content_image/307039.jpg content_image/307038.jpg content_image/307037.jpg
in the same span, the DGDs of different subcarriers are the same. 

## 3 The Linear MMSE Coherent Receiver 

Let F be the M × M DFT matrix with its element given by 

<img src='content_image/307039.jpg'>

Denote the transmitted QAM symbols on all subcarriers along the k th polar- ization as s ( k ) ≜ [ s ( k ) 1 , s ( k ) 2 , · · · , s ( k ) M ] $^{T}$. As shown in Fig. 1, a DFT operation is first applied to s ( k $^{)}$, to obtain 

<img src='content_image/307038.jpg'>

which is effectively the input to a traditional OFDM system. At the receiver, we assume the frequency and time offset can be perfectly estimated and com- pensated before detection. Then the received signal on the m th subcarrier is given by 

where x$_{m}$ ≜ [ x (1) m , x (2) m ] $^{T}$, and v$_{m}$ ∼ N $_{c}$( 0 , σ $^{2}$I ). 

<img src='content_image/307037.jpg'>

To demodulate the symbol vector s ( k $^{)}$, we first estimate the DFT-spread symbol x ( k ) and then recover the data symbol vector s ( k ) by an IDFT. In 

