## ECE 5325/6325 Spring 2013 Schedule

Lecture notes are linked to the topics for the lecture, in the "Topics" column. They are posted as the semester progresses. Previous years' lecture notes are also available on the main 5325/6325 site. The book (Mol) is Andreas F. Molisch, Wireless Communications, Wiley, 2nd edition, 2010.
Homework questions with a "1" number are questions turned in with homework 1, those with a "2" number are turned in with homework 2, etc.

 No. Date Topics (link to lecture notes) Reading HW 6325-only HW Due 1 1/8/2013 Course Outline, Power, Path Loss Mol 1, 2 1a: If P is a power in mW, and P[dBm] is P in dBm, calculate the following in dBm: (i) 2*P, (ii) P/2, (iii) 20*P, (iv) 1.25*P, (v) P/50, (v) P/40? Use the "easy" rules described in class, and then check your answers with the formula ($10\log_{10}$). 1b: Assume you know the average received power $P_0$[dBm] in dBm at a reference distance of $d_0$ meters from a WiFi access point (AP). You measure received power in many different positions, all $r$ meters from the AP, and find that the average received power is $P_r$[dBm]. Write a formula to determine $n$, the path loss exponent. 1c: Assume you know a threshold power $P_{min}$ below which a mobile receiver will not be able to receive a base station's signal, and you are given $P_0$, $d_0$, and $n$. Determine two formulas for the range, i.e., the distance at which the power is equal to the threshold, one when the powers are given in linear units, and one when the powers are given in dBm. 1d: Given: You are given the path loss $P_0$[dBm] in dBm at a reference distance $d_0$. You measure received power $P_i$[dBm] in dBm at distance $d_i$, for $i=1, \ldots, K$. Goal: You want to estimate the path loss exponent $n$ for the path loss exponent model discussed at the end of Lecture 1. Come up with a formula for the $n$ that minimizes the mean squared error (MSE). Note $MSE = \frac{1}{K}\sum_{i=1}^K e^2$, where $e$ is the error, that is, the difference between $P_i$ and what the model would predict for distance $d_i$. 2 1/10/2013 Cellular frequency reuse, interference Mol 17.6 Homework 2 problems: 2a: Develop an expression for the SIR in terms of the distance $d$ from the serving BS to mobile and the distances $d_i$ for i=1...K for K co-channel base stations, and the path loss exponent $n$. Next, assume that $d=1$ km and the interfering base stations: five are at a distance of 7 km, three are at a distance of 9 km, and eight are at a distance of 13 km. Assume n=3.7. Finally, what is the error if you had ignored the base stations with $d_i=13$ km? What if you had only included those with $d_i=7$ km? 2b: (The default settings at this site make nice hex graph paper) For N=12, N=7, N=4: Sketch a frequency re-use pattern, showing which hexagons have frequency allocations (1-12, 1-7, or 1-4). Verify that there are always six co-channel cells in the first tier (count them). 2c: Relationship between S/I ratio, n and N for a hexagonal cellular system: (i) For an N=9 system, determine the S/I ratio in dB for path loss exponent n=3.5 and 4.0. (ii) If S/I of 16 dB is required, and n=3.6, what is the lowest N possible? 2d: Now assume cells are square, with an N=9 cluster size, as seen in this figure. Consider a forward link from a serving BS to a mobile in the corner of the cell. Derive a formula for the S/I ratio as a function of n, the path loss exponent, including only the first-tier co-channel base stations. Calculate the value for n=3.5 and 4.0, and compare to the answer for 2c. 3 1/15/2013 Trunking / GOS, Capacity Mol 17.2.2 Homework 2 problems, continued: 2e: Compare the total number of users you can have in an Erlang-B system with probability of blocking of 1% (leave the result as a function of $A_u$) for two conditions: (a) Two cells with Number of channels per cell = 10, vs. (b) One cell with Number of channels in that cell = 20. Which system is able to handle more users, assuming a fixed $A_u$? 