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Modeling the Impact of Phase Noise on the Performance of Crystal-Free Radios Osama Khan, Brad Wheeler, Filip Maksimovic, David Burnett, Ali M

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Modeling the Impact of Phase Noise on the Performance of Crystal-Free Radios Osama Khan, Brad Wheeler, Filip Maksimovic, David Burnett, Ali M IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 64, NO. 7, JULY 2017 777 Modeling the Impact of Phase Noise on the Performance of Crystal-Free Radios Osama Khan, Brad Wheeler, Filip Maksimovic, David Burnett, Ali M. Niknejad, and Kris Pister Abstract—We propose a crystal-free radio receiver exploiting a free-running oscillator as a local oscillator (LO) while simulta- neously satisfying the 1% packet error rate (PER) specification of the IEEE 802.15.4 standard. This results in significant power savings for wireless communication in millimeter-scale microsys- tems targeting Internet of Things applications. A discrete time simulation method is presented that accurately captures the phase noise (PN) of a free-running oscillator used as an LO in a crystal- free radio receiver. This model is then used to quantify the impact of LO PN on the communication system performance of the IEEE 802.15.4 standard compliant receiver. It is found that the equiv- alent signal-to-noise ratio is limited to ∼8 dB for a 75-µW ring oscillator PN profile and to ∼10 dB for a 240-µW LC oscillator PN profile in an AWGN channel satisfying the standard’s 1% PER specification. Index Terms—Crystal-free radio, discrete time phase noise Fig. 1. Typical PN plot of an RF oscillator locked to a stable crystal frequency modeling, free-running oscillators, IEEE 802.15.4, incoherent reference. matched filter, Internet of Things (IoT), low-power radio, min- imum shift keying (MSK) modulation, O-QPSK modulation, power law noise, quartz crystal (XTAL), wireless communication. puts a size limitation on miniaturization and adds to the bill of material cost of a sensor node. Alternatively, MEMS technology is showing promising I. INTRODUCTION results for replacing the XTAL in commercial products in CONOMIES of scale require the millimeter-scale space-constrained applications [1], [2]. However, it is still an E wireless sensing systems that form the foundation of off-chip frequency reference and the packaging adds to the the Internet of Things (IoT) to be low-cost and energy cost of a sensor node. Attempts have been made to gener- autonomous. This vision is driving complete system integra- ate a precise on-chip frequency reference using calibration tion on a single piece of silicon to improve the system energy techniques [3], [4]. But the achieved accuracy is still insuf- efficiency for continuous operation on harvested energy and ficient to satisfy stringent wireless standards specification for to reduce cost. low-power radios, e.g., BLE/IEEE 802.15.4. In contrast, we Almost all commercial microsystems today rely on off-chip have presented a network level solution that allows a crystal- quartz technology for precise timing and frequency reference. free sensor node to derive an accurate time and frequency The quartz crystal (XTAL) is a bulky off-chip component that reference in the absence of an off-chip frequency refer- ence (XTAL) [5]. In this brief, we specifically address the impact of phase noise (PN) on the communication system Manuscript received August 26, 2016; accepted September 11, 2016. Date of publication September 20, 2016; date of current version June 23, 2017. performance of a crystal-free radio. This work was supported in part by the DARPA Vanishing Programmable In a traditional radio architecture the RF oscillator (LC/ring) Resources (VAPR) Program, in part by the Berkeley Wireless Research Center, is locked in a phase locked loop (PLL) to a stable crystal in part by the National Science Foundation Graduate Research Fellowship under Grant 1106400, and in part by the Morphing Autonomous Gigascale frequency reference (XO) to improve the close-to-carrier PN Integrated Circuits (MAGIC) under Grant DARPA-BAA-13-23. This brief was which determines the long-term frequency drift of an oscillator recommended by Associate Editor F. C. M. Lau. (excluding environmental and aging effects) as shown concep- O. Khan, B. Wheeler, F. Maksimovic, D. Burnett, and K. Pister are with Berkeley Sensor and Actuator Center, University of California at tually in Fig. 1. In the absence of a stable XO, the free-running Berkeley, Berkeley, CA 94720 USA (e-mail: [email protected]; RF oscillator is tuned to operate at the desired RF channel [email protected]; fi[email protected]; [email protected]; ksjp@ frequency using a network calibrated on-chip frequency ref- berkeley.edu). A. M. Niknejad is with the