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- Question : 2.1 - Explain, in your own words, the distinction between average path loss, shadow fading, and multipath fading. How are they related to one another?
- Question : 2.2 - Using Table 2.1, plot PR,db ? PT,db for Orlando as a function of distance d, in meters, with 0 < d < 200 m. Assume transmitter and receiver antenna gains are both 1.
- Question : 2.3 - Determine the shadow-fading parameter ? for each of the four measured curves of Figs. 2.4 and 2.5, and compare. Hint: First calculate the average value of each curve and then the root-mean-squared value about these averages.
- Question : 2.4 - The average power received at mobiles 100 m from a base station is 1 mW. Lognormal, shadow, fading is experienced at that distance. (a)
- Question : 2.5 - (a) Fill in the details of the derivation of the two-ray average received power result given by (2.13a). (b) Superimpose a 1/d4 curve on the measured curves of Figs. 2.7 and 2.8, and compare with the measured curves. (c) Do the results of Fig. 2.8 validate (2.13a)? Explain.
- Question : 2.6 - (a) Verify, as indicated in the text, that, for the Rayleigh-distributed random variable ? in (2.15), ?r2 must equal 1/2. (b) Derive (2.17a) from (2.17) and show that x and y are zero-mean random variables, each with variance ?R2 as defined.
- Question : 2.7 - (a) Show, following the hints provided in the text, that the Ricean distribution (2.25) approaches a gaussian distribution centered about A for A (b) Verify that the instantaneous received power distribution in the case of a direct ray is given by (2.27). Show that, as the K factor gets smaller (the direct line-of-sight ray decreases relative to the scattered signal terms), the fading distribution of (2.27) approaches an exponential distribution.
- Question : 2.8 - As will be seen throughout the text, simulation is commonly used to determine the performance, as well as verify analysis, of cellular systems. Most critical here is the simulation of fading conditions. This problem provides an introduction to the simulation of Rayleigh fading.
- Question : 2.9 - Consider the average fade duration equation (2.39). Take the case of a vehicle moving at a speed of 100 km/hr. The system frequency of operation is 1 GHz. Say the ratio ? = 1. Show the average fade duration is 8 msec, as noted in the text. Now let the received signal amplitude be 0.3 of the rms value. Show the average fade duration is now 1 msec.
- Question : 2.10 - (a) Summarize, in your own words, the discussion in the text on time dispersion and frequency-selective fading. (b) Consider several cases: a delay spread of 0.5 sec, one of 1 sec, and a third one of 6 sec. Determine whether individual multipath rays are resolvable for the two transmission bandwidths, 1.25 MHz used in IS-95 and cdma2000, and
- Question : 2.11 - Indicate the condition for flat fading for each of the following data rates: 8 kbps, 40 kbps, 100 kbps, 6 Mbps. Indicate which, if any, radio environments would result in flat fading for each of these data rates.
- Question : 2.12 - (a) Consider the transversal filter equalizer of Fig. 2.20. A training sequence of K binary digits is used to determine the 2N + 1 tap gains, as described in the text. Show that, under a minimum mean-squared performance objective, the optimum choice of tap gains is given by (2.53). (b) Show the vector form of (2.53) is given by (2.56), with the solution given by(2.57).
- Question : 2.13 - (a) Work out a simple example of the transversal filter equalizer: Say the equalizer has three taps to be found using the minimum mean-squared performance objective. Choose a set of K = 10 arbitrarily chosen binary digits as the training sequence and then let some of these digits be received in
- Question : 2.14 - (a) Plot the improvement in performance obtained with the use of dual selection diversity as the ratio of local-mean power to the threshold varies. Use at least the following cases: (1) the local-mean power 20 times the threshold; (2) local-mean power 10 times the threshold; (3) local-mean power equal to the threshold; (4) local-mean power 0.1 of the threshold. Note: Performance may be defined as outage rate or the probability thatat least oneof the channels has an instantaneous power greater than the threshold.
- Question : 2.15 - Show the optimum maximal-ratio combining gain for the kth diversity branch is given by (2.64). Explain the statement that the SIR is then the sum of the SIRs, summed over the N diversity branches.
- Question : 2.16 - (a) Explain how equal-gain combining differs from maximal-ratio combining. In particular, write an expression for the SIR in the case of equal-gain combining. Hint: How would this expression compare with (2.61)? (b) Why would you expect the performance of diversity schemes to be ranked in the order maximal-ratio combining best, equal-gain next best, selection diversity last?
- Question : 2.17 - (a) Explain the operation of the RAKE receiver in your own words. (b) Two third-generation CDMA systems are discussed in Chapter 10. The first, W-CDMA, uses a chip rate of 3.84 Mcps (million chips per second), with a corresponding chip duration of 0.26 sec; the second system, cdma2000, uses a chip rate of 1.2288 Mcps, with a chip duration of 0.81 sec. (This is the same chip rate used by the second-generation CDMA system IS-95 discussed in Chapters 6 and 8.) Explain the statements made in Chapter 10 that RAKE receivers can be used to provide multipath time-diversity for paths differing in time by at least those two chip durations, respectively. Which system potentially provides better RAKE performance?

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