Efficient Spectrum Utilization via Pulse Shape Design for Fixed Transmission Networks Elena-Iulia Dobre∗, Ayman Mostafa∗, Lutz Lampe∗, Hoda ShahMohammadiany, Ming Jiany Abstract—Microwave backhaul links are characterized the base stations worldwide are connected through by high signal-to-noise ratios permitting spectrally-efficient microwave links [1], [2]. The data rate requirements transmission. The used signal constellation sizes and for these links are continuously increasing to sup- achievable data rates are typically limited by transceiver port the fast growing demands of radio access net- impairments, predominantly by phase noise from non- ideal carrier generation. In this paper, we propose a new works. Improving the data rate of fixed microwave method to improve the data rate over such microwave links has a long history [3]. Modulation formats links. We make use of the fact that adjacent frequency have evolved from 128-ary quadrature amplitude channels are inactive in many deployment scenarios. We modulation (QAM) [4] to 1024-QAM [5], and lately argue that additional data can be transmitted in the up to 8192-QAM [6]. Microwave systems use large skirts of the spectral mask imposed on the transmission constellation sizes as part of adaptive modulation signal by regulation. To accomplish this task, we present a shaped wideband single-carrier transmission using non- schemes, which select the modulation depending Nyquist pulse shapes. In particular, we design spectrum- on the fairly slowly varying signal-to-noise ratio skirt filling (SSF) pulse shaping filters that follow the (SNR) of the communication link. The throughput spectral mask response, and perform detection using an of microwave links can be further improved by the accordingly increased sampling frequency at the receiver. use of dual-polarization and spatial multiplexing, We evaluate the achievable information rates of the SSF- where the latter requires an appropriate antenna based transmission considering practical dispersive chan- nels and non-ideal transmitter and receiver processing. To arrangement to achieve a multiplexing gain in line- compensate for phase noise impairments, we derive carrier of-sight conditions [7]. Another possibility is the phase tracking and estimation techniques, and utilize them use of additional frequency bands. While fixed in tandem with nonlinear precoding which mitigates the microwave systems have commonly operated in intersymbol interference introduced by the non-Nyquist frequency bands from 6 GHz to 42 GHz, more SSF shaping filter. Quantitative performance evaluations recently, millimeter wave bands, in particular the show that the proposed system design achieves higher data 57-66 GHz V-band and the 71-86 GHz E-band, have rates in a dispersive microwave propagation environment with respect to the conventional transmission with Nyquist been used [2], [5], [6]. pulse shaping. In this paper, we propose a method to enhance the data rate of microwave transmission systems arXiv:2010.05162v1 [eess.SP] 11 Oct 2020 Index Terms—Shaped wideband transmission, pulse shaping filter, Tomlinson-Harashima precoding, phase that is complementary to all of the above-mentioned noise. approaches. The essence of our approach is to replace conventional waveforms, which utilize a Nyquist pulse in the main lobe of the spectral mask, I. INTRODUCTION by a pulse shape that fills the entire area of the Microwave transmission systems have widely mask, including the spectrum skirts. The main mo- been used for fixed broadband and mobile back- tivation of the proposed spectrum-skirt filling (SSF) haul networks. For example, about 50%-60% of wideband transmission derives from the numerous instances in which the adjacent frequency channels ∗Department of Electrical and Computer Engineering, The Univer- are not utilized in the same transmission hop. To sity of British Columbia, Vancouver, Canada demonstrate the feasibility of transmission in the yHuawei Technologies, Ottawa, Canada Resubmission. Original manuscript submitted to IEEE Transactions skirts, we computed the fraction of channels with on Communications on 15 November 2019. active neighbours in the same hop, based on the 1 28 MHz channel spacing (details will be provided USA in Section II-B and Figure 3), and considering a typical link SNR of 50 dB at the carrier frequency, an improvement of 50% in data rate is possible UK according to the communication-theoretic limit for transmission with a given PSD [16]. Canada We note that enhanced RRC pulse shape designs such as the ones considered in [17]–[19] for improv- 0 0.2 0.4 0.6 0.8 1 1.2 ing robustness against timing jitter, in [20] to match 18 GHz 23 GHz 26-28 GHz the pulse shaping filter to the channel characteris- tics, or in [21] to minimize the multiplicative com- Fig. 1. Percentage of fixed point-to-point microwave frequency plexity of the pulse shaping filter implementation channels with active neighbours in the same transmission hop. would not improve the rate of the RRC benchmark system in our microwave transmission link. In par- ticular, we assume accurate timing