem of source-channel coding over a multiple-antenna channel with quantized channel state information at the transmitter (CSIT) is considered. Upperbounds on the distortion exponents achieved with partial CSIT are developed. The achievable distortion exponent of some hybrid schemes with heavily quantized feedback under both short- and long-term power constraints is also derived. The results demonstrate that excellent performance can be achieved by combining simple schemes with a very coarse feedback link.

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

The diversity-multiplexing (D-M) tradeoff in a multi antenna channel with optimized resolution-constrained channel state feedback is characterized. The concept ofminimum guaranteed multiplexing gainin the forward link is introduced and shown to significantly influence the optimal D-M tradeoff. It is demonstrated that power control based on the feedback is instrumental in achieving the D-M tradeoff, and that rate adaptation is important in obtaining a high diversity gain even at high rates. A criterion to determine finite-length codes to be tradeoff optimal is presented, leading to a useful geometric characterization of the class ofextended approximately universal codes. With codes from this class, the optimal D-M tradeoff is achievable by the combination of a feedback-dependent power controller and a single code-book for single-rate or two codebooks for adaptive-rate transmission. Finally, lower bounds to the optimal D-M tradeoffs based on Gaussian coding arguments are also studied. In contrast to the no-feedback case, these random coding bounds are only asymptotically tight, but can quickly approach the optimal tradeoff even with moderate codeword lengths.

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is obtained via a resolution-constrained feedback link, combined with a unitary transformation based on the long-term channel statistics. The feedback link is optimized to maximize the expected achievable rate under different power constraints, using vector quantization techniques. Simulation indicate the benefits of the proposed scheme in all scenarios considered.

Transmit power control to minimize the outage probability over a slowly fading multiple-antenna channel utilizing partial channel state information at the transmitter is studied. The optimal power quantizer is shown to have a "circular" structure. The design problem is then explicitly formulated and numerically solved based on a Gaussian approximation. Asymptotic behavior of the outage probability achieved with a finite-size power codebook is investigated. It is shown that the diversity gain of such a system is a K-order polynomial of the product of the number of transmit and receive antennas, where K is the size of the power codebook. The interesting concept of power-control diversity is discussed.

The diversity-multiplexing (D-M) tradeoff over a multiantenna channel with resolution-constrained feedback is characterized. The concept of minimum guaranteed multiplexing gain in the forward link is introduced and shown to significantly influence the optimal D-M tradeoff. It is demonstrated that rate adaptation is important in obtaining a high diversity gain even at high rates. The class of extended approximately universal codes is shown to be tradeoff optimal. With codes from this class, the optimal D-M tradeoff is achievable by the combination of a feedback-dependent power controller and only two codebooks. Two novel lower bounds to the optimal D-M tradeoff based on Gaussian coding arguments are presented. These bounds are only asymptotically tight, but can quickly approach the optimal tradeoff even with moderate codeword lengths

We present a novel structure to efficiently exploit channel state information at the transmitter (CSIT) of a multiple-input multiple-output system. At the heart of our transmission scheme lies a mixing matrix that constructively combines the coded symbols before a CSIT-dependent weighting matrix is applied. A method to design the mixing matrix is presented. When combined with turbo-coded modulation, our system performs very close to the capacity limits. With only a few bits per channel use to feedback CSIT, we can achieve a substantial portion of the possible gain with perfect CSIT.