H234246

Reducing the jitter noise power by oversampling in high speed ofdm system Where nM-pM=dM. When the timing jitter is white, then {đ?œ?đ?‘›đ?‘€đ?œ?đ?‘›đ?‘€âˆ’đ?‘‘đ?‘€} = 0 for đ?‘‘đ?‘€ ď‚š 0 so 2

ď …{ wlM ,k } ď‚ť

1 ďƒŚ 2ď °k ďƒś 2 ďƒ§ ďƒˇ ď …{ď ´ n M } NM ďƒ¨ T ďƒ¸ 2

k ď‚š lM

(9)

From (9) it can be seen that white timing jitter E{âˆŁđ?‘¤đ?‘™đ?‘€,đ?‘˜âˆŁ2} is inversely proportional to đ?‘€ so increasing the integer oversampling factor reduces the inter carrier interference (ICI) due to timing jitter. It is also that E{âˆŁđ?‘¤đ?‘™đ?‘€,đ?‘˜âˆŁ2}depends onđ?‘˜2 but not on đ?‘™đ?‘€, so higher frequency subcarriers cause more ICI, but the ICI affects all subcarriers equally.

AVERAGE JITTER NOISE POWER FOR EACH SUBCARRIER

Yl M  H lM X lM 

ďƒĽ w NU

k  N L

l ,k



 I lM ,k H k X k  N (l )

(10)

where the second term represents the jitter noise.we consider a flat channel with,đ??ťđ?‘˜ = 1 and assume that the transmitted signal power is distributed equally across the used subcarriers so that for each used subcarrier đ??¸{đ?‘‹2đ?‘˜}= đ?œŽ2đ?‘ . Then the average jitter noise power, đ?‘ƒđ?‘— (đ?‘™) to received signal power of đ?‘™th subcarrier is given by

ď …{ Pj(l )

ď łs

2



ďƒĽ w

2

Nv

k  Nl

l ,k

 I l ,k X k }

ď łs



2

Nu

ďƒĽ ď …{ w

k  N L

l ,k

2

 I l ,k }

(11)

Rearranging the terms in (11)equation

Pj(l )

ď łs

2



ď ° 2 ďƒŚďƒ§ N v N ďƒśďƒˇ

ď …{ď ´ n } 3M ďƒ§ďƒ¨ TN 2 ďƒˇďƒ¸ 2

(12) If there is no integral oversampling or fractional oversampling, = 1 and đ?‘ đ?‘Ł = đ?‘ , Comparing (12) and (13) it can be seen that the combination of oversampling reduces the jitter noise power by a factor of đ?‘ đ?‘Ł/đ?‘ đ?‘€.

VII.

Pj(l )

ď łs

2



ď ° 2 ďƒŚďƒ§ N 2 ďƒśďƒˇ 2 ď …{ď ´ n } (13) 2 ďƒˇ ďƒ§ 3 ďƒ¨ TN ďƒ¸

integral oversampling and fractional

SIMULATION RESULTS:

By using mat lab software, the simulation results are shown below.

Figure 1: The graph is drawn between the oversampling factor and jitter noise power .

Result: due to oversampling, whenever increases the sampling Factor by two, there was the decreases in jitter noise power by 3db.

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