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Quadratic forms with random kernel matrices are ubiquitous in applications of multivariate statistics, ranging from signal processing to time series analysis, biomedical systems design, wireless communications performance analysis, and other fields. Their statistical characterization is crucial to both design guideline formulation and efficient computation of performance indices. To this end, random matrix theory can be successfully exploited. In particular, recent advancements in spectral characterization of finite-dimensional random matrices from the so-called polynomial ensembles allow for the analysis of several scenarios of interest in wireless communications and signal processing. In this work, we focus on the characterization of quadratic forms in unit-norm vectors, with unitarily invariant random kernel matrices, and we also provide some approximate but numerically accurate results concerning a non-unitarily invariant kernel matrix. Simulations are run with reference to a peculiar application scenario, the so-called spectrum sensing for wireless communications. Closed-form expressions for the moment generating function of the quadratic forms of interest are provided; this will pave the way to an analytical performance analysis of some spectrum sensing schemes, and will potentially assist in the rate analysis of some multi-antenna systems. [ABSTRACT FROM AUTHOR]

This paper studies the performance of the communication link between a ground station and the satellites of a LEO constellation, employing code division multiplexing and a non-linear high-power amplifier. The analysis shows that the input power selection at the high-power amplifier of the ground station has a significant impact on overall system performance. The results concerning output power, the challenge of adjusting the back-off with a continuously changing number of satellites, and improved energy efficiency suggest operating in saturation. In this scenario, we can choose to transmit directly the sign of the sum of the signals directed to individual satellites. Analytical exact and simplified results are derived, enabling the estimation of performance as a function of the number of satellites being served when the amplifier operates at saturation. These analytic results are further validated through simulations. A formula to compute the loss across different numbers of satellites is also presented. The performance under saturated amplifier conditions is evaluated, compared, and discussed, providing valuable insights for simplifying the design and operation of satellite uplink communication systems under power amplifier constraints. [ABSTRACT FROM AUTHOR]

The number of applications of low-power wide-area networks (LPWANs) has been growing quite considerably in the past few years and so has the number of protocol stacks. Despite this fact, there is still no fully open LPWAN protocol stack available to the public, which limits the flexibility and ease of integration of the existing ones. The closest to being fully open is LoRa; however, only its medium access control (MAC) layer, known as LoRaWAN, is open and its physical and logical link control layers, also known as LoRa PHY, are still only partially understood. In this paper, the essential missing aspects of LoRa PHY are not only reverse engineered, but also, a new design of the transceiver and its sub-components are proposed and implemented in a modular and flexible way using GNU Radio. Finally, some examples of applications of both the transceiver and its components, which are made to be run in a simple setup by using cheap and widely available off-the-shelf hardware, are given to show how the library can be used and extended. [ABSTRACT FROM AUTHOR]

The well-known uniform error property for signal constellations and codes is extended to encompass information bits. We introduce a class of binary labelings for signal constellations, called bit geometrically uniform (BGU) labelings, for which the uniform bit error property holds, i.e., the bit error probability does not depend on the transmitted signal. Strong connections between the symmetries of constellations and binary Hamming spaces are involved. For block-coded modulation (BCM) and trellis-coded modulation (TCM) Euclidean-space codes, BGU encoders are introduced and studied. The properties of BGU encoders prove quite useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, error probability. Applications to the analysis and the design of serially concatenated trellis codes are presented, together with a case study which realizes a spectral efficiency of 2 b/s/Hz. Index Terms--Coding, concatenated codes, constellations, encoding, labeling, trellis codes, uniform error property.

Summary: This paper presents a thorough analysis of the spectral characteristics of space telemetry signals when randomizers are used to counter the power excess, that is, the increase of the power spectrum in some measurement bandwidths with respect to the transmission of an ideal random signal. We show that a long randomizer actually improves the spectral characteristics but is not able to solve some critical problems appearing when all‐zero frames or almost constant data are transmitted. Suitable solutions are proposed to face these cases, ensuring a small power excess in all possible operation conditions. The impact of high‐order modulations and error correcting codes is also investigated. [ABSTRACT FROM AUTHOR]

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the "best" recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error probability performances of some turbo codes using them. Index Terms - Concatenated coding, convolutional codes, encoders, turbo codes.

We present a theoretical framework for rotational invariance of trellis codes. The distinction between codes and encoders plays a pivotal role. Necessary and sufficient conditions for rotational invariance are derived under general assumptions, and a construction is presented that obtains a rotationally invariant encoder for almost any rotationally invariant code, independent of the code's algebraic structure. Encoders that use a differential precoder are considered as a separate case, where a system-theoretic characterization of precoding is used to find two alternative and slightly less general encoder constructions. Index Terms - Trellis codes, rotational invariance, symbolic dynamics, encoders, differential precoding.

In Part I, general results on rotationally invariant codes and encoders were derived assuming no algebraic structure. In Part II, trellis codes based on group systems are considered as a special case for which code and encoder constructions are particularly simple. Rotational invariance is expressed as an algebraic constraint on a group code, and algebraic constructions are found for both "absorbed precoder" encoders and for encoders with separate differential precoders. Finally, the various encoder forms used to achieve rotational invariance are compared based on their performance on an AWGN channel. Index Terms - Trellis codes, rotational invariance, group systems, encoders, differential precoding

New geometrically uniform trellis codes over multidimensional unbalanced 4-, 8-, and 16-PSK constellations, obtained with the group code approach, are presented. They improve up to 1.25 dB the asymptotic performances of the best known trellis codes over multidimensional balanced PSK. To check their 'optimality', an upper bound on the free distance of group trellis codes is derived. Some of the new codes achieve the largest obtainable free distance, and several others are close to the bound. Exploiting the symmetry properties of the codes, curves of tight upper bounds to the error probability are also presented.

The theory of geometrically uniform signal sets and codes over groups is applied to the case of LxMPSK constellations. Conditions for rotational invariance of group codes are discussed. The tables of geometrically uniform partitions recently found in (1) are used to construct good geometrically uniform trellis codes over nonbinary Abelian groups. We consider Lx4PSK and Lx8PSK constellations used to transmit information rates of 1 and 2 bit/two dimensions, respectively, and present tables of good codes over generating groups (Z4)(super L) and (Z8)(super L), for L ranging from 1 to 4. In most cases, they improve the tables of codes known so far. Moreover, the geometrical uniformity of codes allows a very easy performance evaluation, so that we also present a complete set of curves of error event probability for the obtained codes.

The recently developed theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK constellations. The symmetry group of an L X MPSK constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L X MPSK (M = 4, 8, 16 and L = 1, 2, 3, 4) constellations are found, which present good characteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes.

Abstract This paper considers a VDSL downstream system where crosstalk is compensated by linear precoding. Starting from a recently introduced mathematical model for FEXT channels, simple analytical methods are derived for evaluating the average bit rates achievable, taking into account three of the most important nonidealities. First, absolute and relative estimation errors in the crosstalk coefficients are discussed, and explicit formulas are obtained to express their impact. A simple approach is presented for computing the maximum line length where linear precoding overcomes the noncoordinate system. Then, the effect of out-of-domain crosstalk is analyzed. Finally, quantization errors in precoding coefficients are considered. We show that by the assumption of a midtread quantization law with different thresholds, a relatively small number of quantization bits is sufficient, thus reducing the implementation complexity. The presented formulas allow to quantify the impact of practical impairments and give a useful tool to design engineers and service providers to have a first estimation of the performance achievable in a specified scenario.