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Math Help - need halp for basic question

  1. #1
    Member moonnightingale's Avatar
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    need halp for basic question

    The question says

    The interferer
    is ON with probability .25 and OFF with probability .75.
    The average transmit power is 10 mW,

    And solution says

    0.75P1 + 0.25P2 = 10

    and then he gives the answer
    P1= 12.25 mW
    P2=3.25mW


    How he calculated P1 and P2
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  2. #2
    MHF Contributor Unknown008's Avatar
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    I think that there is a problem in the question, or that there is a part of the question you omit to consider or post. With one equation and two unknowns, it's not possible to get those answers, because there are infinity solutions.
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  3. #3
    Member moonnightingale's Avatar
    Joined
    Sep 2009
    Posts
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    This is complete question
    The channel has a combination of AWGN n[k] and interference I[k]. We model I[k] as AWGN. The interferer
    is on (i.e. the switch is down) with probability .25 and off (i.e. the switch is up) with probability .75.
    The average transmit power is 10 mW, the noise spectral density is 10−8 W/Hz, the channel bandwidth B is
    10 KHz (receiver noise power is NoB), and the interference power (when on) is 9 mW.
    (a) What is the Shannon capacity of the channel if neither transmitter nor receiver know when the interferer
    is on?
    (b) What is the capacity of the channel if both transmitter and receiver know when the interferer is on?

    and this is solution

    The solution

    (a) If neither transmitter nor receiver knows when the interferer is on, they must transmit assuming
    worst case, i.e. as if the interferer was on all the time,
    C = B log

    1 + S
    N0B + I

    = 10:7Kbps:
    (b) Suppose we transmit at power S1 when jammer is o and S2 when jammer is o,
    C = B max

    log

    1 + S1
    NoB

    0:75 + log

    1 + S2
    NoB + I

    0:25

    subject to
    0:75S1 + 0:25S2 = S:
    This gives S1 = 12:25mW, S2 = 3:25mW and C = 53:21Kbps.
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