Carrier frequency offset

Carrier frequency offset (CFO) is one of many non-ideal conditions that may affect in baseband receiver design. In designing a baseband receiver, we should notice not only the degradation invoked by non-ideal channel and noise, we should also regard RF and analog parts as the main consideration. Those non-idealities include sampling clock offset, IQ imbalance, power amplifier, phase noise and carrier frequency offset nonlinearity. Carrier frequency offset (CFO) is one of many non-ideal conditions that may affect in baseband receiver design. In designing a baseband receiver, we should notice not only the degradation invoked by non-ideal channel and noise, we should also regard RF and analog parts as the main consideration. Those non-idealities include sampling clock offset, IQ imbalance, power amplifier, phase noise and carrier frequency offset nonlinearity. Carrier frequency offset often occurs when the local oscillator signal for down-conversion in the receiver does not synchronize with the carrier signal contained in the received signal. This phenomenon can be attributed to two important factors: frequency mismatch in the transmitter and the receiver oscillators; and the Doppler effect as the transmitter or the receiver is moving. When this occurs, the received signal will be shifted in frequency. For an OFDM system, the orthogonality among sub carriers is maintained only if the receiver uses a local oscillation signal that is synchronous with the carrier signal contained in the received signal. Otherwise, mismatch in carrier frequency can result in inter-carrier interference (ICI). The oscillators in the transmitter and the receiver can never be oscillating at identical frequency. Hence, carrier frequency offset always exists even if there is no Doppler effect. In a standard-compliant communication system, such as the IEEE 802.11 WLAN the oscillator precision tolerance is specified to be less than ±20 ppm, so that CFO is in the range from - 40 ppm to +40 ppm. If the TX oscillator runs at a frequency that is 20 ppm above the nominal frequency and if the RX oscillator is running at 20 ppm below, then the received baseband signal will have a CFO of 40 ppm. With a carrier frequency of 5.2 GHz in this standard, the CFO is up to ±208 kHz. In addition, if the transmitter or the receiver is moving, the Doppler effect adds some hundreds of hertz in frequency spreading. Compared to the CFO resulting from the oscillator mismatch, the Doppler effect in this case is relatively minor. Given a carrier frequency offset,Δ f {displaystyle f} , the received continuous-time signal will be rotated by a constant frequency and is in the form of z i , n = z ( t ) e j 2 π Δ f t | t = i ( N + N g ) T s + N g T s + n T s {displaystyle z_{i,n}=z(t)e^{j2pi Delta ft}|_{t=i(N+N_{g})T_{s}+N_{g}T_{s}+nT_{s}}} The carrier frequency offset can first be normalized with respect to the sub carrier spacing ( f S = 1 / ( N T s ) ) {displaystyle f_{S}=1/(NT_{s}))} and then decomposed into the integral component ( ϵ I ) {displaystyle (epsilon _{I})} and fractional component ( ϵ f ) {displaystyle (epsilon _{f})} , that is, Δ f = ( ϵ I + ϵ f ) f S {displaystyle Delta f=(epsilon _{I}+epsilon _{f})f_{S}} and − 0.5 ≤ ϵ f < 0.5 {displaystyle -0.5leq epsilon _{f}<0.5} . The received frequency-domain signal then becomes