Project: Simplified digital communica5on systems Watcharapan Suwansan5suk EIE/ENE 324 King Mongkut’s University of Technology Thonburi Digital comm. systems have these major components Sampler message (input waveform) Quan5zer Source encoder Channel encoder Modulator Interpolator Table lookup Source decoder Channel decoder message (output waveform) Channel transmiRer receiver Demodulator 2 A focus of this project The project covers the simplest case: the case of no channel encoding • is a guess of 3 Channel encoder Modulator Channel decoder Gaussian Channel transmiRer receiver Demodulator X 1 ,X 2 ,X 3 ,... ˆ X 1 , ˆ X 2 , ˆ X 3 ,... X i 2 {-1, 1} where independent and iden5cally distributed (iid) ˆ X i X i This block can be simplified (see next slide) By using orthornormal signals to modulate, we can simplify the diagram • Random variables appear at the input/output of each block • Given independence, the decoder decoders each separately 4 Channel encoder Channel decoder transmiRer receiver X 1 ,X 2 ,X 3 ,... ˆ X 1 , ˆ X 2 , ˆ X 3 ,... X i 2 {-1, 1} where iid + X 1 ,X 2 ,X 3 ,... iid Gaussian N (0, σ 2 ) Z 1 ,Z 2 ,Z 3 ,... Y 1 ,Y 2 ,Y 3 ,... Y i = X i + Z i where (given) (given) (consequence: Y i ’s are iid) Y i
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Digital comm. systems Project: Simplified digital have ...webstaff.kmutt.ac.th/~watcharapan.suw/class/324/doc/commsys.pdf · encoder Channel encoder Modulator Interpolator Table
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tothebaseline(themaximumlikelihoodes5mateorMLE)6. SubmitMatlab code commsys_4_detect.m and the plot of
BER(hardcopies)
SNR (dB) = 10 log10
E�X2
2E {Z2} = 10 log10p
�2
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Anexampleofanaivedecisionruleistoalwaysguess.
• ThentheMatlabcodeforfunc5ondecidewillbe% Decode the received symbols% Input:% y - a vector of received symbols (real numbers)% p - the probability that a bit +1 is sent at the % transmitter% sig - the standard deviation of Gaussian noise% Output:% xhat - a vector of +1's and -1's, of the same % size of 'y’. xhat(i) is the decoded bit for % the received symbol y(i)function xhat = decide( y, p, sig ) xhat = ones( size(y) ); end
X̂ = 1
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ThentheBERwillbeatthedots
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−10 −5 0 510−4
10−3
10−2
10−1
100
SNR (dB)
BER
Part 4: Bit error rate (BER) at different signal to noise ratios (SNRs)