GPS L1 coarse/acquisition (C/A) code generation and correlation.

The C/A code is the family of 1023-chip Gold codes broadcast by GPS satellites on the L1 carrier. Each satellite's code is the modulo-2 sum (XOR) of two 10-stage maximal-length linear feedback shift registers (LFSRs), G1 and G2, as defined in IS-GPS-200 (Section 3.3.2.3 and Figure 3-9):

• G1 uses the polynomial 1 + x^3 + x^10 (feedback from stages 3 and 10).
• G2 uses the polynomial 1 + x^2 + x^3 + x^6 + x^8 + x^9 + x^10 (feedback from stages 2, 3, 6, 8, 9, and 10).

Both registers are initialized to the all-ones state and clocked at the 1.023 Mcps chipping rate; the sequence repeats every 1023 chips (1 ms).

The per-satellite code is G1 XOR G2i, where G2i is a delayed copy of the G2 sequence formed by the modulo-2 sum of two G2 register stages. The stage pair is fixed per PRN by the IS-GPS-200 Table 3-I code-phase-selection table (PRN 1 selects stages 2 and 6, PRN 2 selects 3 and 7, and so on); selecting a stage pair is equivalent to an integer cyclic delay of the G2 m-sequence.

Chip mapping (BPSK)

Binary chips are mapped to bipolar ±1 values using the standard BPSK convention:

• binary 0 maps to +1
• binary 1 maps to -1

With this mapping a code's circular autocorrelation peaks at +1023 at zero lag, and the codes are nearly balanced (512 chips of -1 and 511 of +1, so the chip sum is -1).

Supported PRNs are the 32 GPS space-vehicle assignments, PRN 1 through 32.

Examples

iex> Orbis.GNSS.Signal.CA.code_length()
1023

iex> Orbis.GNSS.Signal.CA.chip_rate_hz()
1_023_000

iex> {:ok, chips} = Orbis.GNSS.Signal.CA.code(1)
iex> length(chips)
1023

iex> Orbis.GNSS.Signal.CA.chip(1, 0)
{:ok, -1}

iex> Orbis.GNSS.Signal.CA.code(33)
{:error, {:unsupported_prn, 33}}