1. Z. Ghassemlooy 1 Noise in Communication Systems Professor Z Ghassemlooy Electronics and IT Division School of Engineering Sheffield Hallam University U.K.

2. Z. Ghassemlooy 2 Contents Interference Types of noise Electrical noise Gaussian noise White noise Narrow band noise Noise equivalent bandwidth Signal-to-noise ratio

3. Z. Ghassemlooy 3 Interference Is due to: Crosstalk Coupling by scattering of signal in the atmosphere Cross-polarisation: two system that transmit on the same frequency Interference due to insufficient guard bands or filtering

4. Z. Ghassemlooy 4 Types of Noise 1- Manmade (artificial): These could be eliminated via better design - Machinery - Switches - Certain types of lamps 2- Natural - Atmospheric noise: causing crackles on our radios - Cosmic noise (space noise): Noise in Electrical Components Thermal noise: Random free electron movement in a conductor (resistor) due to thermal agitation Shot noise: Due to random variation in current superimposed upon the DC value. It is due to variation in arrival time of charge carriers in active devices. Flicker noise: Observed at very low frequencies, and is thought to be due to fluctuation in the conductivity of semiconductor devices.

5. Z. Ghassemlooy 5 Gaussian Noise Each noise types outlined before (except flicker noise) is the result of a large number of statistically independent and random contributions. The distribution of such random noise follow a Gaussian distribution with zero mean. 0  22 33 -2  -3  -- 0.4/  vnvn p(vn)p(vn) Probability density function of zero mean and standard deviation  Where  2 is the variance of noise voltage v n For zero mean, normalised noise power or mean square voltage:

6. Z. Ghassemlooy 6 White Noise t t+t+ vnvn t The time-average autocorrelation function of the noise voltage is: Assumptions: v n (t+  ) is random value that does not depend on v n (t). The above condition holds no matter how small  is, provided it is not zero. White noise w(t) (i.e perfect randomness, which can not be attained in real systems) White noise w(t) (i.e perfect randomness, which can not be attained in real systems)

7. Z. Ghassemlooy 7 White Noise - cont. R w (t) is a zero width of height P n The autocorrelation of white noise is: with an area under the pulse =  o /2  f Sw(f)Sw(f) f Sw(f)Sw(f)  o /2 oo Double-sided power spectral density Single-sided power spectral density

8. Z. Ghassemlooy 8 Narrowband Noise Communication Receiver H(f) Communication Receiver H(f) White noise w(t)  S w (f) Narrow band noise v n (t)  S v (f) Ideal LPF Sw(f)Sw(f) f oo Sv(f)Sv(f) f Ideal BPF Sv(f)Sv(f) f oo f c +B/2f c -B/2 fcfc f c +B/2f c -B/2 fcfc oo B B

9. Z. Ghassemlooy 9 Narrowband Noise - cont. Bandpass Filter H(f) Bandpass Filter H(f) White noise w(t)  S w (f) Narrow band noise v n (t)  S v (f) Sw(f)Sw(f) f Sv(f)Sv(f) f oo f c +B/2f c -B/2 fcfc f c +B/2f c -B/2 fcfc Bandlimited noise oo x(t) and y(t) have the same power as the band pass noise v n (t) 1

10. Z. Ghassemlooy 10 Narrowband Noise - Phasor diagram Bandlimited noise x(t) and y(t) have the same power as the band pass noise v n (t) (t)(t) R(t)R(t) and y(t)y(t) Quadrature component x(t)x(t) Inphase component

11. Z. Ghassemlooy 11 Noise Equivalent Bandwidth The power P n of the band limited noise v n (t) is given bt the area under its power spectral density as: Realisable filter H(f) Realisable filter H(f) w(t)w(t)vn(t)vn(t) B eq oo Sv(f)Sv(f) Noise equivalent bandwidth We replace realisable filter H(f) with a unit-gain ideal filter of bandwidth B eq. Ideal filter

12. Z. Ghassemlooy 12 Noise - Example: a simple RC low-pass filter V in (t)V out (t) C = 132.63 nF R = 300  Find the noise equivalent bandwidth B eq ? Find the 3-dB bandwidth B of the filter? Calculate the noise power P n at its output when connected to a matched antenna of noise temperature T a = 80 K? (Assuming the filter is noise free) How much error is incurred in noise power calculation by using the 3-dB bandwidth in place of the B eq ? A simple RC low-pass filter is shown in figure below:

13. Z. Ghassemlooy 13 Solution The transfer function of the filter is: where Amplitude response Phase response Equivalent bandwidth Note:  = 2  f and a = 2  RC The form of integral suggest the to use substitution of af = tan 

14. Z. Ghassemlooy 14 System Signal-to-Noise Ratio (SNR) BPF (f c ) BPF (f c ) + + Demodulator (G d ) Demodulator (G d ) Output signal Incoming signal White noise w(f) SNR i SNR o SiSi NiNi S o & N o - Band limited noise power N i = P n =  2 The SNR at the demodulator output is: Where - SNR i is the input signal (modulated carrier) to noise ratio - G d is the demodulator gain. - S i = Total power in the received modulated signal - S o = Power in the recovered message signal m(t)