A Method for RFO Estimation Using Phase Analysis of Pilot Symbols in OFDM Systems

However, ICI may be caused due to the superposition of spectra of sub-carriers when there is CFO. Because of the negative influence of ICI, CFO estimation and compensation, i.e., frequency synchronization is important in OFDM system.

In [2], CFO, due to mismatching of LO (Local Oscillators) in transmitter and receiver and Doppler shift, may reach 0.2, normalized by cub-carrier bandwidth.

To support enough reliability of communication, CFO, normalized by sub-carrier bandwidth, should be less than 0.1.

In OFDM system, auto-correlation of OFDM symbols, auto-correlation based on CP, and pilot symbols are used for frequency synchronization [1]~ [4]. These are all based on auto-correlation, among which auto-correlation of OFDM symbols have been widely studied.

The most representative is MOOSE method [3], [4].

In this method frame header consists of two equal OFDM symbols with no guard interval.

Disadvantage of Moose method is that it can estimate frequency offset smaller than the half of frequency interval. CFO normalized by sub-carrier interval may be divided into IFO and FFO, and MOOSE method can estimate only FFO.

In Schmidl-Cox method in [5] and [6], special series of two OFDM symbols are used to estimate both IFO and CFO. Main algorithm of Schmidl-Cox method is same as Moose method.

In addition, there is M&M method, which is an improved Schmidl method.

Advantage of CP based method over auto-correlation method of Moose is that it is simple and doesn’t use pilot symbol. But it is not robust in multipath environment.

A variant of CP-based method is training series based method, which is multidimensional generalization of CP-based CFO estimation.

Frequency synchronization methods in IEEE 802.11a and 802.16b are based on MOOSE and Schmidl-Cox algorithm. Though CFO is compensated by frequency synchronization, there remains RFO in data OFDM symbol transmission. Because CFO is not completely compensated and output frequencies of LO (Local Oscillator)s of transceiver are changing with time. Estimation and compensation of such RFO/CFO is discussed in [7,8,9] in which estimation is based on CP (or training sequence like CP).

In [3], final frequency offset coefficients are calculated by linearly combining frequency coefficients on each pilot symbol point with COMB pilot pattern using the method similar to MRC method in RAKE receiver of WCDMA system, which is similar to MOOSE method. On suitable L OFDM symbols CFO coefficients of all the sub-carriers are supposed to be constant.

In [10], RFO/CFO is estimated with block pilot pattern under the assumption of flat fading channel. And in [11], possibility of frequency/time/phase synchronization with rectangular pattern is discussed with channel-delay-Doppler response in time-frequency plane. In [12], though time synchronization is considered, but synchronization using non-rectangular pilot pattern is considered with correlation method.

At the moment, study on frequency synchronization in OFDM system may be divided into two categories. One is CFO estimation in frame header based on MOOSE and Schmidl-Cox auto-correlation method. The other is in data OFDM symbol based on CP, or training sequence. The former is more studied than the latter.

Pilot pattern based methods are using COMB pilot pattern. And RFO/CFO estimation in data symbol is nearly denied. Furthermore, most of the synchronization uses correlation which depends on time varying or frequency selective characteristics.

And phase noise (PHN) is not considered. (Signal processing order does not allow considering PHN in frequency synchronization, but it is allowed in RFO/CFO estimation in data OFDM symbols).

In this paper RFO in data OFDM symbol after estimating and compensating CFO in frame header and additional CFO caused by CFO change in LO is estimated. Estimation is not based on correlation.

The rest of paper is organized as follows: Section 2 explains proposed RFO/CFO estimation method. At last conclusion in provided at section 3.

Assuming that one OFDM symbol contains p N pilot symbols and summing up phases of p N pilot symbols, then ) 2

(Note: form of (6) depends on the first value of pilot symbol index). Then CFO/RFO is estimated. l ˆ from ( 6) is unbiased and LS estimation.

As discussed in some literatures, PHN gives much influence to RFO/CFO estimation. When dealing CFO, PHN is not discussed, but when dealing PHN, CFO is also discussed.

In this paper we focuses not on CFO synchronization but on RFO/CFO estimation in data OFDM symbol after CFO synchronization, so PHN should be considered. With regard to PHN, Eq (6) may be rewritten as follows.

is the phase of signal. ( 8) may be rewritten as follows.

where first term of right side is linear increasing term with t k , second and third are constants, and the last two terms are zero- mean random variable.

Then Eq (