EE 551/451, Fall, 2006 Communication Systems Zhu Han Department of Electrical and Computer Engineering Class 14 Oct. 5 th, 2006

EE 541/451 Fall 2006 Outline Moon cake tasting Pulse Modulation in Presence of Noise Optimum Pre-emphasis and De-emphasis Pulse Modulation Demo

EE 541/451 Fall 2006 Mid-Autumn Festival 中秋節 August Fifteenth (Lunar Calendar) is a popular Asian celebration of abundance and togetherness, dating back over 3,000 years. Chinese Thanksgiving. At this time, the moon is at its fullest and brightest, marking an ideal time to celebrate the abundance of the summer's harvest. The traditional food of this festival is the moon cake, of which there are many different varieties. Story of the Festival: Archer, Hou Yi, and Chang’e, the Moon Goddess

EE 541/451 Fall 2006 Two Types of Errors Round off error Detection error Variance of sum of the independent random variables is equal to the sum of the variances of the independent random variables. The final error energy is equal to the sum of error energy for two types of errors ( ) Round off error in PCM –Example Page 467

EE 541/451 Fall 2006 Mean Square Error in PCM If transmit 1101 (13), but receive 0101 (5), error is 8 Error in different location produces different MSE Overall error probability –Page 469 –Gray coding: if one bit occur, the error is minimized.

EE 541/451 Fall 2006 Bit Errors in PCM Systems Simplest case is Additive White Gaussian Noise for baseband PCM scheme -- see the analysis for this case. For signal levels of +A and -A we get p e = Q(A/  ) Notes Q(A/  ) represents the area under one tail of the normal pdf (A/  ) 2 represents the Signal to Noise (SNR) ratio Our analysis has neglected the effects of transmit and receive filters - it can be shown that the same results apply when filters with the correct response are used.

EE 541/451 Fall 2006 Q Function For Q function: –The remain of cdf of Gaussian distribution –Physical meaning –Equation Matlab: erfc –y = Q(x) –y = 0.5*erfc(x/sqrt(2)); Note how rapidly Q(x) decreases as x increases - this leads to the threshold characteristic of digital communication systems

EE 541/451 Fall 2006 SNR vs.  Figure 12.14: Exam, Exam and Exam Threshold Saturation –Equation 12.64C, slightly better than ADC Example 12.8 Exchange of SNR for bandwidth is much more efficient than in angle modulation Repeaters

EE 541/451 Fall 2006 Companded PCM Problem of Without compand, With compand, Final SNR 12.72b Saturation 12.72C Small input signal Figure for  law –Even the input signal is very small, the output SNR is still reasonable.

EE 541/451 Fall 2006 Optimal Pre-emphasis and De-emphasis System model: Figure Distortion-less condition –12.76a for amplitude and 12.76b for phase SNR expression Maximize SNR s.t. distortionless Lagrange multiplier Optimal Hp and Hd, 12.83a and 12.83b SNR improvement, 12.83c Example 12.11

EE 541/451 Fall 2006 Pre-emphasis and De-emphasis in AM and FM AM –Figure –No that effective FM –Noise is larger when frequency is high –Optimal pre-emphasis and de-emphasis, 12.88d –Only simple suboptimum is used in commercial FM for historical and practical reasons

EE 541/451 Fall 2006 Homework (graduate) Due 10/10/06, no homework next week

EE 541/451 Fall 2006 Questions?