Volker Pauli

Multiple-symbol differential sphere decoding

In multiple-symbol differential detection (MSDD) for power-efficient transmission over Rayleigh fading channels without channel state information, blocks of N received symbols are jointly processed to decide on N-1 data symbols. The search space for the maximum-likelihood (ML) estimate is therefore (complex) (N-1)-dimensional, and maximum-likelihood MSDD (ML-MSDD) quickly becomes computationally intractable as N grows. Mackenthuns low-complexity MSDD algorithm finds the ML estimate only for Rayleigh fading channels that are time-invariant over an N symbol period. For the general time-varying fading case, however, low-complexity ML-MSDD is an unsolved problem. In this letter, we solve this problem by applying sphere decoding (SD) to ML-MSDD for time-varying Rayleigh fading channels. The resulting technique is referred to as multiple-symbol differential sphere decoding (MSDSD).

Tree-Search Multiple-Symbol Differential Decoding for Unitary Space-Time Modulation

Differential space-time modulation (DSTM) using unitary-matrix signal constellations is an attractive solution for transmission over multiple-input multiple-output (MIMO) fading channels without requiring channel state information (CSI) at the receiver. To avoid a high error floor for DSTM in relatively fast MIMO fading channels, multiple-symbol differential detection (MSDD) has to be applied at the receiver. MSDD jointly processes blocks of several received matrix-symbols, and power efficiency improves as the blocksize increases. But since the search space of MSDD grows exponentially with the blocksize and also with the number of transmit antennas and the data rate, the complexity of MSDD quickly becomes prohibitive. In this paper, we investigate the application of tree-search algorithms to overcome the complexity limitation of MSDD. We devise a nested MSDD structure consisting of an outer and a number of inner tree-search decoders, which renders MSDD feasible for wide ranges of system parameters. Decoder designs tailored for diagonal and orthogonal DSTM codes are given, and a more power-efficient variant of MSDD, so-called subset MSDD, is proposed. Furthermore, we derive a tight symbol-error rate approximation for MSDD, which lends itself to efficient numerical evaluation. Numerical and simulation results for different DSTM constellations and fading channel scenarios show that the new tree-search MSDD achieves a significantly better performance-complexity tradeoff than benchmark decoders.

On the Complexity of Sphere Decoding for Differential Detection

Multiple-symbol differential detection (MSDD) for multiple-input-multiple-output Rayleigh-fading channels is considered. MSDD, which jointly processes blocks of N received symbols to detect N-1 data symbols, allows for power-efficient transmission without requiring channel state information at the receiver. In previous work, the authors showed that computational efficient sphere decoding algorithms can be used to accomplish MSDD. In this correspondence, the computational complexity of this sphere-decoding based MSDD is analyzed. In particular, it is proven by means of a lower bound that the complexity of the Fincke-Pohst multiple-symbol differential sphere decoder (FP-MSDSD), while being very low over wide ranges of N and signal-to-noise ratios, is exponential in N in principle. Furthermore, both exact and simple approximate expressions for the complexity of FP-MSDSD are derived, which allow for quick assessment of ranges of useful window sizes N of FP-MSDSD and show that the exponential rate of growth of the complexity of FP-MSDSD is asymptotically equal to that of brute-force MSDD

Multiple-symbol differential detection based on combinatorial geometry

In this paper, the application of combinatorial geometry to noncoherent multiple-symbol differential detection (MSDD) is considered. The resulting algorithm is referred to as CG-MSDD. Analytical expressions for the complexity of CG-MSDD are derived and it is shown that it is polynomial in the length N of the MSDD observation window if the rank of the N times N channel autocorrelation matrix is fixed, but in fact exponential in N if standard fading models are considered. Compared to popular sphere-decoder based MSDD, CG-MSDD is superior (i) in low-signal-to-noise power ratio (SNR) slow-fading channels as its complexity is independent of the SNR, (ii) as its complexity is constant, i.e., independent of the particular channel and noise realization, and (iii) asymptotically, as its complexity exponent only scales linearly with the bandwidth of the fading process.

Multiple-symbol differential sphere decoding for unitary space-time modulation

We consider multiple-symbol differential detection (MSDD) for multiple-input multiple-output (MIMO) Rayleigh-fading channels. MSDD, which jointly processes blocks of N received symbols to detect N - 1 data symbols, allows for power-efficient transmission over rapid-fading channels. However, the complexity of the straightforward approach to find the maximum-likelihood (ML) MSDD solution is exponential in N, the number of transmit antennas N/sub T/ and the rate R. In this paper, we introduce an MSDD algorithm based on sphere decoding whose average complexity is not exponential in N for interesting ranges of signal-to-noise ratio (SNR) and arbitrary unitary signal constellations. For the interesting special cases of diagonal and orthogonal constellations we achieve a similar complexity reduction in N/sub T/ and R. Based on an error-rate analysis for MSDD we also propose a variant of MSDD that considerably improves power efficiency in relatively fast fading at a very moderate increase in complexity.