2g: Molisch Exercise 17.1 (on page 775-6) 2h: Molisch Exercise 17.2 (on page 776) 2i: For an Erlang-C system, derive Equation (17.3) in Molisch (page 369). You may use the fact discussed in lecture that, given that delay>0, that the wait time is exponentially distributed. HW 1 due 4 1/17/2013 Sectoring Rappaport 3.7.2, log in to Canvas and see the announcement (3a) Make a list of possible reuse factors N by trying all (i,k) combinations (where i and k are non-negative integers). For each 3<= N <= 13, show using hex paper the value of i_0 when using 120 degree sectoring. Verify my claim that if i=k, then i_0=3, otherwise, i_0 =2. (3b) Continue the example in class to find the number of users per cell that could be supported when using (i) omnidirectional antennas, (ii) 120 degree sectors, and (iii) 60 degree sectors. Assume there are U=100 unique channels in the system, that S/I = 15 dB is required, and n=4.0. Assume a $Pr_{block}$ = 0.01 and a blocked calls cleared system, and per user offered traffic of 0.05. (3c) Find the lowest N feasible for hexagonal cells with S/I of 20 dB and n=4.0 for (i) omnidirectional antennas, (ii) 120 degree sectors, and (iii) 60 degree sectors. (3d) Forget about hexagonal cells, and study sectoring when using square cells with N=9 and n=3.5, as you investigated in homework problem 2d. What is the improvement in S/I (dB) when replacing omnidirectional antennas with (i) 180 degree sector antennas, and (ii) 90 degree sector antennas? 5 1/22/2013 Link Budgeting #1 Haykin/Moher handout (2.9-2.10) (go to Canvas if link doesn't work), Mol 3.2 (3e) A satellite in low-earth orbit can transmit 13 W at f_c = 2300 MHz, with an antenna gain of 3 dBi. An earth station, 690 km below, has a parabolic dish antenna with gain of 34 dBi. What is the received power, assuming free space path loss? (3f) For the sensor network example from the lecture 5 notes, what would the range be if the fade margin was zero? In that case, how would the range increase if we used a better RFIC that had a sensitivity of -99 dBm (reduced by 1 dB)? (3g) GSM downlink max range: Assume GSM requires S/N = 11 dB, has a maximum mobile transmit power of 1.0 W (30 dBm), 0 dBd antenna gain at the mobile, and 12 dBd gain at the BS. Assume path loss is given by: L (dB) = 125.8 + 10(3.522) log10 (d/1 km). Assume the mobile receiver has F=8 (linear). What base station transmit power is required for a range of 6 km? What is the EIRP? (3h) Max range for 60 GHz WiFi: Find the maximum range for a 60 GHz data link, which has exponential decay due to oxygen absorption with rate $\alpha$ = 15 dB / km. Assume n=2 (free space) path losses in addition to the oxygen absorption loss, transmit and receive antenna gains of 5 dB, 16 dBm transmit power, 5 dB noise figure, 1GHz bandwidth, and required S/N of 10 dB [Smulder 2003]. HW 2 due 6 1/24/2013 Link Budgeting #2 Same as Lecture 5 None. None. 7 1/29/2013 Review HW 3 due 1/31/2013 Exam 1 (Lectures 1-6) none 8 2/5/2013 Reflection, Diffraction, Scattering Mol 4.2, Mol 4.3, MUSE video Watch from 9:00-16:50. (4a) From the fact that $E_t = (1 + \Gamma) E_e$ for TE waves, and the reflection coefficients ($\rho$ in Molisch, $\Gamma$ in my notes), derive the transmission coefficient $T_{TE}$ in Molisch (4.16). Can the magnitude of the transmission coefficient be greater than 1? Find the transmission coefficient into ground, and the angle of the transmitted wave, when the incident angle is 45 degree and the frequency is 100 MHz. Assume that $\epsilon_r=15$ for ground. (4b) How do you calculate the loss in a reflected wave when the reflecting surface is rough? (4c) As shown in this figure, a WLAN signal arrives at a ground floor access point from a laptop (Pt=100 mW) on the 3rd floor, via scattering from a tree outside of the building. Neglecting wall/window losses, and assuming $\sigma_{RCS}$ is 4 m2 and antenna gains of 3 dBi, what is the received power from the scatter path? (4d) Prove from the basic reflection coefficient expressions given in class, that as $\Theta_e\rightarrow 90$ degrees (not 0 degrees as originally posted), $\Gamma_\parallel \rightarrow -1$ and $\Gamma_\perp\rightarrow -1$. 