arXiv subjects

Erik Agrell

Publications and source records attributed to Erik Agrell.

79 records · Page 5Linked to original sources

arXiv2012

Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems

We optimize modulation formats for the additive white Gaussian noise channel with nonnegative input, also known as the intensity-modulated direct-detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical, average optical, and peak power. The nonnegative constraint on the input to the channel is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1.5 bit/s/Hz, the modulation format optimized for average electrical power has a 2.55 dB average electrical power gain over the best known format to achieve a symbol error rate of 10^-6. The corresponding gains for formats optimized for average and peak optical power are 1.35 and 1.72 dB, respectively. Using modulation formats optimized for peak power in average-power limited systems results in a smaller power penalty than when using formats optimized for average power in peak-power limited systems. We also evaluate the modulation formats in terms of their mutual information to predict their performance in the presence of capacity-achieving error- correcting codes, and finally show numerically and analytically that the optimal modulation formats for reliable transmission in the wideband regime have only one nonzero point.

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arXiv2011

On Optimum Causal Cognitive Spectrum Reutilization Strategy

In this paper we study opportunistic transmission strategies for cognitive radios (CR) in which causal noisy observation from a primary user(s) (PU) state is available. PU is assumed to be operating in a slotted manner, according to a two-state Markov model. The objective is to maximize utilization ratio (UR), i.e., relative number of the PU-idle slots that are used by CR, subject to interference ratio (IR), i.e., relative number of the PU-active slots that are used by CR, below a certain level. We introduce an a-posteriori LLR-based cognitive transmission strategy and show that this strategy is optimum in the sense of maximizing UR given a certain maximum allowed IR. Two methods for calculating threshold for this strategy in practical situations are presented. One of them performs well in higher SNRs but might have too large IR at low SNRs and low PU activity levels, and the other is proven to never violate the allowed IR at the price of a reduced UR. In addition, an upper-bound for the UR of any CR strategy operating in the presence of Markovian PU is presented. Simulation results have shown a more than 116% improvement in UR at SNR of -3dB and IR level of 10% with PU state estimation. Thus, this opportunistic CR mechanism possesses a high potential in practical scenarios in which there exists no information about true states of PU.

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arXiv2011

Designing Power-Efficient Modulation Formats for Noncoherent Optical Systems

We optimize modulation formats for the additive white Gaussian noise channel with a nonnegative input constraint, also known as the intensity-modulated direct detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical and optical power. The nonnegativity input signal constraint is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some remarkably dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1 bit/s/Hz, the obtained modulation format offers a 0.86 dB average electrical power gain and 0.43 dB average optical power gain over the previously best known modulation formats to achieve a symbol error rate of 10^-6. This modulation turns out to have a lattice-based structure. At a spectral efficiency of 3/2 bits/s/Hz and to achieve a symbol error rate of 10^-6, the modulation format obtained for optimizing the average electrical power offers a 0.58 dB average electrical power gain over the best lattice-based modulation and 2.55 dB gain over the best previously known format. However, the modulation format optimized for average optical power offers a 0.46 dB average optical power gain over the best lattice-based modulation and 1.35 dB gain over the best previously known format.

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arXiv2010

On BICM receivers for TCM transmission

Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is in fact the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are also presented. It is shown that the minimum distance of the code is not the relevant optimization criterion for BICM-T. Optimal convolutional codes for different constrain lengths are tabulated and asymptotic gains of about 2 dB are obtained. These gains are found to be the same as those obtained by Ungerboeck's one-dimensional trellis coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be asymptotically as good as 1D-TCM.

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arXiv2010

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit $-1.59 \tr{dB}$. It is shown that the $\Eb/N_0$ required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.

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arXiv2010

Faster Projection in Sphere Decoding

Most of the calculations in standard sphere decoders are redundant, in the sense that they either calculate quantities that are never used or calculate some quantities more than once. A new method, which is applicable to lattices as well as finite constellations, is proposed to avoid these redundant calculations while still returning the same result. Pseudocode is given to facilitate immediate implementation. Simulations show that the speed gain with the proposed method increases linearly with the lattice dimension. At dimension 60, the new algorithms avoid about 75% of all floating-point operations.

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arXiv2010

On the symbol error probability of regular polytopes

An exact expression for the symbol error probability of the four-dimensional 24-cell in Gaussian noise is derived. Corresponding expressions for other regular convex polytopes are summarized. Numerically stable versions of these error probabilities are also obtained.

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