in the same span, the DGDs of different subcarriers are the same. Let F be the M × M DFT matrix with its element given by 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 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 ). 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 y$_{m}$ = H$_{m}$x$_{m}$ + v$_{m}$ , m = 1 , . . . , M, (6) x ( k ) ≜ [ x ( k ) 1 , x ( k ) 2 , · · · , x ( k ) M ] T = Fs ( k $^{)}$, (5) F$_{α,β}$ = (1 $_{/}$√$_{M}$$_{)}$$_{e}$ − j 2 π ( α − 1)( β − 1) $^{/M}$. (4) 3 The Linear MMSE Coherent Receiver 7