Flat fading channel estimation based on dirty paper coding

Resumo

Channel estimation is a transversal problem in signal processing (for example, it is used in digital communications, image restoration, digital forensics, acoustics, etc.). Among channel estimation algorithms, pilot-based estimation techniques stand out as being among the most frequently used. These techniques devote part of the total available power, which is usually limited, to send pilot signals that are used later to estimate the channel. The frequent need to send pilot signals in order to be able to track the channel variations, which lowers the information rate, becomes as one of their major drawbacks. Recently, the idea of concurrently sending a known training sequence with the information-bearing signal (also known as host) by means of arithmetically adding both sequences was proposed. These techniques are usually referred as superimposed training techniques. By implementing this idea, there is no drop in the information rate; however, part of the power available to send the information must be used by the added superimposed sequence thus causing a power loss in the information-bearing sequence. In addition, the original signal interferes with the pilot sequence of the superimposed training techniques, causing a decrease in the estimate performance, which is measured in terms of mean square error between the estimation and the actual channel gain. To tackle this issue, some solutions have been provided that use part of the power to partial cancel the host-interference. In this thesis, we have found a connection between superimposed training and digital watermarking. Indeed, this partially cancellation of the host of pilot sequences, known as PDD was independently proposed in digital watermarking, where is called ISS. We propose to obtain full cancellation of host-interference for estimation by applying the DPC paradigm that successfully was used in digital watermarking with several implementations (e.g., SCS, DC-DM, etc.). Specifically in this thesis, first we focus on the study of the flat fading channel estimation based on dirty paper coding for the case of real valued signals. Due to its interesting asymptotic properties, we design our estimation technique using MLE. In order to do that, the pdf of the random variables modeling the involved signals is required; in general, those pdfs are hard to handle mathematically and, as a consequence, so is the MLE cost function. Therefore, we have proposed a set of approximations of the pdf whose accuracy is validated in the cases for which they have been designed. In addition, a modification of the technique whenever the variances of the original signal and the channel noise are unknown is presented. In addition, this thesis proposes how to make full use of the Spread-Transform (an established concept of digital watermarking) to estimate the channel gain. In addition, a theoretical study is introduced following an estimation theory perspective, which indicates that asymptotically our scheme is not only not harmed by the host but it helps for estimation, and an information theory perspective, whose results determine that the induced structure of the transmitted signal helps the estimation of the gain of the channel. Both analyses show an improvement on the estimation performance of our technique with respect to Spread-Spectrum and PDD. The computational and time requirements needed to implement MLE, even using our pdf approximations, are not affordable in many applications. To tackle this, we introduce a set of MLE-based practical algorithms for estimation, designed with computational and temporal constraints. These algorithms take advantage of the statistical and deterministic properties of the problem. Several performance tests, measuring the accuracy of our algorithm, indicate that it outperforms other existing techniques whenever the structure of the sent signal becomes patent, and requires much shorter computational time than other existing DPC-based estimation techniques. With the aim of gaining insight into the wide range of practical uses of our algorithms, this thesis presents a set of applications of the proposed technique. For example, we use our algorithms to make dirty paper coding watermarking robust to gain attacks. By using both synthetic signals and real images, the obtained results validate the efficacy of our techniques in dealing with such attacks. We also show, in a flat fading channel communications scenario, how to equalize the gain estimated with our algorithms. The results show that our techniques improve the performance with respect to equalizing techniques based either on the second moment estimation or on superimposed training. Finally, we also propose how to adapt our estimation algorithm to the case of complex signals and complex gains, whose performance indicates that host also helps in the estimation.