Optical methods

Let the signal generator A, generates the desired signal and represented as

) 2

sin(

)

( _{Spri c Spri}

GA t V f t

S    (4.15)

Where S_GA S_pri 109.69dBm

fcis the instantaneous frequency, _Spriis the initial phase of the signal, V_Spri is the amplitude of the desired signal at the primary path. The signal power of

Power Splitter

Signal Generator B

Signal Generator A

Receiver

Vector

Modulator Amplifier

DAC

Control System



Sideband noise -108.8dB

Desired Signal (S), (-109.69dB)

ADC Coupler 1

-10dB

Coupler 2 -20dB Coupler A,

-20dB

Spectrum Analyzer i

i X

S_Pr  _Pr XA

XB

Primary Path

Reference Path

Delay element

-109.69dBm considered, was the average desired signal obtained from the field measurement used for the band pass filter design.

Let the signal generator B generates the interfering signal and represented as

) 2

cos( _{c c GB GB}

GB

GB V f I

X     (4.2)

dBm X

X_GB  _ref 108.80

-108.80dBm is the interfering signal power obtained for the band pass filter design analysis. Hence, a dBm-to-Amplitude converter was utilized for the conversion of the signal generator A and B, to facilitate a compromise for the Matlab-simulink design process.

VGB is the amplitude of the undesired signal, generated by the signal generator B, _cis the phase shift constant at f_c for a particular transmission line, I_GB is the length of the transmission path the signal passes before being input to the cancellation coupler, _GB is the initial phase of the signal. Since the cancelation signals are operating at the same frequency, therefore the reference signal and primary cancellation signal are represented to be a two single tone sinusoidal signal. Let the power splitter be represented asSp, from the design, the amplitude of the power splitter is divided in the ratio of 0.2:0.8 at the primary and reference paths. This was prioritized due to the design placement of the antenna.

) ( 8 . 0 ) ( 2 . 0 )

(t X t X t

X

S_P  _GB  _A  _B

 (4.3)

WhereX_Arepresents the cancellation signal at the primary path and X_B, the interfering (jamming) signal at the reference path.

) 2

cos(

) ( )

( _{Pri XPri c XPri XPri}

A t X t V f t cI

X     

 (4.4)

) 2

cos(

) ( )

( _{Rref XRef c XRef XRef}

B t X t V f t cI

X      (4.5)

Coupler A, represented as C_A is the summation point for the uncorrelated signals at the primary path.

) ( ) ( )

(t X t S t

C_A  _A  _GA

 , where X_A  X_Pri and S_GA S_Pri (4.6)

) 2

sin(

) 2

cos(

) ( )

( )

( _{Pri Pri XPri c XPri XPri SPri c SPri}

A t X t S t V f t cI V f t

C          (4.7)

At the input of the Vector Modulator (VM), the interfering signal is represented as:

) 2

cos(

)

( _{Re Re Re}

Ref t VX f fct cIX f X f

X     (4.8)

The basic function of a vector modulator is to ensure that the phase and amplitude is adjusted so that the phase difference of 180⁰ (i.e. out of phase) is obtained in the reference path relative to the primary path with equal amplitude to actualize destructive cancellation. The expected output of the vector modulator is



^{2 ( 180 )}



cos ) ( )

( _{Re Re Re} ⁰

0Re_f t V_{X f} t f_ct cI_{X f}  _{X f} 

X    (4.9)

Transfer function for VM=

 

) 2

cos(

) (

) 180 (

2 cos ) ( )

( ) (

Re Re

Re

0 Re

Re Re

Re 0Re

f X f X c

f X

f X f X c

f X f

f

cI t f s

V

cI t f s

V s X

s X





















 

(4.10)

At the Coupler 1, which is the summation point or cancellation point?

rr i f

R X X e

X  _Re  _Pr 

(4.11) Where X_Ris the residual noise signal .

Hence, it is important to note that the magnitude and phase characteristics of the error signal depends on the phase error, amplitude imbalance and delay mismatch between the primary signal path and reference signal path at the point of cancellation.

Let _Vrepresent the difference in amplitude imbalance _err represent the phase error and

_L represent the delay mismatch

i X f X

V V _Re V _Pr



 , hence V_XRef _V V_XPri (4.12)

_err (_XRef _XPri)180⁰, hence _XRef _err _XPri 180⁰ (4.13) _L I_XRef I_XPri, hence I_XRef _L I_XPri (4.14) Substituting equations 4.12, 4.13 and 4.14 into 4.8. Therefore,

0 Pr

Pr Pr

Re_f (_V V_{X i})cos(2 f_c  c(_L I_{X i}) _err  _{X i} 180

X     (4.15)

Hence, _rris the outcome of the vector addition of the primary signal and the reference signal at the cancellation point, which takes place at coupler 2.

i X Xref

rr   Pr

  

 (4.16)

It is the feedback error that provided the necessary information required for adjustment by the vector modulator. A control algorithm was developed and implemented for the In-phase and Quadrature phase adjustment in a closed loop function to achieve the desired system performance, refer to appendix D for the codes.

For hardware design and implementation, it is recommended to consider using lower couplers as exemplified in Figure 4.23 to minimize the rate of insertion loss and to avoid further signal strength reduction. The implementation of the cancellation performance of the proposed ANCT was developed using a flow chart algorithm as shown Figure 4.24. Figures 4.25- 4.27 illustrated the Matlab-SimulinkTest-bed of the Adaptive Noise Cancellation System, the signal conditioning phase and the power splitter respectively.

Figure 4.24: Steps for implementing the Proposed ANC system using a flow chart algorithm

Display Desired Signal )

(S_GA at Spectrum Analyzer

0

 _B

A X

X A

End Initialize power splitter S_p  X_A X_B

in the magnitude ratio of X_A 0.2 and 8

.

0 XB

Set summation point at Coupler A as

GA A

A X S

C  

Process X_Bat the Vector Modulator

Is

Amplitude Imbalance at coupler 1=0dB?

Yes

Yes is

Phase Error at coupler 1

=0⁰ Yes

Yes

No

No

No No is

Vector Modulator, Amplifier, Feedback

Error, ready?

is Delay Mismatch at coupler 1=0ns

A

Start

Input desired signal from the generator A as S_GA S_Pri 109.69dBm

Input Interfering signal from the generator B as S_GB 108.80dBm

Figure 4.25 Matlab-SimulinkTest-bed of the Adaptive Noise Cancellation System

Figure 4.26 Signal Conditioning Phase

Figure 4.27 Power Splitter

Figure 4.28 ANCT Perfect Time Delay Response

Figure 4.28 represented a time delay response for perfect cancellation. The two linear lines showed the primary signal and the reference signal, absolutely superimposed to each other given rise to absolute time delay match. Figures.

4.29-4.36 show the various noise and signal characteristics for the Matlab-Simulink Test-bed.

Figure 4.29 Original signal from Signal Generator A

Figure 4.30 Noise signal from Signal Generator B

Figure 4.31 Splitted Noise signal from Signal Generator B, Magnitude Ratio of 0.2

Figure 4.32 Noise signal level before the Signal attenuator, Magnitude Ratio of 0.8

Figure 4.33 Noise signal level after the Signal Attenuator

Figure 4.34 Additive Spri and Xpri

Figure 4.35 Error signal before Cancellation

Figure 4.36 Error signal after Cancellation

4.10 Performance Evaluation Decisive Factors for the Proposed Techniques

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