Efficient Link-to-System level Modeling for Accurate Simulations of MIMO-OFDM Systems

This paper focuses on emulation of the linklevel processing for efficient systemlevel simulations of MIMO-OFDM based mobile communication systems. While the downlink of 3GPPs Long Term Evolution (LTE) and the various MIMO transmission modes used therein stand in the focus of our considerations, the proposed techniques can be applied to other MIMO-OFDM based communication systems such as WiMAX. In particular, we compute effective fading gains and interference levels that allow us to very accurately emulate the signal processing at linklevel, i.e. channel en-/decoding, (de-)modulation, layer (de-)mapping, precoding and equalization, with minimal complexity during systemlevel simulations.

A unified performance analysis framework for differential detection in MIMO Rayleigh fading channels

In this paper, a unified framework for the analysis of differential detection (DD) schemes in time-variant multiple- input multiple-output Rayleigh fading channels is provided. The present results are very general in that they apply to transmission with differential phase-shift keying, unitary differential space- time modulation (DSTM), and block DSTM and reception with conventional DD (CDD), multiple-symbol DD (MSDD), decision- feedback DD (DFDD), and (differentially) coherent detection (CD). New result for general quadratic forms of Gaussian random variables are derived which allows us to obtain elegant closed-form expressions for the pairwise error probabilities (PEPs) of the dominant error events of the considered detectors. Furthermore, it is shown that a unified treatment of all considered detectors is possible with a properly defined effective signal- to-noise ratio (ESNR) and a useful connection between MSDD and minimum-mean-squared-error (MMSE) interpolation is established. Interesting novel results obtained from this analysis include: (i) DSTM constellations designed for CDD and CD are also optimum for MSDD and DFDD; (ii) the error floor entailed by MSDD and DFDD in time-variant fading decreases exponentially with the observation window size N; and (iii) in time-variant fading with effective normalized fading bandwidth Bh,effT MSDD with N rarr infin suffers only from an SNR loss of (1-2Bh,effT) compared to CD, whereas DFDD suffers from a diversity loss of (1-2Bh,effT).

Differential Space-Frequency Modulation and 2D-Detection for MIMO-OFDM

In this paper differential space-frequency frequency division multiplexing (MIMO-OFDM) and multiple-symbol differential detection (MSDD) without channel state information (CSI) at the receiver is considered. Inspired by previous work presented in the literature, a novel DSFM scheme is devised, which makes use of spatial and/or spectral (multipath) diversity and is particularly suited for MIMO-OFDM and power-efficient, low-delay MSDD. Furthermore, the application of a two-dimensional (2D) observation window to MSDD (2D-MSDD) in order to exploit channel correlations in both time and frequency direction, is investigated and tree-search decoding is applied to solve the detection problem efficiently. An analytical approximation of the symbol-error rate of 2D-MSDD for MIMO-OFDM under spatially correlated fading is derived, which enables quick and accurate performance evaluations. Numerical and simulation results corroborate the efficacy of our approach and show that power efficiency close to that of coherent detection with perfect CSI is feasible in all standard fading scenarios at reasonable decoder complexity.

Decision-Feedback Subset Multiple-Symbol Differential Detection for Unitary Space-Time Modulation

In this paper, a novel noncoherent detection algorithm for differential space-time modulation (DSTM) over flat-fading multiple-input-multiple-output channels is presented. This algorithm, which is referred to as decision-feedback subset multiple-symbol differential detection (DF-S-MSDD), combines ideas from decision-feedback differential detection (DFDD) and subset multiple-symbol differential detection (S-MSDD). More specifically, the DF-S-MSDD decision metric includes a number of previous decisions (i.e., decision feedback), and the optimization over the remaining hypothetical symbols returns decisions only on a subset of these symbols (i.e., S-MSDD). Furthermore, an implementation of DF-S-MSDD based on tree-search (TS) methods is devised. Due to the concept of subset detection, DF-S-MSDD outperforms MSDD in terms of error-rate performance. At the same time, due to the use of decision feedback, it also requires lower computational complexity than the TS-based MSDD schemes for the DSTM recently proposed in the literature.

On the Complexity of Sphere Decoding for MSDD

We consider multiple-symbol differential detection (MSDD) for multiple-input multiple-output Rayleigh-fading channels. MSDD, which jointly processes blocks of N received symbols to detect N - 1 data symbols, allows for power-efficient transmission without requiring channel state information at the receiver. In previous work, we showed that computationally efficient sphere decoding algorithms can be used to accomplish MSDD. In this paper, we analyze the computational complexity of this sphere-decoding based MSDD. In particular, we prove by means of a lower bound that the complexity of the Fincke-Pohst multiple-symbol differential sphere decoder (FP-MSDSD), while being very low over wide ranges of N and signal-to-noise ratios, is exponential in N in principle. We further derive expressions for the exact complete of FP-MSDSD, which allow for quick assessment of ranges of useful window sizes N