Peter Adam Hoeher

A Viterbi algorithm with soft-decision outputs and its applications

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated.<<ETX>>

A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain

For estimating the states or outputs of a Markov process, the symbol-by-symbol MAP algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of nonlinear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low SNR (a common example is the max-log-MAP because of its use of the max function). A further simplification yields the soft-output Viterbi algorithm (SOVA). We present a log-MAP algorithm that avoids the approximations in the max-log-MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (log-)MAP, max-log-MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example forming the basis for simulations, we consider Turbo decoding, where recursive systematic convolutional component codes are decoded with the three algorithms, and we also demonstrate the practical suitability of the log-MAP by including quantization effects. The SOVA is, at 10/sup -4/, approximately 0.7 dB inferior to the (log-)MAP, the max-log-MAP lying roughly in between. We also present some complexity comparisons and conclude that the three algorithms increase in complexity in the order of their optimality.

Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering

The potential of pilot-symbol-aided channel estimation in two dimensions are explored. In order to procure this goal, the discrete shift-variant 2-D Wiener filter is derived and analyzed given an arbitrary sampling grid, an arbitrary (but possibly optimized) selection of observations, and the possibility of model mismatch. Filtering in two dimensions is revealed to outperform filtering in just one dimension with respect to overhead and mean-square error performance. However, two cascaded orthogonal 1-D filters are simpler to implement and shown to be virtually as good as true 2-D filters.

A statistical discrete-time model for the WSSUS multipath channel

The computation of the tap gains of the discrete-time representation of a slowly time-varying multipath channel is investigated. Assuming the channel is wide-sense stationary with uncorrelated scattering (WSSUS), a known Monte Carlo based method approximating the given scattering function (which fully determines the WSSUS channel) is extended by including filtering and sampling. The result is a closed-form solution for the tap gains. This allows the efficient simulation of the continuous-time channel with, e.g., only one sample per symbol, and without explicit digital filtering. >

Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding

For estimating the states or outputs of a Markov process, the symbol-by-symbol maximum a posteriori (MAP) algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of non-linear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low SNR (a common example is the Max-Log-MAP because of its use of the max function). A further simplification yields the soft-output Viterbi algorithm (SOVA). In this paper, we present a Log-MAP algorithm that avoids the approximations in the Max-Log-MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (Log-)MAP, Max-Log-MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example, we consider Turbo decoding, and we also demonstrate the practical suitability of the Log-MAP by including quantization effects. The SOVA is, at 10−4, approximately 0.7 dB inferior to the (Log-)MAP, the Max-Log-MAP lying roughly in between. The channel capacities of the three algorithms -when employed in a Turbo decoder- are evaluated numerically.

Multiple-antenna techniques for wireless communications - a comprehensive literature survey

The use of multiple antennas for wireless communication systems has gained overwhelming interest during the last decade - both in academia and industry. Multiple antennas can be utilized in order to accomplish a multiplexing gain, a diversity gain, or an antenna gain, thus enhancing the bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. With an enormous amount of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly. To date, there are numerous papers on the performance limits of MIMO systems, and an abundance of transmitter and receiver concepts has been proposed. The objective of this literature survey is to provide non-specialists working in the general area of digital communications with a comprehensive overview of this exciting research field. To this end, the last ten years of research efforts are recapitulated, with focus on spatial multiplexing and spatial diversity techniques. In particular, topics such as transmitter and receiver structures, channel coding, MIMO techniques for frequency-selective fading channels, diversity reception and space-time coding techniques, differential and non-coherent schemes, beamforming techniques and closed-loop MIMO techniques, cooperative diversity schemes, as well as practical aspects influencing the performance of multiple-antenna systems are addressed. Although the list of references is certainly not intended to be exhaustive, the publications cited will serve as a good starting point for further reading.

Pilot-symbol-aided channel estimation in time and frequency

The potentials of pilot-symbol-aided channel estimation in two dimensions are explored for mobile radio and broadcasting applications. In order to procure this goal, the discrete shift-variant 2-D Wiener filter is analyzed given an arbitrary sampling grid, an arbitrary (but possibly optimized) selection of observations, and the possibility of model mismatch. Filtering in two dimensions is revealed to outperform filtering in just one dimension with respect to overhead, mean-square error performance and latency. Conceptually, the discrete shiftvariant 2-D Wiener filter is the optimal linear estimator for the given problem, however, two cascaded orthogonal 1-D filters are simpler to implement and virtually as good as true 2-D filters. Analytical results are presented, verified by Monte-Carlo simulations.

Turbo DPSK: iterative differential PSK demodulation and channel decoding

In the process for the nuclear chlorination of alkylbenzenes, such as toluene, in the presence of a para-directing catalyst system comprising a substantially iron-free Lewis acid catalyst and thianthrene compound co-catalyst, wherein the reaction mixture is in contact with iron or an alloy thereof, the para-directing effect of the catalyst system is improved by the addition of an amide.

Separable MAP "filters" for the decoding of product and concatenated codes

Very efficient signaling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. Powerful codes are obtained by using simple block codes to construct multidimensional product codes. The decoding of multidimensional product codes, using separable symbol-by-symbol maximum a posteriori filters, is described. Simulation results are presented for three-dimensional product codes constructed with the (16,11) extended Hamming code. The extension of the concept to concatenated convolutional codes is given and some simulation results are presented. Potential applications are briefly discussed.<<ETX>>

Channel estimation with superimposed pilot sequence

For the purpose of various synchronization tasks (including carrier phase, time, frequency, and frame synchronization), one may add a known pilot sequence, typically a pseudo-noise sequence, to the unknown data sequence. This approach is known as a spread-spectrum pilot technique or as a superimposed pilot sequence technique. In this paper, we apply the superimposed pilot sequence technique for the purpose of channel estimation (CE). We propose and verify a truly coherent receiver based on the Viterbi algorithm, which is optimal in the sense of per-survivor processing. We also suggest a generic low-cost receiver structure based on reduced-state sequence estimation. Among the distinct advantages compared to conventional pilot-symbol-assisted CE are (i) a lack of bandwidth expansion and (ii) a significantly improved performance in fast fading environments. The proposed Viterbi receiver may also be used as an alternative receiver for pilot-symbol-assisted CE.