Georgia Tech, ECE 4601
Excerpt: ... Spring 2009 EE 4601: Assignment 3 Date Assigned: February 3, 2009. Date Due: February 12, 2009. 1. Text problem 4.1 2. Text problem 4.2 3. Text problem 4.3 4. Assume that s(t) = A T t, 0, 0tT elsewhere is a known signal in the presence of additive white Gaussian noise. a) Design a matched filter for s(t). Sketch the waveform at the output of the matched filter. b) Now assume that a correlation detector is used instead. Sketch the waveform at the output of the correlation detector. 5. Consider binary signaling on an additive white Gaussian noise channel. The conditional probability density functions of the matched filter or correlator outputs are fy|1 (y|1) = fy|0 (y|0) = 1 -(y - E)2 }, exp{ 2 2w 2w 1 -(y + E)2 }, exp{ 2 2w 2w No E 2 No E 2 w = 2 2 w = Decisions are made such that we choose "1" if y > and we choose "0" if y < . In Lecture 9, we have seen that the optimum decision threshold (minimizes the bit error probability) is = 0 if P ( 1 ) = P ( 0 ) = 1/2. What is the optimum decision threshol ...
University of Illinois, Urbana Champaign, EE 467
Excerpt: ... Bsinc(2B) Proof As done in class, the proof involves showing that the process Y (t) = Nc (t) cos ct - Ns (t) sin ct is Gaussian, zero mean, and has the same ACF as NBP (t) EFFECT OF NOISE ON ANALOG COMMUNICATION SYSTEMS AWGN Channel input Hc () N(t) output PSfrag replacements The additive white Gaussian noise (AWGN) channel model accurately describes many point-to-point communication channels (e.g., the telephone line channel). The channel frequency response is represented by c V. Veeravalli, 1999 1 Hc (), and N(t) is WGN. For mobile communications channels, the channel filter is (randomly) time varying. For most cases of interest in this course, we assume that the filter is LTI and distortionless, i.e., Hc () that is roughly constant over the frequency range of the input. Signal-to-noise Ratio (SNR) A measure of fidelity of a communication system is the signal-to-noise ratio (SNR) that is defined by Useful signal power SNR = = Noise power We will use the symbol to denote SNR. SNR for Baseband Communic ...
Stanford, EE 379
Excerpt: ... ITU - Telecommunication Standardization Sector STUDY GROUP 15 Temporary Document RN-072 Original: English Redbank, New Jersey, 21 25 May 2001 Question: 4/15 SOURCE1: IBM, Globespan TITLE: G.gen: G.dmt.bis: G.lite.bis: Further results on the performance of LDPC coded modulation for AWGN channels. _ ABSTRACT We present further simulation results on the performance of LDPC coded modulation over an additive white Gaussian noise channel. Modulation types cover the range from 4-QAM up to 16384-QAM. The performance of LDPC codes of various lengths is illustrated in the spectral-efficiency versus powerefficiency plane. The results show that the proposed multilevel LDPC coding scheme exhibits uniform efficiency over all constellation sizes in terms of gap to capacity. 1 Contacts: E. Eleftheriou ele@zurich.ibm.com S. ler oel@zurich.ibm.com IBM Zurich Research Laboratory M. Sorbara M. Eyvazkhani Globespan msorbara@globespan.net meyvazkhani@globespan.net 1 ...
Ill. Chicago, EECS 422
Excerpt: ... 2 2 2 u(t) : normalized current of voltage The problem of fast fading is that when the actual signal level at receiver is comparable to the noise level and SNR (signal-to-noise ratio) is below the max tolerable level. In order to understand the SNR issue, we assume that our radio channel is an additive white Gaussian noise (AWGN) channel. If the noise signal is n(t) then the actual received signal at time t is y (t ) = Au(t ) + n(t ) A : is the overall path loss and is assumed invariant with time, particularly true when the mobile moves within a small distance. n(t) is a complex phasor and is written as n(t ) = x n (t ) + jy n (t ) Then the mean noise power is 1 E [n (t )n* (t )] 1 2 2 = E [xn (t )]+ E [yn (t )] Pn = 2 2 2 Note that if xn(t) and yn(t) both have a standard deviation n (usually the case) Pn = n2 The SNR then is 2 2 A2 A2 signal power E A u (t ) 2 = SNR = = = E [u (t )] = noise power 2 Pn 2 Pn 2 Pn [ ] with the signal power out of a modulator normalized to 1. We can now in ...
University of Illinois, Urbana Champaign, ECE 459
Excerpt: ... as Y = AX + b. Find A and b such that Y is zero mean with covariance matrix I. (Hint: Diagonalize .) 2. (15 pts total) Bounds on the Q function. Q(x) = x e-t /2 dt 2 2 (a) (8 pts) For x > 0 show that the following upper and lower bounds hold for the Q function: 1 1- 2 x e-x /2 e-x /2 Q(x) x 2 x 2 2 2 2 Hint: For the upper bound, write the integrand as a product of 1/t and te-t /2 , use integration by parts, and bound. For the lower bound, integrate by parts once more and bound. c V. V. Veeravalli, 2000 1 (b) (7 pts) As you know from your undergraduate communications course, the bit error probability for BPSK signaling in additive white Gaussian noise (AWGN) with PSD N0 /2 is given by: 2Eb Pe = Q N0 where Eb is the bit energy. Plot the error probabililty Pe (on a log scale) versus signal-to-noise ratio Eb /N0 (in dB) using Matlab or Mathematica. (You may need to use an appropriately modified version of the error function in these packages.) Consider Eb /N0 ranging from -5 dB to 15 dB. Also plot th ...