An Investigation of the Pseudolite's Signal Structure for Indoor Applications

The signal specifications for GPS (and consequently for most Pseudolites are well known and well researched for typical GPS based applications. However, when using GPSlike technology for indoor applications the requirements of the signal may be significantly different. This paper begins a detailed investigation into pseudolite signal structures for indoor systems, which will ultimately lead into the corresponding receiver’s design investigation. Analytical results are presented and remain to be supported by simulation results. This research seeks to provide a powerful analysis tool that will produce the minimum performance requirements for improving indoor geolocation systems. Introduction An overwhelming amount of work went into the design, implementation, and test of the current GPS signal structure [1]. The proposed, new civil GPS signal at 1176.45 MHz has recently opened new avenues to revisit some of the political, architectural design and implementation issues associated with the GPS signal structure both from the designer and the user/application point of view. Recent work by Spilker and Van Dierendonck [2] proposes a new GPS signal at 1176.45 MHz that will: • Improve multiple access signal cross-correlation statistics; most important are the cross-correlation properties in the presence of Doppler shift. • Improve ionosphere delay correction capability. • Improve interference protection and integrity. • Provide capabilities for instantaneous carrier phase accuracy and ambiguity resolution [3]. • Improve multipath performance. Based on their preliminary investigation, these capabilities can be achieved through the proper selection of the chipping rate and code type and length. In order to maintain compatibility with the current C/A code (on L1 and L2) if a code chipping rate of 10.23 Mbps (Mega chips (bits) per second) is selected, a Newman-Hoffman code period of 10230 (10 times longer then the current C/A code) would be required [2]. The foundation of their investigation is based upon the autocorrelation of the codes assuming that the same properties will be extended to the autocorrelation and crosscorrelation of the signals. Hence, the first and most important objective of our preliminary investigation consists on providing a detailed analysis that links the autocorrelation and cross-correlation of the signals with the autocorrelation and cross-correlation of the codes. Other work by Van Dierendonck and Reddan [4] appears to indicate that split C/A codes and longer Gold-Codes, limited to a 20-MHz bandwidth, can provide superior performance (cross-correlation properties) relative to the wide bandwidth C/A codes. The reader is reminded that a split C/A code is a C/A code that is modulated with a square wave to spread its spectrum over a wider bandwidth. While we appreciate the authors’ contribution, the details of their analysis are hidden; hence, it is hard to determine the optimality of their findings. Another important aspect of our investigation is the bandwidth allocation on the new pseudolite’s signals. Some of the issues related to the impact of bandwidth allocation on the new signal structure with higher code chipping rates and power are discussed in [5]. It appears that the higher the bandwidth and the chipping rate the smaller the receiver’s tracking error [5]. This result is very desirable and it remains to be investigated for indoor applications as well. The Interagency GPS Executive board (IGEB) proposal recommends that the GPS L5 signal contains a pair of carriers (in-phase and quadrature) at 1176.45 MHz that are Binary Phase Shift Keying (BPSK) modulated by a code with a length of 10230 and a 10.23 Mbps chipping frequency; thus, maintaining a 1 ms repetition period [6]. Moreover, the in-phase signal is BPSK modulated by data at a rate of 50 bps encoded with a rate of 1⁄2 forward error correction (FEC) code yielding 100 symbols per second; and the in-phase signal is BPSK modulated by a 1 kHz Neumann-Hoffman sequence to improve symbol synchronization and cross-correlation properties [6]. Although our investigation focuses on a proper selection of the signal characteristics for indoor applications, some of recommendations of [6] can be utilized as test scenarios, which increases the level of confidence of our investigation. Some important observations are provided by Hegatry et. al. [7], which include space vehicle code selection, definition of the data messages, the addition of the coherent-carrier Newman-Hoffman code modulation on the coherent carrier and the resolution of the L5 signal timing. A group of German researchers lead by Hein and Eissfeller et. al. indicate that the Galileo system must be fully compatible and fully independent from the GPS [8]. This is another important aspect of the autonomous pseudolite system that we are investigating. Rabinowitz et. al. reminds us about possible enhanced capabilities of a joint GPS-LEO navigation