Noura Sellami

Turbo channel estimation for TDMA systems on highly time and frequency selective channels

In this paper, we consider a Time Division Multiple Access (TDMA) transmission of coded symbols over a time and frequency selective channel. We consider at the receiver a turbo-detector consisting of a Maximum A Posteriori (MAP) equalizer and a MAP decoder. We assume that the channel is unknown at the receiver. Thus, we develop a MAP iterative burst by burst channel estimation algorithm using the Expectation-Maximization (EM) algorithm. It needs a convenient representation of the channel based on the Karhunen-Love expansion theorem. It also needs a posteriori probabilities (APPs) on the coded symbols. These probabilities are provided by the MAP decoder at each iteration of the receiver. Simulations show that the performance of our iterative receiver approaches the performance obtained when the channel is perfectly known.

A Proof of Convergence of the MAP Turbo-Detector to the AWGN Case

In this paper, we consider a coded transmission over a frequency-selective channel. We propose to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We show that the densities of the extrinsic log likelihood ratios (LLRs) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to perform a one-dimensional (1-D) analysis of the turbo-detector. By deriving the analytical expressions of the extrinsic LLR distributions under the Gaussian approximation, we prove that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency-selective channel.

The impact of both a priori information and channel estimation errors on the MAP equalizer performance

To combat the effects of intersymbol interference (ISI), the optimal equalizer to be used is based on maximum a posteriori (MAP) detection. In this paper, we consider the case where the MAP equalizer is fed with a priori information on the transmitted data and propose to study analytically their impact on the MAP equalizer performance. We assume that the channel is not perfectly estimated and show that the use of both the a priori information and the channel estimate is equivalent to a shift in terms of signal-to-noise ratio (SNR) for which we provide an analytical expression. Simulation results show that the analytical expression approximates well the equalizer behavior

Scheduling scheme for cognitive radio networks with imperfect channel Knowledge

Cognitive radio is a promising technique for efficient spectrum utilization in wireless systems. In this paper, we consider an underlay cognitive radio system where a large number of secondary users (SUs) can share the spectrum with a primary user (UP). We assume that M antennas are used at the cognitive base station (CBS) and the CBS does not have the full channel state information (CSI) from secondary users. We propose to study the problem of secondary users scheduling under the assumption of imperfect CSI of the interference channel between the CBS and the primary receiver. In order to minimize the interference to the UP, we propose to generate orthogonal beams to the estimate of the channel between the CBS and the PU. Then, to reduce the amount of required feedback, we propose a scheduling algorithm based on opportunistic beamforming. To further reduce the amount of feedback, a threshold is applied to the signal to interference and noise ratio (SINR) feedback. For the proposed scheme, we develop a statistical analysis for the interference caused to the PU as well as the throughput of the secondary system.

Mapping Optimization for a MAP Turbo Detector Over a Frequency-Selective Channel

In this paper, we consider a bit interleaved coded modulation (BICM) scheme over a frequency-selective channel. At the receiver, a turbo detector composed of a maximum a posteriori (MAP) detector and a MAP decoder is used. We propose to optimize the mapping choice in this context since it is well known that it has a significant impact on the performance of iterative receivers. We consider fixed and Rayleigh fading channels. Based on the Gaussian approximation, we give an analytical upper bound of the bit error probability (BEP) at the output of the detector for fixed channels. Then, we derive an approximate analytical expression of the BEP for both fixed and Rayleigh fading channels when the a priori information provided by the decoder is reliable, and then, most errors at the output of the detector are isolated. We find that the mapping minimizing this expression corresponds to a move away from the symbols differing by only one bit, unlike the Gray mapping. Since an exhaustive search to find this mapping is complicated for high-order modulations, we propose to use the binary switching algorithm (BSA) to approach the solution. Then, based on these results, we propose to adapt the mapping according to the signal-to-noise ratio (SNR) of the transmission.

A closed-form solution to the power minimization problem over two orthogonal frequency bands under QoS and Cognitive Radio interference constraints

This paper considers a Cognitive Radio (CR) channel composed of a secondary user (SU) and a primary user (PU). An analysis of the power minimization over several orthogonal frequency bands at the SU level under the following constraints is provided: a minimum Quality of Service (QoS) constraint, maximum peak and average interference to the PU constraints. The general solution, when it exists, is a water-filling type of solution which can be computed via iterative algorithms. It turns out that, in the case of two orthogonal bands a closed-form analytical solution can be found and a complete analysis of the feasibility of these opposing constraints is presented in details. Several numerical results that sustain and give inside into the analysis are also discussed.

Training sequence optimization for frequency selective channels with MAP equalization

In this paper, we address the problem of optimization of the training sequence length for frequency selective channels when a maximum a posteriori (MAP) equalizer is used. The optimal length of the training sequence is found by maximizing an effective signal-to-noise ratio (SNR) and an effective channel capacity of the training-based transmission scheme. We study these problems of optimization when the training and data powers are equal and when they are allowed to be different. When the powers can be different, we give the optimal power allocation.

Performance analysis of the MAP equalizer with a priori and distribution of the extrinsic LLRs

To combat the effects of intersymbol interference, the optimal equalizer to be used is based on maximum a posteriori (MAP) detection. We consider the case where the MAP equalizer is provided with a priori information on the transmitted data, as in a turbo equalizer. We propose to study analytically the impact of the a priori on the MAP equalizer performance. We distinguish two cases: the case of unreliable a priori and the case of reliable a priori. We show that when the a priori is reliable, it is better to perform the detection of the transmitted symbols based on the a posteriori outputs of the MAP equalizer rather than on the a priori only. In a turbo equalizer, the equalizer and the decoder exchange extrinsic log likelihood ratios (LLRs). We propose here to study analytically their distribution. The aim of this study is to perform in the future the analytical convergence analysis of turbo equalizers using the MAP equalization.

Generalized Map: Sequence Detection for Non-Ideal Frequency Selective Channel Knowledge

In this paper, we consider the problem of maximum a posteriori (MAP) equalization of the received signal over a frequency selective channel when the channel is not perfectly known at the receiver. The derivation of the MAP criterion in this case leads to an expression for which no exact implementation exists in the literature. In this paper, we propose to solve the problem by using the expectation-maximization (EM) algorithm. The algorithm we propose has linear-time complexity per iteration. Simulations show that few iterations are required to reach the performance of the MAP equalizer with perfect channel knowledge.

Efficient nodes identification based on embedded signaling using the fast walsh hadamard transform in multi-sources multi-relays systems

In relay wireless systems, a data packet transmitted by a source node is forwarded by one or many relays nodes before reaching the destination node. In actual technologies, the destination recovers the identities of the sources and relays of received signals by using signaling information exchange before the data exchange and by including identities information (addresses) in data sequences. In this paper, we propose a novel nodes identification scheme, where a precoding sequence is embedded into the data sequence at each source and relay node, in a multi-sources multi-relays wireless system. The precoding sequences are Maximum Length Sequences (MLS). We propose to efficiently reduce the computational complexity at the receiver by using the Fast Walsh Hadamard Transform (FWHT). The proposed technique allows the destination node to recover the nodes identities without using additional signaling bits. Numerical results validate the proposed identification scheme performance.