2.1 Data Transmission in OFDMA Uplink
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.