Data transmission through frequency-selective block fading channels is considered in the case where neither the transmitter nor the receiver has any knowledge of the channel coefficients. Standard code design approaches for this scenario take channel uncertainty at the receiver into account by splitting the available channel coherence time into a part dedicated to training symbols utilized for channel estimation and a second part using an error-control coding scheme that is designed without channel uncertainty in mind. In contrast, in this correspondence joint codes are designed that are optimized for communication over the unknown channel and operate over the full coherence time. Using an approximation of the union bound on codeword error probability as design criterion, codes based on general complex-valued symbols are obtained with a gradient search optimization technique. Numerical examples for both single antenna as well as multiple-antenna systems illustrate that significant improvement over training-based schemes can be obtained

The design of signal constellations for a communication system using multiple transmitter antennas over a Rayleigh-fading channel is considered under the assumption that no channel state information (CSI) is available at the transmitter and the receiver has acquired a CSI estimate with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge at the receiver and allows a smooth transition between these two cases. The data detection performance as a function of the CSI error covariance is analyzed and used to investigate the design of training blocks if such blocks are transmitted to provide CSI to the receiver. Moreover, two approaches to design constellations adapted to the error covariance of the receiver CSI are presented. Whereas the first approach is based on a generic gradient search method, the second approach uses an appropriate combination of constellations designed for perfect and no CSI at the receiver. Simulations confirm the benefits of the presented designs.

We consider the design of space-time constellations when the channel state information that is available at the receiver is an estimate of the channel coefficients with known error covariance. This setup encompasses the well-studied scenarios of perfect and no channel knowledge and allows a smooth transition between these two cases. We perform an asymptotic pairwise error probability analysis and derive a criterion to design constellations matched to the level of channel knowledge available at the receiver. Moreover, we use the criterion to assess the power tradeoff between data transmission and channel coefficient acquisition for any given specific set of constellations. Simulation results illustrate the benefit of the proposed criterion

We consider the design of space-time constellations for communication over frequency-selective fading channels where neither the transmitter nor the receiver has any channel state information. The design is based on the asymptotic union bound on error probability as design criterion and the optimization is carried out using a gradient search algorithm. Full multi-antenna multipath diversity gains are demonstrated to be achieved by the designed codes. Compared to other constellations proposed by Hochwald et al., power savings of up to 2 dB are shown to be possible.

The design of space-time codes has so far mostly focused on one-tap channel models while in this paper code design for multi-tap (frequency-selective) channels is discussed when joint channel estimation and data detection is used at the receiver. A transmission model using multiple transmitter and receiver antennas for multi-path propagation through unknown channels is presented and shown to be closely linked to a single-antenna model which has been investigated earlier. Using a randomized search strategy, codes of arbitrary rates for combined channel estimation and error protection over these channels can be designed. Simulations demonstrate the performance of codes designed with the proposed scheme. An example code outperforms an approach based on an extension of the Alamouti scheme.

We consider the problem of data transmission over a linear-filter channel with an unknown filter response. Traditionally, the various operations (equalization, detection, decoding) carried out by the receiver of a system that operates over an unknown channel assume access to high-quality estimates of the channel parameters. Such estimates are typically computed by a separate device for channel identification. In contrast, this paper focuses on combined channel estimation, equalization, and decoding. We also study the problem of code design, assuming such combined decoding. More precisely, we investigate nonlinear block coding and present a design criterion and a design algorithm, under the assumptions that a statistical description of the channel is available, and that the structure of the decoder is known to the transmitter. Numerical simulations demonstrate that the new scheme is capable of outperforming four different benchmark schemes.