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Spectrum sensing based on goodness of fit test with unilateral alternative hypothesis

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D
Devanshi Piprottar

The document contains mathematical equations and expressions involving integrals, sums, and functions. Variables include expressions like f(x), a, b, and n. The equations integrate and take sums of functions between boundary values and involve nested terms in brackets. The document appears to be detailing steps in a mathematical proof or calculation.

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〈 , ( ) ( )- ( ( )) ( ) 〈, ( ) ( )- ( ( )) ( ) 〈 , ( ) ( )- ( )( ( )) ( ) 〈 , ( ) ( )- ( )( ( )) ( ) [ 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( )] ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) Note: ( ) ------------------------------------------------------------------------------------------------------------------------------- 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( )
{ ( ( ))} { ( ( ))} { ( ( ))} { ( ( ))} { ( ( )) } { ( ( )) ( ( ))} { ( ( )) ( ( ))} { ( ( ))} ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 ( )( ( )) ( ) 〈 [ ? ] ( )( ( )) ( ) 〈 [ ? ] ( )( ( )) ( ) 〈 , ? - ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 , -* ( ) ( ( ))+ ( )( ( )) ( ) [ 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 , -* ( ) ( ( ))+ ( )( ( )) ( )]
[[ ? ]{ ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( ))} { ( ( )) ( ( ))} ] [[ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} { ( ( )) ( ( ))}] [ ? ] [ ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ] [ ? ] ‘ ( ( )) ( ( )) ( ) Now, from equation (1) ( ) Put values from equation (4) and (5) [ [ ? ] ‘ ( ( )) ( ( )) ] [‘ ( ( )) ( ( ))]

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Spectrum sensing based on goodness of fit test with unilateral alternative hypothesis

  • 1. 〈 , ( ) ( )- ( ( )) ( ) 〈, ( ) ( )- ( ( )) ( ) 〈 , ( ) ( )- ( )( ( )) ( ) 〈 , ( ) ( )- ( )( ( )) ( ) [ 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( )] ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) Note: ( ) ------------------------------------------------------------------------------------------------------------------------------- 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( )
  • 2. { ( ( ))} { ( ( ))} { ( ( ))} { ( ( ))} { ( ( )) } { ( ( )) ( ( ))} { ( ( )) ( ( ))} { ( ( ))} ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) 〈 , ( )- ( )( ( )) ( ) ( ) 〈 ( )( ( )) ( ) 〈 [ ? ] ( )( ( )) ( ) 〈 [ ? ] ( )( ( )) ( ) 〈 , ? - ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 , -* ( ) ( ( ))+ ( )( ( )) ( ) [ 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 [ ? ]* ( ) ( ( ))+ ( )( ( )) ( ) 〈 , -* ( ) ( ( ))+ ( )( ( )) ( )]
  • 3. [[ ? ]{ ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( ))} { ( ( )) ( ( ))} ] [[ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} [ ? ]{ ( ( )) ( ( )) ( ( )) ( ( ))} { ( ( )) ( ( ))}] [ ? ] [ ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ] [ ? ] ‘ ( ( )) ( ( )) ( ) Now, from equation (1) ( ) Put values from equation (4) and (5) [ [ ? ] ‘ ( ( )) ( ( )) ] [‘ ( ( )) ( ( ))]