Probabilistic amplitude shaping for a 64-QAM OFDM W-band RoF system Citation for published version (APA): Wu, K., He, J., Zhou, Z., & Shi, J. (2019). Probabilistic amplitude shaping for a 64-QAM OFDM W-band RoF system. IEEE Photonics Technology Letters, 31(13), 1076 - 1079. [8718998]. https://doi.org/10.1109/LPT.2019.2917925 DOI: 10.1109/LPT.2019.2917925 Document status and date: Published: 01/07/2019 Document Version: Accepted manuscript including changes made at the peer-review stage Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 29. Sep. 2021 PTL-35788-2019.R1 1 Probabilistic Amplitude Shaping for a 64-QAM OFDM W-band RoF System Kaiquan Wu, Jing He, Zhihua Zhou, and Jin Shi resilience and finer capacity granularity. Abstract—In the paper, probabilistic amplitude shaping (PAS) PAS has been investigated in single-carrier transmission [7, is performed in the case of orthogonal frequency division 8]. However, in the scenario of multi-carrier transmission such multiplexing (OFDM) by combining with orthogonal circulant as OFDM, the PAS implementation faces a challenge of matrix transform (OCT) precoding. Thanks to the precoding adaptivity. Since the optimal probabilistic distribution is method, one optimized probabilistic distribution is globally implemented across 240 subcarriers by merely one distribution channel-dependent, frequency selective fading (mainly caused matcher (DM). The proposed probabilistic shaping scheme for by limited device bandwidth) leads to various subcarrier signal- OFDM is experimentally demonstrated in a 64-ary quadrature to-noise ratios (SNRs). One optimal approach is bit-loading that amplitude modulation (QAM) W-band radio-over-fiber (RoF) treats each subcarrier separately [9]. It requires multiple DMs, system using direct-detection (DD), with 20-km single-mode fiber modulation formats and an additional uplink. Alternatively, in (SMF) and 0.5-m free-space transmission. Experimental results order to implement a global probabilistic distribution, the show that compared to the uniform 64-QAM, there is 1.07 dB shaping gain for system sensitivity at BER of 10-4. Meanwhile, it subcarriers uniformity must be realized. This can be achieved inherits the advantage of flexible capacity granularity from the by the precoding methods such as orthogonal circulant matrix conventional single-carrier PAS. transform (OCT) precoding [10]. Ideally, only one DM and one modulation format are required in this case, which significantly Index Terms—probabilistic amplitude shaping, OFDM, QAM, reduces the complexity. However, the concatenation of the millimeter wave, radio over fiber communication. precoding method and PAS for OFDM has seldom been studied. In this paper, PAS combined with OCT precoding is I. INTRODUCTION proposed and experimentally demonstrated in a 64-QAM he W-band (75~110 GHz) microwave signal exhibits OFDM W-band RoF system. OCT precoding is used to equalize T advantages of precise directionality and low atmospheric subcarrier noises so that all data subcarriers can be treated attenuation, while radio-over-fiber (RoF) systems possess equally by one DM with an optimized probabilistic distribution. abundant bandwidth, low transmission loss, and high mobility. Moreover, when probabilistic shaping is used in the OFDM, we Hence, RoF systems exploiting the W-band can expand the analyze that the bit-level achievable information rate (AIR) transmission reach and capacity of wireless data service [1]. cannot reflect the gain brought by OCT precoding. The Faced with increasing demands for high-bandwidth services, experimental results show that the OCT-based single-carrier higher-order modulation format, frequency division PAS implementation grants the system with capacity multiplexing, and constellation shaping are the enabling granularity, flexibility and shaping gain. technologies for the next-generation optical communication [2]. In the W-band RoF system with limited receiver bandwidth, II. PRINCIPLES orthogonal frequency division multiplexing (OFDM) is superior