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Helmut Bölcskei

Publications and source records attributed to Helmut Bölcskei.

At least 91 records · Page 5Linked to original sources
arXiv2011

High-SNR Capacity of Wireless Communication Channels in the Noncoherent Setting: A Primer

This paper, mostly tutorial in nature, deals with the problem of characterizing the capacity of fading channels in the high signal-to-noise ratio (SNR) regime. We focus on the practically relevant noncoherent setting, where neither transmitter nor receiver know the channel realizations, but both are aware of the channel law. We present, in an intuitive and accessible form, two tools, first proposed by Lapidoth & Moser (2003), of fundamental importance to high-SNR capacity analysis: the duality approach and the escape-to-infinity property of capacity-achieving distributions. Furthermore, we apply these tools to refine some of the results that appeared previously in the literature and to simplify the corresponding proofs.

cs.IT↗
arXiv2011

Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets

We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. This uncertainty relation is relevant for the analysis of signals containing two distinct features each of which can be described sparsely in a suitable general signal set. Furthermore, the new uncertainty relation is shown to lead to improved sparsity thresholds for recovery of signals that are sparse in general dictionaries. Specifically, our results improve on the well-known $(1+1/d)/2$-threshold for dictionaries with coherence $d$ by up to a factor of two. Furthermore, we provide probabilistic recovery guarantees for pairs of general dictionaries that also allow us to understand which parts of a general dictionary one needs to randomize over to "weed out" the sparsity patterns that prohibit breaking the square-root bottleneck.

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arXiv2010

Where is Randomness Needed to Break the Square-Root Bottleneck?

As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all the positions of the nonzero entries of the sparse coefficient vector. Rather the positions corresponding to one of the two ONBs can be chosen arbitrarily. The two-ONB structure is, however, restrictive and does not reveal the property that is responsible for allowing to break the bottleneck with reduced randomness. For general dictionaries we show that if a sub-dictionary with small enough coherence and large enough cardinality can be isolated, the bottleneck can be broken under the same probabilistic model on the sparse coefficient vector as in the two-ONB case.

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arXiv2009

Interpolation-Based QR Decomposition in MIMO-OFDM Systems

Detection algorithms for multiple-input multiple-output (MIMO) wireless systems based on orthogonal frequency-division multiplexing (OFDM) typically require the computation of a QR decomposition for each of the data-carrying OFDM tones. The resulting computational complexity will, in general, be significant, as the number of data-carrying tones ranges from 48 (as in the IEEE 802.11a/g standards) to 1728 (as in the IEEE 802.16e standard). Motivated by the fact that the channel matrices arising in MIMO-OFDM systems are highly oversampled polynomial matrices, we formulate interpolation-based QR decomposition algorithms. An in-depth complexity analysis, based on a metric relevant for very large scale integration (VLSI) implementations, shows that the proposed algorithms, for sufficiently high number of data-carrying tones and sufficiently small channel order, provably exhibit significantly smaller complexity than brute-force per-tone QR decomposition.

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arXiv2009

Improved Sparsity Thresholds Through Dictionary Splitting

Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather pessimistic thresholds as it captures only limited information about the dictionary. In this paper, we show that viewing the dictionary as the concatenation of two general sub-dictionaries leads to provably better sparsity thresholds--that are explicit in the coherence parameters of the dictionary and of the individual sub-dictionaries. Equivalently, our results can be interpreted as sparsity thresholds for dictionaries that are unions of two general (i.e., not necessarily orthonormal) sub-dictionaries.

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arXiv2009

Optimal Diversity-Multiplexing Tradeoff in Selective-Fading MIMO Channels

We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency, and time-frequency selective-fading multiple-input multiple-output (MIMO) channels and provide a code design criterion for DM tradeoff optimality. Our results are based on the new concept of the "Jensen channel" associated to a given selective-fading MIMO channel. While the original problem seems analytically intractable due to the mutual information between channel input and output being a sum of correlated random variables, the Jensen channel is equivalent to the original channel in the sense of the DM tradeoff and lends itself nicely to analytical treatment. We formulate a systematic procedure for designing DM tradeoff optimal codes for general selective-fading MIMO channels by demonstrating that the design problem can be separated into two simpler and independent problems: the design of an inner code, or precoder, adapted to the channel statistics (i.e., the selectivity characteristics) and an outer code independent of the channel statistics. Our results are supported by appealing geometric intuition, first pointed out for the flat-fading case by Zheng and Tse, IEEE Trans. Inf. Theory, 2003.

cs.IT↗
arXiv2009

Selective-Fading Multiple-Access MIMO Channels: Diversity-Multiplexing Tradeoff and Dominant Outage Event Regions

We establish the optimal diversity-multiplexing (DM) tradeoff for coherent selective-fading multiple-access MIMO channels and provide corresponding code design criteria. As a byproduct, on the conceptual level, we find an interesting relation between the DM tradeoff framework and the notion of dominant error event regions, first introduced in the AWGN case by Gallager, IEEE Trans. IT, 1985. This relation allows us to accurately characterize the error mechanisms in MIMO fading multiple-access channels. In particular, we find that, for a given rate tuple, the maximum achievable diversity order is determined by a single outage event that dominates the total error probability exponentially in SNR. Finally, we examine the distributed space-time code construction proposed by Badr and Belfiore, Int. Zurich Seminar on Commun., 2008, using the code design criteria derived in this paper.

