Fine-frequency offset estimation

A method for fine frequency-offset error determination in a radio receiver, comprising the steps of:

• sampling an OFDM radio transmission, wherein fifty-two non-zero equal magnitude subcarrier measurements are obtained that collectively represent a reference signal comprising a signal subspace and a non-signal subspace, and is such said OFDM radio transmission is typically measured in 16-bit I/Q samples every 0.05 μS, and overall can be mathematically modeled as,
• 10 x ⁢ ( n ) = A ⁢ ( n ) ⁢ e jΦ ⁢ ( n ) + j2π ⁢ v F s ⁢ n + jϕ + η ⁢ ( n )
• where,
• Φ(n):
• long preamble phase
• μ:
• residual frequency offset
• φ:
• phase offset
• η(n):
• additive white Gaussian noise (AWGN)
• determining a coarse frequency offset of said OFDM radio transmission;
• compensating any coarse frequency offset determined in a previous step to at worst approximately ±10 kHz;
• finding a timing reference boundary between a short preamble and said long preamble in said OFDM radio transmission;
• assuming a coarse frequency offset after compensation by a previous circuit will not exceed approximately ±10 kHz;
• and
• using a cost function to determine a fine-frequency offset of said OFDM radio transmission for use in a subsequent circuit providing for frequency compensation of any fine-frequency offset, wherein said cost function generally conforms to
• 11 C ⁡ ( v ^ ) = [LeftBracketingBar] V 0 ⁢ X v ^ [RightBracketingBar] 2 = [LeftBracketingBar] ∑ n = 0 63 ⁢ x ⁡ ( n ) ⁢ ⅇ - ⅈ ⁢ ⁢ 2 ⁢ ⁢ π ⁢ v ^ F i ⁢ n [RightBracketingBar] 2 .