Suppose the FCC allocates 300 kHz channels for a high quality video conference s

Question

Suppose the FCC allocates 300 kHz channels for a high quality video conference
service. A service provider decides that this service requires 720 kbps (not including
overhead and error control) for each channel.

a. Specify a modulation format (other than OFDM) that can provide this service along
with the symbol rate and signal constellation. Allow for at least 25% excess
bandwidth.

b. Suppose that the target error rate required is 10^5. Estimate the Signal-to-Noise
Ratio (SNR) required at the receiver by using the following procedure: (i) Determine
the SNR needed for BPSK from the error rate curves in Week4.ppt. It turns out that the
probability of error for QPSK is the same as that for BPSK. (This is because the
distance between nearest QPSK constellation points is the same as the distance
between the BPSK points.) (ii) Doubling the number of points in a PSK constellation
with more than 2 points requires approximately 6 dB more transmit power to maintain
the same error rate. (That is, 8-PSK requires about 6 dB more than QPSK. This is
due to the decrease in distance between nearest neighbor points.) Doubling the number
of points in a QAM (rectangular) constellation requires approximately 3 dB more
transmit power. (That is, 16 QAM requires approximately 6 dB more than QPSK, 32
QAM requires approximately 3 dB more than 16 QAM, and so forth.)


c. For the SNR computed in part b., what is the maximum data rate that is achievable
according to Shannon? What is the minimum SNR required to achieve the 720 kbps
data rate? (The difference between this SNR and the SNR computed in part b
represents the amount of power that can be saved by using sophisticated coding
methods.)


d. Suppose that OFDM is used with 15 kHz subchannels. (Two subchannels are used
as guard channels on either side of the band.) Specify an OFDM symbol rate and
modulation format for each subchannel that can achieve the target rate.

Explanation / Answer

1. Suppose the FCC allocates 300 kHz channels for a high quality video conference service. A service provider decides that this service requires 720 kbps (not including overhead and error control) for each channel. a. Specify a modulation format (other than OFDM) that can provide this service along with the symbol rate and signal constellation. Allow for at least 25% excess bandwidth. b. Suppose that the target error rate required is 10 -5 . Estimate the Signal-to-Noise Ratio (SNR) required at the receiver b y using the following procedure: (i) Determine the SNR needed for BPSK from the error rate curves in Week4.ppt. It turns out that the probability of error for QPSK is the same as that for BPSK. (This is because the distance between nearest QPSK constellation points is the same as the distance between the BPSK points.) (ii) Doubling the number of points in a PSK constellation with more than 2 points requires approximately 6 dB more transmit power to maintain the same error rate. (That is, 8-PSK requires about 6 dB more than QPSK. This is due to the decrease in distance between nearest neighbor points.) Doubling the number of points in a QAM (rectangular) constellation requires approximately 3 dB more transmit power. (That is, 16 QAM requires approximately 6 dB more than QPSK, 32 QAM requires approximately 3 dB more than 16 QAM, and so forth.) c. For the SNR computed in part b., what is the maximum data rate that is achievable according to Shannon? What is the minimum SNR required to achieve the 720 kbps data rate? (The difference between this SNR and the SNR computed in part b represents the amount of power that can be saved b y using sophisticated coding methods.) d. Suppose that OFDM is used with 15 kHz subchannels. (Two subchannels are used as guard channels on either side of the band.) Specify an OFDM symbol rate and modulation format for each subchannel that can achieve the target rate.2. Suppose that you wish to offer a voice over I P wireless service. The target packet error rate (or drop rate) is 10 -3 and you determine that if the signal is con?ned to within a coherence band, about 20% of the packets are dropped due to fading. To solve this problem, you introduce frequency div ersity by spreading the signal over multiple coherence bands. a. If each coherence band is 100 kHz and experiences independent fading, about how much bandwidth does your system require? (Hint: calculate the probability that at least one of the coherence bands will not be faded according to the slides on selection diversity.) b. Now suppose that an error correction code is introduced into the original (narrowband) system that reduces the packet drop rate to 5%. How does this change the bandwidth your system requires? 3. Suppose two users in a Direct Sequence-CDMA system have signatures (that is, sequences of chips) given b y ( 1 -1 1 -1) and (1 1 -1 -1), respectively. (a) Evaluate the correlation between the two signatures. (b) Sketch the baseband signals for the two users when user 1 sends the bits 011, and user 2 sends the bits 101. Add the signals for the ?rst bit only, and show that the output of the correlator for user 1 is -4, corresponding to a 0, and the output of the correlator for user 2 is 4, corresponding to a 1. (c) Suppose now that user 2 is assigned the signature (1 -1 1 1). Adding the signals as in part (b), what is the output of the correlator for user 1 for the ?rst bit? Explain the effect of changing the signature in terms of the likelihood of making an error when additional noise and interference is present. 4. Explain the relationships between processing gain, bandwidth expansion, and ability to tolerate interference in a CDMA system. 5. In a single-cell CDMA system, suppose that the SNR, or Eb /N0 , required for each user is 10 dB. What processing gain is needed to accomodate 100 users, each with a data rate of 13 kbps? What is the corresponding chip rate

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