Berkeley Wireless Research Center, erence (see Fig. 2). Then the error in the desired RF channel University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: frequency will be determined by the accuracy of the on-chip [email protected]). frequency reference [5]. The noisy local oscillator (LO) in the Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. architecture proposed in Fig. 2 is operating open-loop as a fre- Digital Object Identifier 10.1109/TCSII.2016.2611643 quency calibrated free-running RF oscillator and therefore the 1549- c 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 778 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 64, NO. 7, JULY 2017 Fig. 2. Free-running RF oscillator used as an LO. impact of its PN on the communication system performance needs to be carefully evaluated. To accurately model a free-running oscillator, one has to Fig. 3. Phase spectral density plot for power law noise [7]. model the power law noise that is nonstationary and difficult to analyze analytically [6]. In this brief, we resort to numerical a unique slope as shown in Fig. 3 [7]. The y-axis unit on a log simulation and present a discrete-time simulation model for the scale is decibel relative to 1 rad2/Hz [6]. power law noise that accurately captures the close-in PN of The fractional frequency deviation y(t) of an oscillator is a free-running oscillator. This model is then used to quantify defined as [8] its impact on the communication system performance of an 1 ∂∅ (t) IEEE 802.15.4 standard compliant radio receiver. An effort y(t) = . (3) is made to provide a summary of the relevant equations and 2πfo ∂t a discrete-time simulation model is presented that is cross- The spectral density Sy( f ) of fractional frequency deviation validated with foundry computer-aided design models of an y(t) is related to the phase spectral density Sphi( f ) as RF oscillator. f 2 Sy( f ) = Sphi( f ). (4) II. POWER LAW NOISE fo Consider a sinusoidal oscillator signal v(t) with a nominal The Sphi( f ) or Sy( f ) characterizes the power law noise in the oscillation frequency fo Hz frequency domain. In the time-domain, due to the nonstation- ary nature of the power law noise, several statistical measures v(t) = [A + a(t)] cos 2πf t + φ(t) (1) o have been defined to estimate the frequency stability of an where A is the mean amplitude, a(t) is the zero-mean ampli- oscillator. One widely used measure to estimate frequency tude modulation (AM) noise and φ(t) contains all phase and stability is the Allan variance defined as [7], [9] frequency errors from the nominal oscillation frequency fo and M−1 πf t φ(t) 2 1 2 phase 2 o . Phase disturbance includes random zero- σ (τ) = (y¯k+ −¯yk) (5) y 2(M − 1) 1 mean phase modulation noise, initial phase and integrated k=1 effects of frequency offset and drift [6]. Oscillators contain where y¯ are the M average fractional frequency measurements an amplitude control mechanism that suppresses AM noise k with zero dead-time and τ is the frequency measurement time and it is therefore usually neglected. interval [7]. PN φ(t) is characterized in the frequency domain. The ran- The measurement interval τ over which the frequency is dom PN φ(t) spreads the spectrum of an ideal sinusoid in the averaged acts as a low-pass transfer function while the differ- frequency domain which otherwise is a Dirac-delta function. encing operation between two successive fractional frequency It is important to distinguish between a pass-band spectrum measurements acts as a high-pass transfer function in the P ( f ) of an oscillator which is a Fourier transform of RF frequency domain [10]. Therefore the transfer function that v(t) from the baseband noise spectrum which is a Fourier φ( ) relates the time-domain Allan variance with frequency-domain transform of the autocorrelation of t and is known as ( ) 2 PN spectral density measurement Sphi f has a band-pass phase spectral density Sphi( f ) with units rad /Hz. The phase ( ) characteristic and is given by [8] spectral density Sphi f is a frequency domain measure of 2 4 PN. Empirical measurements have shown that the Sphi( f ) can fh f sin (πf τ) σ 2(τ) = 2 ∫ S ( f ) df . (6) be well approximated by [6] y phi 2 fl fo (πf τ) h4 h3 h2 h1 S ( f ) ≈ + + + + h The lower limit of integration fl is approximated by the recip- phi 4 3 2 1 0 (2) f f f f rocal of the total measurement time of interest while the upper where the hx are coefficients that are oscillator specific and limit of integration fh is determined by the bandwidth of the the power x models a particular noise process. There are five oscillator circuit or the PN measurement instrument, which distinct noise processes, which are called the power-law noise ever is smaller [6], [10].
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