respectively; ωc = 2πfc, where fc is the carrier frequency; and Δ is the absolute clock bias of the BTS from GPS time. The total clock bias Δ is defined as
Figure 38.8 Paging channel message structure (Khalife et al. [18]; 3GPP2 [50]).
Source: Reproduced with permission of IEEE.
where PNoffset is the PN offset of the BTS,
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 δts in navigation applications can be disastrous, and it is therefore crucial for the receiver to know the BTS’s clock bias. The estimation of δts can be accomplished via the frameworks discussed in Section 38.4.
38.5.1.6 Received Signal Model
Assuming the transmitted signal to have propagated through an additive white Gaussian noise channel with a power spectral density of
where ts(tm) ≜ δtTOF + Δ(tk − δtTOF) is the PN code phase of the BTS, tm = mTs is the sample time expressed in receiver time, Ts is the sampling period, δtTOF is the time of flight (TOF) from the BTS to the receiver, θ is the beat carrier phase of the received signal, and n[m] = nI[m] + jnQ[m] with nI and nQ being independent and identically distributed Gaussian random sequences with zero mean and variance
38.5.2 CDMA Receiver Architecture
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 38.5.2.1 describes the correlation process in the receiver. Sections 38.5.2.2 and 38.5.2.3 discuss the acquisition and tracking stages, respectively. Section 38.5.2.4 details decoding the sync and paging channel messages.
38.5.2.1 Correlation Function
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
where
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.
| m′ | h[m′] | m′ | h[m′] | m′ | h[m′] |
|---|---|---|---|---|---|
| 0, 47 | −0.02528832 | 8, 39 | 0.03707116 | 16, 31 | −0.01283966 |
| 1, 46 | −0.03416793 | 9, 38 | −0.02199807 | 17, 30 | −0.14347703 |
| 2, 45 | −0.03575232 | 10, 37 | −0.06071628 | 18, 29 | −0.21182909 |
| 3, 44 | −0.01673370 |
|
