Frequency Division Multiplexing and OFDM 1. Given a Baseband

Frequency Division Multiplexing and OFDM

1. Given a baseband bandwidth of 180 kHz for signals x1(t), x2(t), x3(t)…. xM(t), i.e., Bi=180 kHz for each signal xi i=1…M. These signals are modulated using DSB-SC modulation. The modulated DSB-SC signals are combined using FDM with assigned RF spectrum of 60 MHz. a. Assuming no guard band find M. b. Assuming a 10 KHz guard band find M. c. Compare the required RF bandwidths found in part a) with the TDM/PAM case. Here TDM is used to create a composite baseband signal and then modulating the baseband signal using DSB-SC. Assume Nyquist sampling and 1 sample/timeslot.

2. What are guard bands and why are they needed?

3. All the colors can be formed from the combination of the Red, Green and Blue. To transmit a color video signal, it takes three colors signals, i.e., r(t), g(t) and b(t). Assume the baseband bandwidth of r(t), g(t) and b(t) is 4 Mhz. A composite baseband signal xbb(t) is generated using the system shown with fSC=11 Mhz.

a. What is the baseband bandwidth? b. The composite baseband signal xbb(t) is transmitted using DSB-SC, what is the required RF band- 2 7-Frequency Division Multiplexing and OFDM-2021.nb

width?

c. A coherent (synchronous) detector is required to recover composite baseband signal xbb(t) from the received DSB-SC RF signal. TRUE or FALSE. d. A coherent (synchronous) detector is required to recover r(t) from the composite baseband signal

xbb(t) signal. TRUE or FALSE. e. A coherent (synchronous) detector is required to recover b(t) from the composite baseband signal

xbb(t). TRUE or FALSE. f. What is the width in Hz of the guard bands used in this system? g. Draw a block diagram of the receiver.

4. How many subcarriers are used for a system with a symbol time of 1/15000 and an IFFT length 128?

5. A system uses OFDM with a 20 MHz channel bandwidth in the downlink, the OFDM symbol time is T=1/15000 sec with a subcarrier separation of 15kHz. There are 1200 occupied subcarriers. Assume this system uses 7 OFDM symbols per time slot and 20 time slots per frame. a. Why is the OFDM symbol time = 1/subcarrier spacing? b. If all subcarriers (1-1200) use 64 -QAM in all 20 time slots (1-20) what is the total transmission bit rate for this system. User A is assigned subcarriers 1 - 1200 using (64-QAM) for 10 time slots, i.e., time slots 1-10. User B is assigned subcarriers 1 - 600 using 16-QAM for 10 time slots, i.e., time slots 11-20. User C is assigned subcarriers 601 - 1200 using QPSK (4-QAM) for the 10 time slots, i.e., time slots 11-20. c. What is user A’s bit rate b/s? d. What is user B’s bit rate b/s? e. What is user C’s bit rate b/s? 7-Frequency Division Multiplexing and OFDM-2021.nb 3

6. In LTE the OFDM symbol time, T=1/15000 sec = 1/Δf; Δf=15kHz. Here each subcarrier transmits 16- QAM.

Map bits 1100 ⟶s 1(t) = cos(2π(f c+Δf)t) + sin(2π(f c+Δf)t) 0

Map bits 1101 ⟶s 2(t) = -3 cos(2π(f c+3Δf)t) + sin(2π(f c+3Δf)t) 0

The signal s(t)=s1(t)+s2(t) 0

Assume the carrier frequency, fc = 900 Mhz. a. What is the bit rate of s(t) in b/s. b. Show that s1(t) and s2(t) are orthogonal over 0

7. When an LTE operator uses a 10 MHz channel bandwidth in the downlink there are 600 occupied subcarriers. In LTE the OFDM symbol time, T=1/15000 sec with a subcarrier separation of 15kHz. a. If all 600 subcarriers use QPSK what is the total bit rate of in b/s. b. If all 600 subcarriers use 16-QAM what is the total bit rate of in b/s. c. If 300 subcarriers use QPSK and 300 subcarriers use 16-QAM what is the total bit rate of in b/s.

8. Given a baseband bandwidth of 90kHz for signals x1(t), …. xN(t), i.e., Bi=90kHz for each signal xi i=1…N. These signals are modulated using DSB-SC modulation. The modulated DSB-SC signals are frequency division multiplexed using a shared assigned RF spectrum of 30 MHz. a. Assuming no guard band find N. 4 7-Frequency Division Multiplexing and OFDM-2021.nb

b. Assuming a 20 KHz guard band find N.

9. To deploy their LTE system a telecommunications company has leased 13.515 MHz of occupied bandwidth which supports 901 downlink subcarriers. Assume that every subcarrier uses 16-QAM. What is the downlink bit rate?

10. Your company has purchased access to 1 MHz of RF spectrum. How many users can be supported using the following multiplexing techniques? Each user has a baseband bandwidth of 25kHz. Clearly state any assumptions. a) FDM/DSB-SC b) Baseband TDM/PAM then DSB-SC c) TDM/PCM with 8 bits/sample.

11. Four baseband signals, m1(t), …. m4(t), are combined at baseband using DSB-SC to create a compos-

ite baseband signal. The bandwidth of each baseband signal mi(t) is 10kHz for i=1…4; a 5 kHz guard is used. a. Sketch the spectrum of the composite baseband signal; label all frequencies. b. What is the bandwidth of the composite baseband signal?

c. The composite baseband signal is DSB-SC modulated onto a 100 MHz carrier to create yDSB-SC(t).

Sketch the block diagram the receiver that recovers the information signals from yDSB-SC(t). 7-Frequency Division Multiplexing and OFDM-2021.nb 5

12. In LTE the OFDM symbol time, T=1/15000 sec and Δf=15kHz. An LTE operator uses a 10 MHz channel bandwidth in the downlink and there are 601 occupied subcarriers. The downlink is from the base station (eNodeB) transmitting to the smartphone (UE). a. Find s(t) where Re((1+ⅈ) exp(-j2π (Δf+f c)t)) for fc=900MHz. b. If all 601 subcarriers use 16-QAM what is the total bit rate of in b/s in the downlink. c. The frame time in LTE is 10ms, the base station uses 14 16-QAM OFDM symbols/frame to transmit to a specific smartphone (UE). What is the bit rate of in b/s in the downlink for this specific user? d. An OFDM system could use an OFDM symbol time, T=1/15000 sec and a Δf=13kHz. TRUE or FALSE. Circle the correct answer. e. The base station can transmit 16-QAM on 301 subcarriers and QPSK on the remaining 300 subcarriers. TRUE or FALSE.

13. Explain the role of the IDFT and DFT in the generation and demodulation of OFDM signals.

14. What is FDMA?

15. What is FDD?

16. Explain how TDMA and FDMA are combined using OFDM and the Time/Frequency resource grid.

17. For a system with a symbol time of 1/15000 and an IFFT length 128 what is the RF bandwidth?

18. You have access to 10 MHz of RF spectrum. How many users can be supported using the following multiplexing techniques? Each user has a baseband bandwidth of 100 kHz. Clearly state any assumptions. a. FDM/DSB-SC. b. TDM/PCM with 8 bits/sample. c. Why is frame synchronization needed in TDM/PCM and what does it cost the system to provide frame synchronization? 6 7-Frequency Division Multiplexing and OFDM-2021.nb