Indoor GNSS Signal Acquisition Performance using a Synthetic Antenna Array ALI BROUMANDAN JOHN NIELSEN G ´ ERARD LACHAPELLE University of Calgary GNSS (Global Navigation Satellite System) signal reception in indoor environments is susceptible to spatial fading and signal attenuation. An antenna array utilizing spatial diversity can be implemented to improve detection performance which reduces the required fading margin. However for the typical handheld GNSS receiver, constrained to a single antenna, spatial processing gain is possible only if the antenna is physically translated as the signal is being captured by the receiver. This is equivalent to realizing a spatially distributed synthetic array (SA) antenna. An investigation of the indoor detection performance of a GNSS receiver based on SA processing with optimized combining algorithms is made and compared with the detection performance of the equivalent static antenna. The processing gain achievable through spatial combining of a synthetic antenna is considered from a general theoretical perspective and validated with an extensive set of experimental measurements satisfying statistical significance criteria. The performance of the proposed method is theoretically analyzed in terms of the probability of false alarm (P FA ) and probability of detection (P D ). It is shown that the significant processing gain resulting from randomly moving the antenna relative to a stationary position can be large, exceeding 10 dB in practically encountered usage cases for a GNSS handset. Manuscript received January 13, 2009; revised June 25 and December 23, 2009; released for publication January 8, 2010. IEEE Log No. T-AES/47/2/940849. Refereeing of this contribution was handled by P. Willett. Authors’ addresses: A. Broumanden and G. Lachapelle, Dept. of Geomatics Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta T2N 1N4, Canada, E-mail: (abrouman@ucalgary.ca); J. Nielsen, Schulich School of Engineering, PLAN Group, University of Calgary, 2500 University Dr. NW, Calgary, Alberta T2N 1N4, Canada. 0018-9251/11/$26.00 c ° 2011 IEEE I. INTRODUCTION Global Navigation Satellite System (GNSS) receivers produce estimates of the position and time based on a set of observables typically consisting of the measurement of the pseudo ranges of each detectable satellite. The transmitted GNSS signals are modulated by pseudo random noise (PRN) spreading sequences, which are known to the receiver, with the possible exception of an incidental low-rate data modulation. The autocorrelation of PRN sequences is negligibly small except at zero lag, which facilitates the estimation of the code phase relative to the receiver’s internal clock; this is accomplished by generating a local despreading signal [1]. Based on the joint estimation of the receiver clock offset, this despreading correlation process provides an estimate of the time of arrival (TOA) of the satellite signal. Associated with this is the estimate of the complex channel gain of the propagation path between the GNSS satellite and the receiver. The magnitude of the channel gain relative to the noise level provides a measure of the uncertainty of the TOA measurement that is necessary for appropriate weighting of the observable in the overall position estimate. If multipath propagation is encountered, as is typical for indoor and urban receiver locations, then the GNSS signal will travel over multiple reflective paths en route from the satellite to the receiver [1]. If the relative delay of the various multipath components is small within the chip interval of the GNSS modulation signal, then a flat fading condition results, characterized by fluctuations of the received signal’s amplitude, phase, and apparent angle of arrival [2]. The excess delay of the signal can be approximately represented by a biased random variable with a support of less than the chip interval. Stated otherwise, flat fading results in unresolvable multipath where the complex envelope of the received signal is characterized by a single random complex amplitude variable and a single random delay variable. If the spread of the relative delay of the various multipath components of the GNSS signal is larger, exceeding a chip interval, then frequency selective fading results such that the multipath becomes resolvable and is characterized by several distinguishable peaks. In this paper indoor multipath propagation conditions applied to a GNSS signal with a complex envelope signal bandwidth on the order of a megahertz will be assumed such that a flat fading model is appropriate. Hence the correlation peak associated with the unresolvable multipath will conform approximately to Rayleigh statistics [3—6]. This implies that the amplitude of the received GNSS signal is random with a probability density function (pdf) that is approximated as being complex normal. Hence given a stationary antenna, the received signal amplitude will vary significantly, resulting in the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 2 APRIL 2011 1337