synchronization, latest frequency allocation tables for Canada [8], an adequate number of taps for pulse shaping and the UK [9], and the USA [10]. Figure 1 shows the equalization filters, and a mild intersymbol inter- results in percent for several microwave bands for ference (ISI) channel, for which the conventional point-to-point fixed links. The very low neighbour- RRC pulse provides the best performance, and thus activity rates demonstrate the potential for using the is the appropriate benchmark to compare against. spectrum skirts to achieve higher data rates. Our The proposed shaped transmission has similarities second premise is the high SNR experienced by to Faster-than-Nyquist (FtN) signaling [16] through fixed microwave links for 99% − 99:9% of the time enabling faster rates at the cost of losing pulse of operation [11]. This suggests data transmission orthogonality. However, unlike FtN, which starts with non-negligible rates is possible in spectrum from a Nyquist pulse and in essence uses the excess skirts with a power spectral density (PSD) of 35- bandwidth, i.e., the difference between transmission 45 dB below the level at the carrier frequency. It rate and pulse shape bandwidth, to increase data follows that the regulated spectrum skirts could be rate, our SSF transmission shapes the signal PSD. used to transmit additional data without the need to This, in turn, suggests much higher potential rate lease another channel, and thus without additional improvements than for FtN. For example, for the costs for the setup of a microwave link, including case of an RRC pulse with a roll-off factor β, the costs for spectrum licenses. achievable rate gain for FtN would be limited to A contrasting method of improving the data rate the factor of (1 + β). For SSF, the potential rate in a conventional root-raised cosine (RRC) sys- gain is determined by the achievable rate given the tem is increasing the spectral efficiency. Although spectrum mask. commercial systems use high-resolution analog-to- Several works propose the design of pulse shap- digital converters to process large constellations, ing filters which conform to spectral mask con- phase noise (PN) sets a constraint on the QAM al- straints. In [22], the objectives of the design are phabet size due increased PN sensitivity for higher- to minimize the stopband energy for a fixed filter order modulation [12]. This can partially be ad- length, to trade-off the ISI introduced by the filter dressed by effective PN compensation techniques, and the channel distortion, or to minimize the band- often devised jointly with equalization [13], or as it- width for a fixed admissible ISI. Similarly, in [23], erative trellis-based PN compensation and decoding the authors propose a design which minimizes the [14], [15]. In this context, it is insightful to compare stopband energy of the filter under frequency re- the possible relative rate improvement from the use sponse constraints. In [24], an orthogonal multirate of an increased constellation size with that from filter which concentrates most of the pulse’s energy using spectrum skirts. Replacing 4096-QAM by in a minimum bandwidth for a given length, or in 8192-QAM leads to an 8% rate increase, assuming a minimum filter length for a fixed bandwidth, or that a reliable detection is possible. Using instead which maximizes the spectral energy concentration the spectrum skirts provided by a spectral mask with within most of a given bandwidth and fixed length 2 is presented. Other avenues which make use of a bit error rate (BER) of the transmission with spectral mask to find a pulse shaping filter, albeit for forward error correction (FEC) to analyze the entirely different use cases, are proposed in [25] and performance of our transceiver. The perfor- [26]. The work in [25] shapes orthogonal frequency- mance results of our simulated transmission division multiplexing waveforms to be compliant scenarios show that the proposed transmission to a block-edge mask to enable dynamic spectrum technique achieves significant data rate gains access while suppressing out-of-band radiation. The from 23% to 40% in comparison to the stan- filter design in [26] maximizes the signal-to-noise- dard RRC-based transmission, depending on and-interference ratio while meeting the mask con- the applied PN compensation method. straints in a multiple access ultra-wideband commu- The remainder of this paper is organized as nication system. What differentiates our paper from follows. In Section II-A, we describe the proposed these previous works is the pulse shape design with system architecture, followed by a summary of the express purpose of exploiting spectrum skirts for the pulse shaping filter design in Section II-B and increasing data rates in the case of vacant adjacent equalization and pre-equalization methods in Sec- channels. Furthermore, our focus is not on resource tion II-C. In Sections III and IV, we derive the optimality, such as filter length or signal energy details of the two proposed joint precoding and concentration, for which we could however adopt PN compensation techniques.