| 1. |
- Durisi, Giuseppe, 1977, et al.
(författare)
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On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 58:10, s. 6372-6391
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Tidskriftsartikel (refereegranskat)abstract
- he 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 support of the fading-process power spectral density (PSD) determines if noncoherent capacity grows logarithmically in SNR or slower than logarithmically. Such a result is unsatisfactory from an engineer- ing point of view, as the support of the PSD cannot be determined through measurements. The aim of this paper is to assess whether, for general continuous-time Rayleigh-fading channels, this sensi- tivity has a noticeable impact on capacity at SNR values of prac- tical interest.To this end, we consider the general class of band-limited continuous-time Rayleigh-fading channels that satisfy the wide- sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, underspread. We show that, for all SNR values of practical interest, the noncoherent capacity of every channel in this class is close to the capacity of an AWGN channel with the same SNR and bandwidth, independently of the measure of the support of the scattering function (the two-dimensional channel PSD). Our result is based on a lower bound on noncoherent capacity, which is built on a discretization of the channel input-output relation induced by projecting onto Weyl-Heisenberg (WH) sets. This approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous-time random signals.
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| 2. |
- Kuppinger, Patrick, et al.
(författare)
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Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets
- 2012
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 58:1, s. 263 - 277
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Tidskriftsartikel (refereegranskat)abstract
- We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. 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, the new uncertainty relation is shown to lead to improved sparsity thresholds for recovery of signals that are sparse in general dictionaries. 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.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.
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| 3. |
- Morgenshtern, Veniamin I., et al.
(författare)
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Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka’s Theorem
- 2013
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 59:7, s. 4213-4229
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Tidskriftsartikel (refereegranskat)abstract
- We find the capacity pre-log of a temporally correlatedRayleigh block-fading single-input multiple-output (SIMO)channel in the noncoherent setting. It is well known that for blocklength $L$ and rank of the channel covariance matrix equal to $Q$, the capacity pre-log in the single-input single-output (SISO) case is given by $1-Q/L$. Here, $Q/L$ can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to $1/L$ and can, hence, be made to vanish for the blocklength$L\to\infty$, even if $Q/L$ remains constant as $L\to\infty$. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna’s channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka’s Theorem on the Resolution of Singularities.
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| 4. |
- Seethaler, Dominik, et al.
(författare)
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On the Complexity Distribution of Sphere Decoding
- 2011
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Ingår i: IEEE Transactions on Information Theory. - : IEEE. - 0018-9448 .- 1557-9654. ; 57:9, s. 5754-5768
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Tidskriftsartikel (refereegranskat)abstract
- 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 fully determined by the inverse volume of the fundamental regions of the underlying lattice. Particularizing this result to N x M, N ≥ M, i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. A more refined analysis reveals that the corresponding average complexity of SD is infinite for N = M and finite for N >; M. Finally, for i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we analyze SD preprocessing techniques based on lattice-reduction (such as the LLL algorithm or layer-sorting according to the V-BLAST algorithm) and regularization. In particular, we show that lattice-reduction does not improve the tail exponent of the complexity distribution while regularization results in a SD complexity distribution with tails that decrease faster than polynomial.
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