Implementation of a High-Sensitivity Global Navigation Satellite System Receiver on a System-on-Chip Field-Programmable Gate Array Platform

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. 2024 Feb 22;24(5):1416. doi: 10.3390/s24051416

Algorithm 1 High-sensitivity acquisition

1:
Set the total number of GPDIT iterations $N_{n c} = 7$
2:
Buffer 700 ms worth of samples: $x_{I N} [0], x_{I N} [1], \dots, x_{I N} [N \cdot N_{n c}]$
3:
Set the current GPDIT iteration $n_{n c} = 1$
4:
While $n_{n c} \leq N_{n c}$ do
5:
Take the next 100 ms worth of samples from the acquisition buffer:

$x [n] = {x_{I N} [(n_{n c} - 1) \cdot N], x_{I N} [(n_{n c} - 1) \cdot N + 1], \dots, x_{I N} [(n_{n c} - 1) \cdot N + N - 1]}$
6:
For $f_{d} = f_{m i n}$ to $f_{d} = f_{m a x}$ in $f_{s t e p}$
7:
Perform Doppler wipe-off: $x_{d} [n] = x [n] \cdot e^{- j 2 π f_{d} n T_{s}}$ , for $n = 0, \dots, N - 1$
8:
Compute $X_{d} [k] = F F T_{N} (x_{d} [n])$
9:
Compute $Y [k] = X_{d} [k] \cdot C [k]$ , for $k = 0, \dots, N - 1$
10:
Compute $R_{n_{n c}} (τ, f_{d}) = \frac{1}{N^{2}} I F F T_{N} (Y [k])$
11:
Compute $Z_{GPDIT} (τ, f_{d}) = \sum_{k = 1}^{n_{n c}} | R_{k} (τ, f_{d}) |^{2} + 2 | \sum_{k = 2}^{N_{n c}} R_{k} (τ, f_{d}) R_{k - 1}^{*} (τ, f_{d}) |$
12:
End for
13:
Search the peak value and its indices in the search grid: ${S_{m a x}, f_{i}, τ_{j}} = m a x_{f, τ} Z_{GPDIT} (τ, f_{d})$
14:
Compute input signal power estimation ${\hat{P}}_{I N} = \frac{1}{N} \sum_{n = 0}^{N - 1} {| x [n] |}^{2}$
15:
Compute the GLRT function with normalized variance $Γ = \frac{2 N S_{m a x}}{{\hat{P}}_{I N}}$
16:
If $Γ_{GLRT} > γ$ (Compare with threshold value)
17:
Declare positive acquisition and provide $f_{d_{a c q}} = f_{i}$ and $τ_{a c q} = τ_{j}$
18:
Break;
19:
Else
20:
If $n_{n c} = N_{n c} - 1$ (last GPDIT iteration)
21:
Declare negative acquisition
22:
End if
23:
End if
24:
End while