Simulating Ionosphere-Induced Scintillation for Testing GPS Receiver Phase Tracking Loops Todd E. Humphreys, Mark L. Psiaki, Joanna Hinks, Brady O'Hanlon, and Paul M. Kintner, Jr. Summary: A simple model is proposed for simulating equatorial transionospheric radio wave scintillation. The model can be used to test Global Positioning System phase tracking loops for scintillation robustness because it captures the scintillation properties that affect such loops. In the model, scintillation amplitude is assumed to follow a Rice distribution, and the spectrum of the rapidly-varying component of complex scintillation is assumed to follow that of a low-pass 2nd-order Butterworth filter. These assumptions are justified, and the model validated, by comparison with phase-screen-generated and empirical scintillation data in realistic tracking loop tests. The model can be mechanized as a scintillation simulator that expects only two input parameters: the scintillation index S4 and the decorrelation time tau0. Background: Increased dependence on the Global Positioning System (GPS) and other satellite navigation systems makes users vulnerable to signal loss or degradation caused by ionospheric effects. Radio wave scintillation, the temporal fluctuation in phase and intensity caused by electron density irregularities along the propagation path, stresses a GPS receiver's carrier tracking loop, and, as severity increases, can lead to navigation bit errors, cycle slipping, and complete loss of carrier lock [11, 9, 14, 12, 6, 15, 4, 7, 2]. In anticipation of the 2011 solar maximum, when scintillation effects will be more severe, there is great interest in testing civilian and military GPS receivers for scintillation robustness. Such testing entails subjecting a receiver's tracking loops to realistic phase and amplitude scintillation. This can be done by passing scintillation time histories through a software model of the tracking loops [3, 7, 8, 12, 10]; or by forcing phase and amplitude variations in the output of a GPS signal simulator [2, 16]; or, in the ultimate confrontation with reality, by field testing receivers in a region prone to strong scintillation [6]. The first two of these testing strategies can give misleading results if the scintillation time histories are not realistic. For example, in field testing on Ascension Island during the 2000 solar maximum, researchers noted receiver performance degradations much worse than those predicted by simulations conducted prior to the campaign [6, 2]. In a previous paper [11], the current authors propose a receiver testing strategy that is based on drawing scintillation time histories from a large library of empirical equatorial scintillation data. The scintillation library includes severe complex signal scintillation from the Wideband Satellite experiment [5] and from specially-processed GPS data. The data reveal a universal feature of strong equatorial scintillation: deep power fades (> 15 dB) accompanied by abrupt, approximately half-cycle phase transitions. These ``canonical fades'' are shown in [9] to be the primary cause of loss of carrier lock in GPS phase tracking loops. Although a receiver testing strategy based on empirical data is attractive for its realism, it nonetheless has several drawbacks: (1) A test engineer is only at liberty to adjust the scintillation behavior insofar as this behavior is represented in the recorded data; (2) thermal noise in the receiver that was originally used to record the data can leave high-frequency variations that make it difficult to precisely specify the carrier-to-noise ratio of a given test (this is the case in [10] for the scintillation library's GPS data); and (3) the empirical scintillation data is only stationary over short time intervals, making impossible extended testing under consistent scintillation statistics. These limitations can be overcome by generating synthetic scintillation via computer simulation. Techniques for synthesizing scintillation include first-principles physics-based ionospheric models [13]; phase screen models [18, 17, 1]; and statistical models [2, 3, 7]. For testing carrier tracking loops, one seeks the simplest scintillation model---in terms of number of parameters and computational expense---that faithfully retains the scintillation properties that are relevant to carrier tracking. This goal favors statistical models over the computationally expensive and parameter-laden first-principles and phase-screen models. Because statistical models are abstractions of the physics that inspires them, extra effort must be made to ensure that their outputs are realistic. As noted in [9], the methods used in [7]---and likely in [2] and [3], though details are not provided---shape the phase and amplitude spectra independently. This practice tends to produce scintillation time histories that are artificially easy to track because they do not manifest realistic canonical fades. As demonstrated in the present paper, the key to synthesizing realistic scintillation is to focus on properly shaping the spectrum of the entire complex scintillation signal, not the amplitude and phase data taken independently. The proper spectral shape of the complex scintillation signal and the general structure of the scintillation model proposed in this paper are inspired by the model of equatorial scintillation effects on GPS phase tracking loops developed in [9]. The result is a simple and computationally efficient technique for simulating realistic equatorial scintillation. This paper also demonstrates how phase and amplitude time histories produced by the scintillation simulator can be used to modulate the phase and amplitude outputs of a commercial GPS signal simulator, thereby enabling realistic scintillation testing of any GPS receiver. References: [1] T L Beach. Global Positioning System Studies of Equatorial Scintillations. 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