# Frequency Offset Estimation Algorithm of OFDMA Wireless Communication System Based on Compressed Sensing

Ma Qinggong (Changzhou University Huaide College, Changzhou, China) and Yang Bo (Changzhou University Huaide College, Changzhou, China)
DOI: 10.4018/IJAPUC.2015070105

## Abstract

The frequency offset problem of OFDMA wireless communication system has been an important obstructive factor for the rapid promotion of this technology. The frequency offset estimation algorithm of OFDMA wireless communication system based on compressed sensing reconstructs the optimized mathematical model of frequency offset. Under the premise of keeping its estimated performance, from the reduction of its computation complexity and the enhancement of real-time performance of the system, it provides an optimized algorithmic approach and thus improves the practicability of algorithm. The compressed sensing algorithm has realized the fast and accurate extraction of the frequency offset parameters, so the overall performance of the system can reach the optimal state.
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## 2. Ofdma Data Transmission And Frequency Analysis Method

Assuming that there are K users in OFDMA system and there are N carriers to bears data of these users. And the N sub-carriers are intertwined into Q sub-channels. Then each sub-channel evenly distributes P sub-carriers. Assumed that the serial number of sub-carrier in q sub-channel is

and one user occupies one sub-channel. Provided that user k occupies sub-channel q, then of the prefixion and postfix at receiving end, the data in the sub-carrier n at the receiving end can be expressed as:

, (1)

In the formula, K represents the total number of active users. represents Gauss white noise. Its mean value is 0 and the variance is . represents data of user k in the sub-carrier n. The equation can be expressed as:

(2)

In the equation, and respectively represent the channel frequency response and load data of k users in p carriers. represents the normalized frequency offset of user k, which can be expressed as. represents sub-carrier spacing and represents the frequency offset of user k in base station. Assumed that, N collected data that will receive constitute a matrix through stack technology.

(2)

In the formula, is a Vandermonde Structure, of which , and the effective frequency offset of user k is . In , represents the schur product. W represents the IFFT matrix. , , ,; Z refers to the matrix of additive Gauss white noise.

Different users have different effective frequency offsets, which is a very important characteristic. One user occupies one sub-channel q, and the range of normalized frequency offset of each user is from -0.5 to 0.5. Then the user's effective frequency offset is within the section range of . Different users are in different sub-channels, so the effective frequency offsets of users are in different section range.

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