Position, Navigation, and Timing Technologies in the 21st Century

It is worth noting that the cdma2000 standard requires the BTS’s clock to be synchronized with GPS to within 10 μs, which translates to a range of approximately 3 km (the average cell size) [51]. Note that a PN offset of 1 (i.e. 64 chips) is enough to prevent significant interference from different BTSs. This translates to more than 15 km between BTSs. Subtracting 6 km from this value due to worst‐case synchronization with GPS (i.e. 3 km for each BTS), BTSs at 9 km or more from the serving BTS could cause interference (assuming all BTSs suffer from the worst‐case synchronizations). But 9 km is larger than the maximum distance for receiving cellular CDMA signals for ground receivers. Therefore, this synchronization requirement is enough to prevent severe interference between the short codes transmitted from different BTSs and maintains the CDMA system’s capability to perform soft hand‐offs [47]. The clock bias of the BTS can therefore be neglected for communication purposes. However, ignoring δt sin navigation applications can be disastrous, and it is therefore crucial for the receiver to know the BTS’s clock bias. The estimation of δt scan be accomplished via the frameworks discussed in Section 38.4.

Assuming the transmitted signal to have propagated through an additive white Gaussian noise channel with a power spectral density of , a model of the received discrete‐time signal r [ m ] after radio frequency (RF) front‐end processing: down‐mixing, a quadrature approach to bandpass sampling [52], and quantization can be expressed as

(38.5)

where t s( t m) ≜ δt TOF+ Δ( t k− δt TOF) is the PN code phase of the BTS, t m= mT sis the sample time expressed in receiver time, T sis the sampling period, δt TOFis the time of flight (TOF) from the BTS to the receiver, θ is the beat carrier phase of the received signal, and n [ m ] = n I[ m ] + jn Q[ m ] with n Iand n Qbeing independent and identically distributed Gaussian random sequences with zero mean and variance . The receiver presented in Section 38.5.2will operate on the samples of r [ m ] in Eq. (38.5).

This section details the architecture of a cellular CDMA navigation receiver, which consists of three main stages: signal acquisition, tracking, and message decoding [18]. The receiver utilizes the pilot signal to detect the presence of a CDMA signal and then tracks it. Section 38.5.2.1describes the correlation process in the receiver. Sections 38.5.2.2and 38.5.2.3discuss the acquisition and tracking stages, respectively. Section 38.5.2.4details decoding the sync and paging channel messages.

Given samples of the baseband signal exiting the RF front‐end defined in Eq. (38.5), the cellular CDMA receiver first wipes off the residual carrier phase and match‐filters the resulting signal. The output of the matched filter can be expressed as

(38.6)

where is the beat carrier phase estimate, and h is a pulse shaping filter, which is a discrete‐time version of the one used to shape the spectrum of the transmitted signal, with a finite‐impulse response (FIR) given in Table 38.3. The samples m ′ of the FIR in Table 38.3are spaced by .

Table 38.3 FIR of the pulse shaping filter used in cdma2000 [50]

Source: 3GPP2, “Physical layer standard for cdma2000 spread spectrum systems (C.S0002‐E),” 3rd Generation Partnership Project 2 (3GPP2), TS C.S0002‐E, June 2011. Reproduced with permission of 3CPP2.

Next, x [ m ] is correlated with a local replica of the spreading PN sequence. In a digital receiver, the correlation operation is expressed as

(38.7)

where Z kis the k ‐th subaccumulation, N sis the number of samples per subaccumulation, and is the code start time estimate over the k ‐th subaccumulation. The code phase can be assumed to be approximately constant over a short subaccumulation interval T sub= N s T s; hence, . It is worth mentioning that theoretically, T subcan be made arbitrarily large since no data is transmitted on the pilot channel. Practically, T subis mainly limited by the stability of the BTS and receiver oscillators. In the following, T subis set to one PN code period. The carrier phase estimate is modeled as , where is the apparent Doppler frequency estimate over the i ‐th subaccumulation, and θ 0is the initial beat carrier phase of the received signal. As in a GPS receiver, the value of θ 0is set to zero in the acquisition stage and is subsequently updated in the tracking stage. The apparent Doppler frequency is assumed to be constant over a short T sub. Substituting for r [ m ] and x [ m ], defined in Eqs. (38.5)– (38.6), into Eq. (38.7), it can be shown that