The effect of phase-noise in OFDM system 指導老師 : 高永安 學 生 : 蘇家弘

OFDM flow chart 升頻發射 降頻接收

Signal definition Index definition: : a data symbol for k-th sub-carrier T : OFDM symbol duration : time-varying phase noise process at TX : time-varying phase noise process at RX n(t) : Gaussian noise : k-th sub-carrier signal after FFT

The complex base band OFDM signal can be written as fallow :

The s(t) is affected by the phase noise of TX OSC before it is transmitted over AWGN channel, also,the received signal is influenced by the phase noise of RX OSC It can be expressed as follows :

K-th sub-carrier signal after FFT at the receiver can be written as :

is so small that can be approximated into Then

is an error term for each sub-carrier. is separated into two components, one is generated by the signal of k-th sub-carrier, the other is by other signals of adjacent sub- carriers

1st component is as follows : a) ; common phase error (CPE) :

Phase rotation

Rotation : causes rotation of the constellation is an average of total phase noise and it is constant for total sub-carriers Common phase error can be corrected by the aid of pilots

2nd component is as follows : b) ; Inter-carrier interference (ICI)

ICI caused by phase noise

The desired sub-carrier signal is changed by the magnitude attenuation and phase rotation from its own noise carrier and ICI from N-1 noise carrier

SNR Analysis : average power of the desired signal : power of noise : power of common phase error : interference power between adjacent sub- carrier

is zero mean and variance is

The signal-to-noise ratio with phase noise is :

: is variance of random variable, with Gaussian distribution. It can be found by integrating phase noise power spectrum density of oscillator.

PSD of