9 2/7/2013 Multipath fading Mol 5.2, 5.3. Watch MUSE Video (5a) Represent the bandpass signal $E_b$ = 4 cos(2 $\pi 1.4 \times 10^9$ Hz $t + \pi/6$) in complex baseband notation, where the carrier frequency is $1.4\times 10^9$ Hz. For the same carrier, convert the complex baseband signal E = $1.5\times 10^{-3}(1 + j)$ to a bandpass signal. (5b) Consider two multipath, $V_0=1$ and $V_1=0.5$, with phases $\theta_0=0$ and $\theta_1=\pi/2$ radians (at $f_c=914MHz$), and delays $\tau_0=10$ ns and $\tau_1=100$ ns. Assume amplitudes and delays are constant across $f_c$. (i) Compue the RMS delay spread. (ii) If BPSK modulation is used, what is the maximum bit rate that can be sent through the channel without needing an equalizer? (iii) Sketch or plot the frequency response for $f_c$ in the range 900-928 MHz. (5c) For a three-path channel with $V_0=1$, $V_1=0.5$, $V_2 = 0.5$, and $\theta_0=0$, $\theta_1=2\pi f_c \tau_1$ and $\theta_2=2\pi f_c \tau_2$, what are the conditions on $\tau_1$ and $\tau_2$ which put the channel in a deep fade, that is, with $V_{TOT}=0$? (5d) Prove that the expected value of the power, that is, E[ $|V_{TOT}|^2$ ], is equal to the sum of the power of the individual paths, that is, $\sum_{i=0}^{M-1} |V_i|^2$. To do this, assume that the phases $\{\phi_i\}$ are independent and identically distributed uniform $[0,2\pi)$ random variables. 10 2/12/2013 Fade Distribution Mol 5.4, 5.5, 5.6 (5e) Find the fade margin required when in a Ricean fading channel for 7% and 0.1% probability of failure (received power being more than that margin down from the median power), when the K factor is 12 dB, 6 dB, or -infinity dB (the Rayleigh case). (5g) Consider the case of log-normal fading (power is Gaussian when expressed in dB) with fading variance $\sigma = 8$ dB. What is the fading margin required for 1% and 0.1% probability of failure? How is this margin related to $\sigma$? (5h) Plot (in Matlab or equivalent) a Fade Margin plot like Figure 1 in the lecture notes, for Nakagami fading, for a few different parameters of the distribution. Note that in Nakagami fading, power is Gamma distributed. Make the y-axis on a log scale from 0.1 to 100 percent, and make the x-axis "dB about median". HW 4 due 11 2/14/2013 Doppler, Diversity Mol 13.1, 13.2, 13.4 (5i) Determine the fading margin required using the following combining methods, assuming Rayleigh fading and M=1,2, 3, or 4 independent channels, for a 99.9% probability of having acceptable SNR: (i) selection, (ii) maximal ratio. (5j) A car with a mobile communicating at 1.8 GHz is traveling at 25 mph on Main Street. A mobile in the car is in a Rayleigh fading channel. Determine the average duration of fades 10 dB below the rms amplitude. How often does the signal amplitude cross this same threshold? 12 2/19/2013 Intro to Digital Modulation Mol 11, up to 11.3.6, and MUSE video (6a) Come up with an example of two orthogonal signals. Prove that they are orthogonal. Repeat this exercise and find another, different, set of two orthogonal signals, and prove that they are orthogonal. (6b) Do the "Frequency Shift Keying" example from the lecture notes. (6c) How does orthogonality relate to the concept that two signals can be separated at a receiver if they occupy different parts of the frequency band? Make an argument that if two signals $x(t)$ and $y(t)$ occupy non-overlapping parts of the frequency band, that is, $X(f)$ and $Y(f)$ are non-overlapping, then $x(t)$ and $y(t)$ must be orthogonal. 13 2/21/2013 PAM, QAM, and PSK Modulation Types Mol 12.1 (6d) Write the four different symbols $s_1(t)$ through $s_4(t)$ for QPSK. Do this for both of the constellation diagrams shown in Figure 1(a) of the Lecture 12 notes. Assume that the constellation points lie on the unit circle. (6e) Draw a block diagram for a receiver for QAM modulation. That is, apply what is discussed in Section 1.4 of lecture 12 to the particular waveforms used in QAM. none HW 5 due 2/26/2013 Exam 2 (Lectures 8-11) none 14 2/28/2013 FSK, Modulation Performance Mol 11.3, Mol 12.1 (7a) For the following modulations: BPSK, DPSK, QPSK, 16-QAM, 64-QAM, 2-non-co-FSK, 2-co-FSK, make a table, for each modulation, listing the orthogonal waveforms used; P[bit error] formula; and bandwidth. Next, (e.g., using Matlab) plot