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By Sergios Theodoridis, Rama Chellappa

This moment quantity, edited and authored by means of global top specialists, supplies a evaluate of the rules, equipment and strategies of significant and rising study themes and applied sciences in communications and radar engineering.

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    Sample text

    We refer the reader to [27] for details. So let us start with the introduction of the ML estimator for the joint synchronization parameters. The likelihood function can be written as follows p(y(t)|τ, φ, f ) ∝ e − R y(t)− N −1 2iπ( f t+φ) n=0 sn h a (t−nTs −τ )e 2 dt/2N0 , where the training sequence, {sn }, is known. The ML estimator is given by [τˆN , φˆ N , fˆN ] = arg min τ,φ, f 2 N −1 R sn h a (t − nTs − τ )e y(t) − 2iπ( f t+φ) dt. 2) sn∗ e−2iπ φ e−2iπ f Ts n z τ (n) = 0, ⎪ n=0 ⎪ ⎪ ⎪ ⎪ ⎪ N −1 ⎪ ⎪ ⎪ sn∗ e−2iπ φ ne−2iπ f Ts n z τ (n) = 0, ⎩ n=0 where z τ (n) = z τ (n) = R R ya (t)h a (t − nTs − τ )∗ dt = h a (−t)∗ ya (t)|t=nTs +τ ya (t)h a (t − nTs − τ )∗ dt = h a (−t)∗ ya (t)|t=nTs +τ with h a (t) is the derivative of h a (t).

    When the synchronization parameters are non-zero but known, the continuous-time received signal is given by ya (t) = sn n (t − nTs ) + ba (t) n with n (t) = h a (t − nTs − τ0 )e2iπ( f 0 t+φ0 ) . Once again, the optimal operation at the receiver side is to project ya (t) onto the function n (t). 2. 2 since it commutes with the other operators. The CFO compensator can be located anywhere if and only if the CFO is small enough compared to the filter bandwidth1 . This last assumption is usually satisfied as mentioned earlier.

    N=0 Once again the likelihood can be written as follows: p(y(t)|φ, f ) ∝ e − R N −1 2iπ( f t+φ) n=0 sn h a (t−nTs )e ya (t)− 2 dt/2N0 . Recall that the sequence {sn } is known. So the joint ML estimator for the phase and CFO takes the following form: [φˆ N , fˆN ] = arg min φ, f 2 N −1 R ya (t) − sn h a (t − nTs )e 2iπ( f t+φ) dt . 7) where b(n) is still a white noise process due to the square-root Nyquist property of the shaping filter. By letting N −1 1 sn∗ z(n)e−2iπ f Ts n , αN ( f ) = N n=0 26 CHAPTER 2 Synchronization we have that J N (φ, f ) = −2N {α N ( f )e−2iπ φ } + const.

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