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Register a new userA General Conditional BER Expression of Rectangular QAM in the Presence of Phase Noise
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Thanh Pham
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper, we newly present a closed-form bit-error rate (BER) expression for an $M$-ary pulse-amplitude modulation ($M$-PAM) over additive white Gaussian noise (AWGN) channels by analytically characterizing the bit decision regions and positions. The obtained expression is then used to derive the conditional BER of a rectangular quadrature amplitude modulation (QAM) for a given value of phase noise. Numerical results show that the impact of phase noise on the conditional BER performance is proportional to the constellation size. Moreover, it is observed that given a constellation size, the square QAM achieves the lowest phase noise-induced performance loss compared to other rectangular constellations.
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Grant-free non-orthogonal multiple access (GF-NOMA) is a potential technique to support massive Ultra-Reliable and Low-Latency Communication (mURLLC) service. However, the dynamic resource configuration in GF-NOMA systems is challenging due to random traffics and collisions, that are unknown at the base station (BS). Meanwhile, joint consideration of the latency and reliability requirements makes the resource configuration of GF-NOMA for mURLLC more complex. To address this problem, we develop a general learning framework for signature-based GF-NOMA in mURLLC service taking into account the multiple access signature collision, the UE detection, as well as the data decoding procedures for the K-repetition GF and the Proactive GF schemes. The goal of our learning framework is to maximize the long-term average number of successfully served users (UEs) under the latency constraint. We first perform a real-time repetition value configuration based on a double deep Q-Network (DDQN) and then propose a Cooperative Multi-Agent learning technique based on the DQN (CMA-DQN) to optimize the configuration of both the repetition values and the contention-transmission unit (CTU) numbers. Our results show that the number of successfully served UEs under the same latency constraint in our proposed learning framework is up to ten times for the K-repetition scheme, and two times for the Proactive scheme, more than that with fixed repetition values and CTU numbers. In addition, the superior performance of CMA-DQN over the conventional load estimation-based approach (LE-URC) demonstrates its capability in dynamically configuring in long term. Importantly, our general learning framework can be used to optimize the resource configuration problems in all the signature-based GF-NOMA schemes.
Consider a channel ${bf Y}={bf X}+ {bf N}$ where ${bf X}$ is an $n$-dimensional random vector, and ${bf N}$ is a Gaussian vector with a covariance matrix ${bf mathsf{K}}_{bf N}$. The object under consideration in this paper is the conditional mean of ${bf X}$ given ${bf Y}={bf y}$, that is ${bf y} to E[{bf X}|{bf Y}={bf y}]$. Several identities in the literature connect $E[{bf X}|{bf Y}={bf y}]$ to other quantities such as the conditional variance, score functions, and higher-order conditional moments. The objective of this paper is to provide a unifying view of these identities. In the first part of the paper, a general derivative identity for the conditional mean is derived. Specifically, for the Markov chain ${bf U} leftrightarrow {bf X} leftrightarrow {bf Y}$, it is shown that the Jacobian of $E[{bf U}|{bf Y}={bf y}]$ is given by ${bf mathsf{K}}_{{bf N}}^{-1} {bf Cov} ( {bf X}, {bf U} | {bf Y}={bf y})$. In the second part of the paper, via various choices of ${bf U}$, the new identity is used to generalize many of the known identities and derive some new ones. First, a simple proof of the Hatsel and Nolte identity for the conditional variance is shown. Second, a simple proof of the recursive identity due to Jaffer is provided. Third, a new connection between the conditional cumulants and the conditional expectation is shown. In particular, it is shown that the $k$-th derivative of $E[X|Y=y]$ is the $(k+1)$-th conditional cumulant. The third part of the paper considers some applications. In a first application, the power series and the compositional inverse of $E[X|Y=y]$ are derived. In a second application, the distribution of the estimator error $(X-E[X|Y])$ is derived. In a third application, we construct consistent estimators (empirical Bayes estimators) of the conditional cumulants from an i.i.d. sequence $Y_1,...,Y_n$.
In this paper, we propose a geometric shaping (GS) strategy to design 8, 16, 32 and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64-ary AWGN shaped formats.
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The current acquisition technology oversamples signals and converts the problem into a denoising problem with multiplicative noise. However, this paper explores the possibility of reducing the number of measurements below the ambient dimension of the signal. The sophistications that appear in the study of multiplicative noises have so far impeded theoretical analysis of such problems. This paper aims to present the first theoretical result regarding the recovery of signals from their undersampled measurements under the speckle noise. It is shown that if the signal class is structured, in the sense that the signals can be compressed efficiently, then one can obtain accurate estimates of the signal from fewer measurements than the ambient dimension. We demonstrate the effectiveness of the methods we propose through simulation results.
In this work, we abstract some key ingredients in previous LWE- and RLWE-based key exchange protocols, by introducing and formalizing the building tool, referred to as key consensus (KC) and its asymmetric variant AKC. KC and AKC allow two communicating parties to reach consensus from close values obtained by some secure information exchange. We then discover upper bounds on parameters for any KC and AKC. KC and AKC are fundamental to lattice based cryptography, in the sense that a list of cryptographic primitives based on LWR, LWE and RLWE (including key exchange, public-key encryption, and more) can be modularly constructed from them. As a conceptual contribution, this much simplifies the design and analysis of these cryptosystems in the future. We then design and analyze both general and highly practical KC and AKC schemes, which are referred to as OKCN and AKCN respectively for presentation simplicity. Based on KC and AKC, we present generic constructions of key exchange (KE) from LWR, LWE and RLWE. The generic construction allows versatile instantiations with our OKCN and AKCN schemes, for which we elaborate on evaluating and choosing the concrete parameters in order to achieve an optimally-balanced performance among security, computational cost, bandwidth efficiency, error rate, and operation simplicity.
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