P[bit error] as a function of Eb/N0 (dB) on the x axis, and P[bit error] on a log-scale on the y-axis (like we did for Figure 1 on page 4 of the lecture 14 notes). You may like my Matlab functions Q.m and Qinv.m. (none) 15 3/5/2013 Link Budget Example, Implementation Costs no new reading (7b) Calculate the (i) bit rate and (ii) range when using the following modulation schemes for a new indoor 2.4 GHz WLAN system you are designing: BPSK, QPSK, 16-QAM, and 64-QAM. Assume that we have 1.0 MHz RF bandwidth available. Assume that we need a P[bit error] of $10^{-4}$. The transmit power can be up to 100 mW, and we will achieve gains of 3 dBi at both TX and RX. We need a fade margin of 20 dB, and the receiver has F=6 dB. Each modulation uses a SRRC pulse shape with alpha = 0.25. The path loss has path loss exponent 3.0 after a reference distance of 1 meter. (7c) What modulations are considered constant envelope? When is it important to use a constant envelope modulation? (none) HW 6 due 3/6 at noon 16 3/7/2013 Multicarrier and OFDM Mol 19.1, 19.2, 19.3, 19.4 (8a) Consider a multicarrier system with total bandwidth B and N subchannels. For each subchannel: (i) how much bandwidth is used, (ii) what data rate is carried, and (iii) what is the center frequency? How should N be chosen as a function of the typical delay spread $\sigma_\tau$ to ensure flat fading on each subchannel? (8b) For OFDM, how should the cyclic prefix length $\mu$ be chosen as a function of the the typical delay spread $\sigma_\tau$? (8c) Calculate the data rate of an 802.11a system assuming QPSK and rate 3/4 coding. (8d) What is the peak to average ratio (PAR) and what is it for OFDM signals? (8e) Simulation: Create, in Matlab or Python, an OFDM transmitted (complex baseband) signal with B=5 MHz, N=8, where each channel is BPSK. Create 10 OFDM symbols, modulating with random zeros and ones. Plot the real and imaginary parts of the signal (in two separate figures). Spring Break 17 3/19/2013 Spread Spectrum Mol 18.1, 18.2 (8f) For the 5-stage linear feedback shift register in today's lecture notes, write a Matlab (or Python) program to compute the PN code output over time (say, 70 bits of output). Plot the output. What is the maximum duration of a streak of ones (the maximum number in a row)? What is the maximum duration of a streak of zeros? (8g) Define the processing gain for a DS-SS signal. HW 7 due 18 3/21/2013 Coding (Lecture notes with solutions) MUSE Channel Coding Video, Mol 14.2 (9a) For the (7,4) block code in the lecture, determine the transmitted data bits if: (i) r = [1 1 1 1 0 0 0]; (ii) r = [0 0 0 1 1 1 0]; (iii) [0 0 1 1 1 1 1]. (9b) For the (6,3) block code in the lecture, determine the coded data bit vector that should be transmitted if the three data bits are: (i) [1 1 1]; (ii) [0 0 1]; (iii) [1 1 0]. (9c) What is the CRC polynomial c(x) for $\mathbf{c}$ = [1, 0, 0, 1, 0, 1]? What CRC would be computed for $\mathbf{d}$ = [1, 1, 1, 1, 1, 1]? 19 3/26/2013 Channel Capacity Mol 14.1 (9d) The Shannon-Hartley bound can be written in terms of path loss parameters by substituting in a received power model for S, the received power; and in terms of the noise figure by substituting in the formula for noise power N. Assume that the S/N is high enough such that $\log (1 + S/N)$ is approximately $\log S/N$ for high S/N, and use the Friis model for received power. Consider the achievable bit rate for a 1 Hz bandwidth. What happens to the achievable bit rate when: (i) the transmit power doubles, (ii) the antenna gain doubles, (iii) the path length doubles, and (iv) the noise figure doubles? none HW 8 due 20 3/28/2013 MIMO, Alamouti Scheme Haykin and Moher Section 6.3-6.7 (On Canvas: Files: Readings) none none 21 4/2/2013 Presentation Format, Packet Radio N. Abramson paper; G. Bianchi paper (Sections I and II only). none none HW 9 due 4/4/2013 Exam 3 (Lectures 12-19) none 22 4/9/2013 Exam 3 Return, 802.11 DCF none 23 4/11/2013 Project Meeting Time tba 24 4/16/2013 Project Meeting Time none 25 4/18/2013, 5-8pm Project Presentation Day none 26 4/23/2013 Final Exam Review none Friday, 4/26/2013, 8–10am Final Exam none