to single-carrier transmission [3]. In [4], a two dual- A. PAS for Single-Carrier QAM Transmission subcarrier D-band wireless system using 64-ary quadrature The rectangular 22m-QAM constellation can be divided into amplitude modulation (QAM) can reach the data rate up to 1 two independent 2m-pulse amplitude modulation (PAM) Tb/s with the help of constellation shaping. In a word, OFDM constellations. We define the symbol set of each PAM with a large number of subcarriers is crucial for high spectral constellation as χ { AA1 , , 2m1 }, and the amplitude AA1m 1 efficiency, while constellation shaping improves the system probability distribution as P PP,,. 2 Obviously, in the robustness against noises given the transmit power budget. case of unshaped uniform QAM, each symbol is chosen and Probabilistic amplitude shaping (PAS) is the state-of-art transmitted with equiprobability. Thus, its probability (m 1) m 1 coded modulation scheme. It can offer the maximum shaping distribution is P PAi 2 ,( i 1, ,2 ) . Given the gain of 1.53 dB that approaches the Shannon limit [5]. Its key employed FEC with code rate RC, the total information rate is elements are a systematic forward error correction (FEC) and a RUNI 2 mR C . By contrast, with the help of DM, PAS assigns distribution matcher (DM) [6]. By employing a carefully the optimized P PAi to amplitudes Ai . The amount of bit designed input probability distribution according to the channel information contained per amplitude in the DM’s output state information (CSI), it provides the system with better noise amplitude sequence is the rate of DM, namely RDM. Regarding the design of P, the Maxwell-Boltzmann (MB) distribution is a This work was supported in part by National Natural Science Foundation of The authors are with College of Computer Science and Electronic China (NSFC) (61775054) and Science and Technology Project of Hunan Engineering, Hunan University, Changsha, China, 410082 (corresponding Province (2016GK2011). author: Jing He, e-mail: [email protected]). PTL-35788-2019.R1 2 TABLE I SNR GAPS TO AWGN SHANNON LIMIT AND SHAPING GAIN OF PPP1,, 2 3 SHAPED-64-QAM (BIT-LEVEL AIR) Rate Shannon Limit Uniform SNR Gap Shaped SNR Gap Gain [bits/symbol] [dB] [dB] [dB] [dB] [dB] [dB] 16-QAM 9.3129 0.8619 P1 Shaped 0.8333 3.0 8.4510 8.4796 0.0286 64-QAM 9.4345 0.9835 64-QAM 0.9549 16-QAM 12.1212 1.6579 P2 Shaped 1.6026 3.6 10.4633 10.5186 0.0553 64-QAM 11.4268 0.9635 64-QAM 0.9082 P3 Shaped 4.0 11.7609 64-QAM 12.7070 0.9641 11.8954 0.1345 0.8296 64-QAM TABLE II FIXED PROBABILITY DISTRIBUTIONS OF 64-QAM ( m 3 ) Parameters P1 P2 P3 Optimized SNR [dB] 6.50 10.70 13.65 1-D Probability Distribution PA1 0.6254 0.5178 0.4371 0.2988 0.3241 0.3210 PA 2 0.0683 0.1270 0.1732 PA 3 0.0075 0.0311 0.0687 P A4 H(P) [bit] 1.2613 1.5523 1.7516 probability distribution P, the channel SNR as well as the labeling rules. Since the adopted 1-D labeling rule is Gray Fig. 1. Bit-level AIR of shaped and uniform QAM over AWGN channel. labeling, it can be represented as AIR = f(χ,P , SNR ) (3) common choice for the additive white Gaussian noise (AWGN) bit channel [5]. The total information rate of PAS-shaped QAM The AIR of 2-D QAM is the sum of AIRs of its divided 1-D PAMs. Fig.1 presents the bit-level AIRs for QAM vs. SNRs in signal is RPAS2 R DM 1 m (1 R C ) . different cases of χ,P . For the channel-dependent shaped 64- B. Bit-Level AIR QAM, the input P is always optimized at the current operating PAS adopts a FEC bit-metric decoder at the receiver. In the point. Hence, it yields the performance near the Shannon limit. case of single-carrier transmission, the bit-level AIR is a good In addition, the MB distributions P1/P2/P3 are employed in the tool to predict the maximum amount of information that can be paper, which are optimized at 6.50/10.70/13.65 dB respectively. recovered by the ideal bit-metric decoding [5, 8]. Table I displays the shaping gains of P1/P2/P3, and Table II For the calculation of the bit-level AIR, considering there are summarizes their parameters.