# Institute of Communications Engineering, NCTU 1 Unit 2 Synchronization.

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Institute of Communications Engineering, NCTU 1 Unit 2 Synchronization

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 2 Synchronization errors  The orthogonality between subcarriers break down in the presence of carrier frequency offsets (CFO) and sampling clock offsets (SCO) Exp{j2  f 0,i nT s,i } Exp{j2  f q,i nT s,i } Exp{j2  f N-1,i nT s,i } X0X0 XqXq X N-1 f q,i =q/NT s,i x(nT s,i ) Exp{-j2  (f 0,o +  f)nT s,o } Exp{-j2  (f k,o +  f)nT s,o } Exp{-j2  (f N-1,o +  f )nT s,o } X 0 + V 0 f k,o =k/NT s,o  X k + V k  X N-1 + V N-1  x(nT s,0 )

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 3 Let the subcarrier spacing of the OFDM be 1/nT s, where T s is sampling clock Define the number of subcarriers to be N, and in order to combat ISI, a cyclic prefix (CP) of N g samples is inserted at the beginning of each symbol  Consequently, each OFDM symbol has N+N g samples Denote the CFO between the transmitter and the receiver by  f and the SCO by  T s Furthermore, define the frequency domain transmitted symbol by X k and the corresponding channel response by H k

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 4 The received signal of the n-th sample of the i-th OFDM symbol after removing the CP can be expressed as The frequency domain received signal Z k,i is of the form

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 5 Define  q,k =(1+  )(  +q)-k where  =  f  nT s and Let Z k,i = S k,i + I k,i + V k,i  Then, the signal component is given by  The inter-carrier interference (ICI) is

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 6 The signal component is shifted in phase by Consider the special case when only the CFO exists. The phase shift results in By the correlation of two consecutive OFDM symbols, it follows that from where one can estimate the normalized CFO

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 7 CFO estimation : An example  Using the short pilot sequence of IEEE802.11 a\g  The sequence is composed of (10) repetitive PN codes  Let the length of the PN sequence x(n) is R and the separation between two adjacent intervals be L  The time-domain received signal is given by where L = L g +R  The maximum likelihood (ML) estimate of the CFO is

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 8  Note that the phase can only be resolved in [- ,  ].  The estimator only gives the estimate of the factional part,  F, of , namely  =  I +  F with -1/2 <  F < 1/2  Another example  Define L=R and there are U identical repetitions  UR=N  The best linear unbiased estimator (BLUE) Define

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 9 The BLUE takes the weighted average of  (u) The optimal K =U/2 The range of the estimated CFO is –Uf s /2   f  Uf s /2

Comm. IC Design Unit 1 Introduction to Filter DesignSau-Hsuan Wu Department of Communication Engineering, NCTU 10 Integer CFO estimation  Recall the influence of CFO  Employ the frequency domain long sequences or pilots  Define  Find the subcarrier index offset g with

Institute of Communications Engineering, NCTU 11

Institute of Communications Engineering, NCTU 12 5.2 Programmable Array Logic