1,721,097 research outputs found
On the distribution of an arbitrary subset of the eigenvalues for some finite dimensional random matrices
Full text linkWe present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues
The PDF of the 1th largest eigenvalue of central wishart matrices and its application to the performance analysis of MIMO systems
No full textThe research of closed form expressions for the pdf of the lth ordered eigenvalue of a Wishart matrix has received a great attention in the past years owing to its applications in the performance analysis of multiple input multiple output (MIMO) systems in fading environments. Although several closed form expressions for this pdf were obtained in the past years, to the authors' knowledge, no one was very friendly for further analysis. We propose a methodology to obtain the pdf for the lth largest eigenvalue whose expression is given as a sum of terms xβe-xδ. This expression is easily usable to obtain closed form results for the performance of many MIMO systems, such as, for instance, MIMO beamforming, and MIMO with Singular Value Decomposition (SVD). The methodology is valid for both uncorrelated and correlated central Wishart, allowing the investigation of MIMO systems with uncorrelated and correlated Rayleigh fading. © 2008 IEEE
On the Distribution of the ({ell }^{\underline {mathrm {th}}}) Largest Eigenvalue of Spiked Complex Wishart Matrices
No full textThe study of the statistical distribution of the eigenvalues of Wishart matrices finds application in many fields of physics and engineering. Here we consider a special case of finite dimensions correlated complex central Wishart matrices, characterized by the fact that the covariance matrix has all eigenvalues equal, except for one which is the largest. Starting from the knowledge of the joint p.d.f. of this kind of Wishart matrices, we focus on the evaluation of a tractable form for the distribution of each individual eigenvalue. In particular, we derive an expression for the p.d.f. of the largest eigenvalue as a sum of terms of the type , which allows to write in closed form a large class of statistical averages involving functions of eigenvalues
Impact of modulation and coding on the outage probability for mobile radio systems over block fading channels
No full textBlock and convolutional codes jointly with some of the most important modulation schemes are analyzed in terms of the frame error rate when used in the presence of block fading and block co-channel interference. This channel model is well suited to describe, e.g., mobile radio transmission with non-ideal interleaving and/or frequency hopping. The results are analytical for block codes, whereas they have been obtained by simulation for convolutional codes. The capacity of a mobile radio system is then derived by including shadowing and users' position. It is shown that block codes outperform uninterleaved convolutional codes when the number of hops per codeword (the diversity degree) is low
A Note on Channel Polarization and Mutual Information Transformation Charts of Polar Codes
No full textThis paper reviews in a tutorial way channel polarization exploited in successive cancellation decoding of polar codes, focusing on the binary erasure channel. Polarization phenomenon is tackled by decomposing a multi-input multi-output channel into virtual channels and by analyzing the mutual information evolution over each such channel. This evolution is shown to be closely related to the binary representation of the virtual channel index, which allows performing an exact mutual information analysis for each virtual channel via a transformation chart and to analyze eigenformations. A simple performance bound for polar codes, exploiting the above described analysis, is also reviewed
On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis
Full text linkAn important modulation technique for Internet of Things (IoT) is the one proposed by the low power long range (LoRa) alliance. In this paper, we analyze the M -ary LoRa modulation in the time and frequency domains. First, we provide the signal description in the time domain, and show that LoRa is a memoryless continuous phase modulation. The cross-correlation between the transmitted waveforms is determined, proving that LoRa can be considered approximately an orthogonal modulation only for large M. Then, we investigate the spectral characteristics of the signal modulated by random data, obtaining a closed-form expression of the spectrum in terms of Fresnel functions. Quite surprisingly, we found that LoRa has both continuous and discrete spectra, with the discrete spectrum containing exactly a fraction 1/M of the total signal power
Piggybacking on quantum streams
Full text linkThis paper shows that it is possible to piggyback classical information on a stream of qubits protected by quantum error-correcting codes. The piggyback channel can be created by introducing intentional errors corresponding to a controlled sequence of syndromes. These syndromes are further protected, when quantum noise is present, by classical error-correcting codes according to a performance-delay trade-off. Classical information can thus be added and extracted at arbitrary epochs without consuming additional quantum resources and without disturbing the quantum stream
A pragmatic approach to space-time coding
No full textA pragmatic approach to space-time codes (STC) over block fading channels (BFC) is proposed. The new approach consists in using common convolutional codes to obtain STC, simplifying the encoder and the decoder. It is shown that pragmatic space-time codes (P-STC) achieve good performance, similar to that of the best known STC, and that they are suitable for systems with different spectral efficiencies and fading velocity (taken into account by the BFC model). To design P-STC we propose a search algorithm based on a new formulation of the pairwise error probability and the error enumerating function for geometrically uniform STC over BFC
Quantum codes for asymmetric channels: ZZZY surface codes
Full text linkWe introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum weight perfect matching (MWPM) algorithm with a suitable pre-processing phase. The resulting decoder exploits the information provided by the modified generators without introducing additional complexity. ZZZY codes demonstrate a significant performance advantage over surface codes when increasing the channel asymmetry, while maintaining the same correction capability over depolarizing channel
Massive Grant-Free Access with Massive MIMO and Spatially Coupled Replicas
Full text linkMassive multiple access schemes, capable of serving a large number of uncoordinated devices while fulfilling reliability and latency constraints, are proposed. The schemes belong to the class of grant-free coded random access protocols and are tailored to massive multiple input multiple output (MIMO) base station processing. High reliability is obtained owing to an intra-frame spatial coupling effect, triggered by a simple device access protocol combined with acknowledgements (ACKs) from the base station. To provide system design guidelines, analytical bounds on error floor and latency are also derived. The proposed schemes are particularly interesting to address the challenges of massive machine-type communications in the framework of next generation massive multiple access systems
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