Minimum BER Block Precoders

In this thesis the linear precoder which minimizes the bit error rate (BER) is derived for block transmission systems in which zero forcing (ZF) equalization and threshold detection are applied. Because the bit error rate for block transmission is a highly non-linear function of the precoder parameters, its minimization has been regarded as being difficult to implement. Therefore designers have attempted to find low BER precoders indirectly by optimizing alternative objectives, such as minimizing the Mean Square Error (MMSE), or maximizing the received signal-to-noise ratio (SNR). However, these precoders do not minimize the BER directly, and it is this problem which is the subject of the thesis. The block transmission systems considered in this thesis employ block by block processing at the receiver, and therefore elimination of inter-block interference (IEI) is desirable. We will design Minimum BER (MBER) precoders for two schemes which eliminate IEI, namely zero padding (ZP) and cyclic prefix (CP). Based on the bit error rate formula derived in the thesis, an analytic solution for the MBER precoder at moderate-to-high SNRs is derived via a two-stage optimization process using Jensen's inequality. At moderate-to-high SNRs, the bit error rate is a convex function of the autocorrelation matrix which is, itself, a function of the precoder matrix because of the use of a zero-forcing equalizer. Simulations and analyses are given to the two sets of precoders based on ZP and CP respectively to verify the optimal precoders derived. The BER improvement of the ZP-MBER/CP-MBER precoders over other ZP/CP precoders is substantial, and the ZP-MBER precoder is superior to the CPMBER precoder in performance. The latter also outperforms the scheme of discrete multitone (DMT) with water filling power loading, and cyclic prefix orthogonal frequency division multiplexing (CP-OFDM). The CP-MBER precoder is shown to be a two-stage modification IV of the transmitting scheme for tandard DMT. Firstly the water filling algorithm is replaced by the MMSE power loading algorithm suggested in the thesis, and secondly, the power loading is augmented by multiplication with a DFT matrix. It is shown that the CP-MBER precoder does not require more power to transmit a cyclic prefix than the CP-OFDM or water-filling DMT precoder. A simple test which determines whether the SNR is high enough for our MBER precoder design to be optimal is provided. Furthermore, methods to guarantee sufficient SNR are suggested. One can either increase the transmitting power, or drop sub-channels and hence avoid transmission on the sub-channels which correspond to the small eigen-values of the channel. The MBER precoder design after dropping sub-channels is also discussed. For the precoders which are characterized by an arbitrary unitary matrix in their solutions, the optimal unitary matrix which minimizes the BER is designed. Therefore, minimization of BER is achieved within the optimal solution set of the precoders. Applications of the design are discussed. Simulations and analytic evaluations are presented to show the BER improvement provided by the optimal unitary matrixMaster of Engineering (ME

Achievable data rates and power allocation for frequency-selective fading relay channels with imperfect channel estimation

Due to copyright restrictions, the access to the full text of this article is only available via subscription.In this article, we investigate the information-theoretical performance of a cooperative orthogonal frequency division multiplexing (OFDM) system with imperfect channel estimation. Assuming the deployment of training-aided channel estimators, we derive a lower bound on the achievable rate for the cooperative OFDM system with amplify-and-forward relaying over frequency-selective Rayleigh fading channels. The bound is later utilized to allocate power among the training and data transmission phases. Numerical results demonstrate that the proposed power allocation scheme brings between 5 and 19% improvement depending on the level of signal-to-noise ratio and relay locations

The amplify-and-forward half-duplex cooperative system: Pairwise error probability and precoder design

Abstract-In this paper, an exact asymptotic pairwise error probability (PEP) is derived for a half-duplex cooperative system employing an amplify-and-forward (AF) protocol. When compared with the PEP of a traditional multiple-input multipleoutput (MIMO) system, the "diversity gain" for the cooperative system is no longer just a simple exponential function of the signal-to-noise ratio (SNR), rather, it involves the logarithm of the SNR. The term diversity gain function is used to designate this characteristic of the PEP. The coding gain, on the other hand, is found similar to that for the MIMO system and is proportional to the determinant of the autocorrelation of the error matrix. Based on our analysis and observations, we propose a design of unitary precoder for the cooperative system to achieve the full diversity gain function. For the case of a 4-QAM signal being transmitted, we further optimize the coding gain, and arrive at a closed-form optimum precoder. Simulations indicate that our proposed precoder designs greatly improve the performance of the cooperative system. Index Terms-Cooperative system, half-duplex, amplify-andforward (AF), pairwise error probability, diversity gain function, precoder

Blind Doppler estimation for satellite with interference EMI

Click on the DOI to access this article (may not be free).Doppler frequency estimation in satellite communications plays an important role in the geolocations of electromagnetic interference (EMI) emitters. Due to the high speed of satellites and various trajectories of the orbits, one cannot assume that the Doppler frequency is constant. The Doppler estimations are usually performed repeatedly for each given time duration, within which the Doppler frequency can be modeled as a chirp. Doppler estimation algorithms based on the phase requires the transmitted signals removed from the received signal. This is hard to do in practical systems, since the transmitted signals from EMI source are unknown. In this paper, blind doppler frequency estimation is considered for unknown EMI signals using frequency analysis. After the received signal at satellite is down converted, the estimation is performed for each given time instants at different signal-to-noise ratios. To reduce the estimation errors at very low signalto-noise ratio (SNR), the extremely bad estimates are detected as outliers and the estimates are replaced by those at previous time instants