Coding Efﬁciency for Bandlimited PWM Based Burst-Mode RF Transmitters Shuli Chi Signal Processing and Speech Communication Laboratory Graz University of Technology, Austria Email: shuli.chi@ieee.org Katharina Hausmair Signal Processing and Speech Communication Laboratory Graz University of Technology, Austria Email:hausmair@tugraz.at Christian Vogel Telecommunications Research Center Vienna (FTW), Austria Email: c.vogel@ieee.org Abstract—The burst-mode transmitter has been proposed as an efﬁciency enhancement technique for signals with high peak-to-average- power ratios (PAPRs), where appropriate modulation schemes such as pulse-width modulation (PWM) are used to generate a switching signal to drive the radio frequency (RF) power ampliﬁer (PA). Ideally, a PWM signal is of inﬁnite bandwidth, however, high-frequency spectral components are attenuated, e.g., by the bandlimitation of the PA matching network or the PWM circuit itself. Bandlimitations introduce ripples in the signal amplitude, which might reduce the PA efﬁciency in burst-mode operation. In this paper, we show that a bandlimited PWM signal does not nec- essarily degrade the overall transmitter efﬁciency because of the higher coding efﬁciency. The coding efﬁciency for bandlimited PWM signals, i.e., PWM signals with a ﬁnite number of harmonics, is derived analytically and veriﬁed by measurements. Additionally, from the measurements, we exemplarily determine the number of harmonics for bandlimited PWM signals with the best transmitter efﬁciency-linearity trade-off, and therefore demonstrate the excellence of bandlimited PWM for burst-mode transmitters in terms of transmitter efﬁciency as well as transmission signal quality. I. I NTRODUCTION The burst-mode operation [1] has been proposed as an efﬁciency enhancement technique for radio frequency (RF) power ampliﬁers (PAs). In order to operate PAs in highly efﬁcient burst mode [1], appropriate modulation techniques such as ΣΔ and pulse-width modulation (PWM) can be employed. These modulation schemes encode the amplitude of a signal into a pulse train signal, where the information is represented by the pulse width. A PWM signal can be generated by analog or digital circuits. Following the growing trend towards digitally assisted analog de- sign [2], a digital implementation of the PWM is advantageous. However, digital PWM signals inherently suffer from aliasing dis- tortion that reduces the signal quality, where several methods have been proposed to reduce or eliminate the distortion [3]–[5]. In [5] the digital aliasing-free PWM was proposed which eliminates all destructive aliasing distortion by introducing a bandlimited kernel of the PWM process, ﬁnally leading to an analog PWM signal with a ﬁnite number of harmonics and bandwidth. A bandlimited PWM signal intrinsically introduces ripples in the ideal switching signal amplitude. As shown in Fig. 1 [4], with a bandlimited PWM, the PA is operated over a slightly wider range of power regions, instead of operating at saturation and in cut-off as in the ideal burst-mode operation with non-bandlimited PWM signals. This might reduce the PA efﬁciency. However, the degraded PA efﬁciency does not necessarily result in a degraded transmitter efﬁciency because of the higher coding efﬁciency [6], which is used to evaluate the performance of the PWM encoder and estimate the overall transmitter efﬁciency. The bandlimitation also has an impact on the signal linearity. The amplitude variation caused by Pout PA Efficiency (%) 0 Pmax with ideal non-bandlimited PWM signals linear PA operation with bandlimited PWM signals η max Fig. 1. Illustration of PA operating regions and the PA efﬁciency. Fig. 2. Block diagram of a PWM based burst-mode transmitter. the bandlimitation in combination with the PA nonlinearity would entail nonlinear distortion on the PA output signal [4]. In this paper, coding efﬁciency for PWM signals with a ﬁnite number of harmonics, i.e., bandlimited PWM signals, is derived an- alytically. The resulting equations are veriﬁed by measurements. Ad- ditionally, the number of harmonics for a good transmitter efﬁciency- linearity trade-off is determined from measurements. It is shown that the number of harmonics can be rather low for achieving a high transmitter efﬁciency as well as good transmission signal quality. II. PWM BASED BURST-MODE RF TRANSMITTERS Fig. 2 depicts a block diagram of a digital PWM based burst-mode RF transmitter. A complex baseband input signal x[n] is separated into a magnitude signal a[n] and a phase component e jφ[n] , which can be expressed in polar form as x[n]= a[n]e jφ[n] . It is assumed that a[n] ∈ [0, 1]. The magnitude signal a[n] is then encoded by the PWM. Afterwards, the generated PWM signal p[n] is combined with the phase component e jφ[n] . Then the upconverted PWM signal is ampliﬁed by the PA before it is passed through the bandpass ﬁlter (BPF) to obtain the transmission signal xPB(t), which is sent to the antenna. The double-edge asymmetric digital PWM signal can be repre- sented by [5] p[n]= a[n]+ K  k=1 2 kπ sin(kπa[n]) cos(2kπfpTsn) (1) where fp =1/Tp is the PWM switching frequency and Tp is the pulse period, Ts =1/fs is the sampling period and fs is the sampling frequency. Unlike the conventional digital PWM, where the number