system [9]. This is another consideration of the system we are investigating; i.e., it would be desirable to have the system augmented by LEO-like signals positioned on the surface of the earth or have the capability of two-way communication. An important analysis tool for the cross-correlation of the C/A code model in GPS/WAAS receivers is provided by Van Dierendonck et. al. [10]. This analysis tool was checked against simulation and laboratory measurements and thus it forms a good baseline for signal structure investigation [10]. Once the pseudolite’s signal structure is completed from the source (or transmitter) design, we will investigate the signal structure from the receiver’s design point of view; hence, Van Dierendonck et. al. [10] can be enhanced for indoor applications as well as [12] through [17]. Although the scope of this investigation is enormous, the autocorrelation and cross-correlation of signals remains its solid foundation; therefore, we first propose a system description. Next, based on a well-accepted signal definition, we provide a detailed analytical derivation, which maps the signals autocorrelation and cross-correlation to the code autocorrelation and cross-correlation from the transmitter’s perspective in a noise-free, interference-free, geometry-free, channel distortion-free, and dynamics-free environment. Numerical results are provided to assess the analyses and; finally, the paper is concluded with the summary and a useful list of references. System Description Consider an indoor geo-location system as shown in Figure 1. This system description includes six pseudolites (three groups of two). The pseudolites of the same group transmit at the same frequency, with separation from the center frequency of the other groups. Within the same group every pseudolite signal is distinguished from the modulated PRN code. We suspect that this system description should be able to provide instantaneous centimeter level positioning and navigation error, based on instantaneous ambiguity resolution under the following conditions: • Severe multipath environment; • Severe narrow/wide band interference; • Severe geometry; thus eliminating the near-far problem, which appears for the single frequency systems. This system should provide the two-way communication, which is also crucial in the environments where human lives are at stake. Figure 1: System description of an indoor application. Composite Signal Generation Up Conversion Down Conversion DLL PLL Correlator Transmitter’s Block Diagram Receiver’s Block Diagram Figure 2: Transmitter’s/Receiver’s block diagram. Three are the most important issues of the Indoor Pseudolitebased positioning and navigation System (IPS) that need to be addressed: • Signal model (code, carrier frequency, sensitivity selection, etc. and the impact on the receiver’s design); • Data model (data message(s) format, etc.); • Network model (protocol, etc.). We have restricted the focus of this investigation on the composite signal model leaving the other two issues for future investigations (see Figure 2). Signal Model The i pseudolite signal model of the h pseudolite group is defined as the sum of an in-phase data channel and a quadrature carrier channel of the same amplitude, ( ) ( ) ( ) ( ) ( ) ( ) ( ) φ ω φ ω + + + = t t l c t p t jd t t n c t s h l h i sin , cos , , (1) where ( ) t l c , is the PN code, ( ) t d l is the data stream coded at d R data rate, l and n correspond to a given i th pseudolite, ( ) t p is an appropriate code which is improves the crosscorrelation sidelobes of the PN code, resolves the bit timing clock, and reduces the spectral density to the appropriate data rate and h h f π ω 2 = with h f the carrier modulation frequency. The ( ) t p sequence has a rate of r p R R = ; i.e., r p T T = and a length of P. First, the analytical expression of the PN code is, ( ) ( ) ( ) ∑∞ −∞ = − = m m mT t q n c t n c , , (2) where ( ) n cm , { } M m , , 1 L ∈ ∀ and M is the code length and of M-chip period and q is the generator polynomial. We rewrite expression (1) in the form of, ( ) ( ) ( ) h t l h t n i jc c t s α α sin cos , 2 , 1 + = ( ) ( ) h t l t n h t l t n j c c j c c α α −         − +         + = exp 2 exp 2 , 2 , 1 , 2 , 1 ( ) ( ) h t i h t i j j α β α β − + = exp exp , 2 , 1 , (3) where, ( ) t n c c t n , , 1 = ( ) ( ) ( ) t l c t p t d c l t l , , 2 = , φ ω α + = t h h 2 , 2 , 1 , 1 t l t n t i c c + = β , and 2 , 2 , 1 , 2 t l t n t i c c − = β . (4) We desire to transmit voice and data at a data rate d R . It is also desirable to maintain compatibility with the GPS signal; thus, allowing minimum changes of the receiver design and at the same time the units should allow voice and data thus enabling the two-way communication. For example, a code repetition rate of 1 ìs would allow a data rate up to 100 kbps, which permits normal voice and data communication. A 100 kbps code rate is sub-multiple of 1 MHz PN code epoch rate, allowing also for data bit detection. And a code length o