cs.IT↗
arXiv2009

Compressed Sensing of Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we introduce. We then show that a block-version of the orthogonal matching pursuit algorithm recovers block $k$-sparse signals in no more than $k$ steps if the block-coherence is sufficiently small. The same condition on block-coherence is shown to guarantee successful recovery through a mixed $\ell_2/\ell_1$-optimization approach. This complements previous recovery results for the block-sparse case which relied on small block-restricted isometry constants. The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.

cs.IT↗
arXiv2009

Soft-Input Soft-Output Single Tree-Search Sphere Decoding

Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context of multiple-input multiple-output (MIMO) wireless communication systems. In this paper, we present a low-complexity SISO sphere-decoding algorithm, based on the single tree-search paradigm proposed originally for soft-output MIMO detection in Studer, et al., IEEE J-SAC, 2008. The new algorithm incorporates clipping of the extrinsic log-likelihood ratios (LLRs) into the tree-search, which results in significant complexity savings and allows to cover a large performance/complexity tradeoff region by adjusting a single parameter. Furthermore, we propose a new method for correcting approximate LLRs --resulting from sub-optimal detectors-- which (often significantly) improves detection performance at low additional computational complexity.

cs.IT↗
arXiv2009

Tail Behavior of Sphere-Decoding Complexity in Random Lattices

We analyze the (computational) complexity distribution of sphere-decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is solely determined by the inverse volume of a fundamental region of the underlying lattice. Particularizing this result to NxM, N>=M, i.i.d. Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. We furthermore show that this tail exponent is not improved by lattice-reduction, which includes layer-sorting as a special case.

cs.IT↗
arXiv2009

On the Sensitivity of Noncoherent Capacity to the Channel Model

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the set of harmonics where the power spectral density of the fading process is nonzero determines if capacity grows logarithmically in SNR or slower than logarithmically. An engineering-relevant problem is to characterize the SNR value at which this sensitivity starts to matter. In this paper, we consider the general class of continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. For this class of channels, we show that the noncoherent capacity is close to the AWGN capacity for all SNR values of practical interest, independently of whether the scattering function is compactly supported or not. As a byproduct of our analysis, we obtain an information-theoretic pulse-design criterion for orthogonal frequency-division multiplexing systems.

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arXiv2009

On the achievable diversity-multiplexing tradeoff in interference channels

We analyze two-user single-antenna fading interference channels with perfect receive channel state information (CSI) and no transmit CSI. For the case of very strong interference, we prove that decoding interference while treating the intended signal as noise, subtracting the result out, and then decoding the desired signal, a process known as "stripping", achieves the diversity-multiplexing tradeoff (DMT) outer bound derived in Akuiyibo and Leveque, Int. Zurich Seminar on Commun., 2008. The proof is constructive in the sense that it provides corresponding code design criteria for DMT optimality. For general interference levels, we compute the DMT of a fixed-power-split Han and Kobayashi type superposition coding scheme, provide design criteria for the corresponding superposition codes, and find that this scheme is DMT-optimal for certain multiplexing rates.

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arXiv2008

Finite Lattice-Size Effects in MIMO Detection

Many powerful data detection algorithms employed in multiple-input multiple-output (MIMO) communication systems, such as sphere decoding (SD) and lattice-reduction (LR)-aided detection, were initially designed for infinite lattices. Detection in MIMO systems is, however, based on finite lattices. In this paper, we systematically study the consequences of finite lattice-size for the performance and complexity of MIMO detection algorithms formulated for infinite lattices. Specifically, we find, considering performance and complexity, that LR does not seem to offer advantages when used in conjunction with SD.

cs.IT↗
arXiv2008

Soft-Input Soft-Output Sphere Decoding

Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The associated computational complexity often poses significant challenges for practical receiver implementations, in particular in the context of multiple-input multiple-output wireless systems. In this paper, we present a low-complexity SISO sphere decoder which is based on the single tree search paradigm, proposed originally for soft-output detection in Studer et al., IEEE J-SAC, 2008. The algorithm incorporates clipping of the extrinsic log-likelihood ratios in the tree search, which not only results in significant complexity savings, but also allows to cover a large performance/complexity trade-off region by adjusting a single parameter.

cs.IT↗
arXiv2008

Infinity-Norm Sphere-Decoding

The most promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l-2 norm. It was, however, recently observed that using the l-infinity norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l-infinity norm SD. For i.i.d. Rayleigh fading MIMO channels, we show that l-infinity norm SD achieves full diversity order with an asymptotic SNR gap, compared to l-2 norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed-form expression for the computational complexity of l-infinity norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l-infinity norm SD and show that it behaves fundamentally different from that of l-2 norm SD.

cs.IT↗
arXiv2008

Diversity-Multiplexing Tradeoff in Selective-Fading Multiple-Access MIMO Channels

We establish the optimal diversity-multiplexing (DM) tradeoff of coherent selective-fading multiple-access multiple-input multiple-output (MIMO) channels and provide corresponding code design criteria. As a byproduct, on the conceptual level, we find an interesting relation between the DM tradeoff framework and the notion of dominant error event regions which was first introduced in the AWGN case by Gallager, IEEE Trans. IT, 1985. This relation allows to accurately characterize the error mechanisms in MIMO fading multiple-access channels. In particular, we find that, for a given rate tuple, the maximum achievable diversity order is determined by the error event that dominates the total error probability exponentially in SNR. Finally, we show that the distributed space-time code construction proposed recently by Badr and Belfiore, Int. Zurich Seminar on Commun., 2008, satisfies the code design criteria derived in this paper.

cs.IT↗
arXiv2008

Noncoherent Capacity of Underspread Fading Channels

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization explicitly takes into account the underspread property, which is satisfied by virtually all wireless communication channels.

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