Assignment 11: Solutions to problems on Multiuser CDMA Networks

Transcription

1 G. S. Sanyal School of Telecommunications Indian Institute of Technology Kharagpur MOOC: Spread Spectrum Communications & Jamming Assignment 11: Solutions to problems on Multiuser CDMA Networks Due date: Max. marks: 20 Note: Please find the table of notations at the end of document. 1. A hand-held direct-sequence spread-spectrum (DS/SS radio is part of a cellular CDMA system. The system specifications are as follows: data and SS-code modulation is BPSK, data rate ( is 8000 bit/s, carrier frequency (f c is 1 GHz, chip rate ( ch is 25 Mchips/s, worst-case path loss (L p is db, gain of transmitting antenna (G t is 5 dbi, receiver figure-of-merit ( G r T is 18 db/k, occasional deep small-scale fading loss ( L o is 30 db, other losses (Lo are 4 db, required N o is 4 db. Assume link Margin, L M is unity. The required transmitted power (P t during deep small-scale feeding Hint: The link margin is given by, L M = and k is Boltzmann s constant. Since, L M = P ( tg t( Gr T kl No pl ol o reqd P ( tg t( Gr T kl No pl ol o reqd We now solve for P t in decibles: P t = L M + ( + + k + L N o p + L o + L reqd o (G t + Gr T where, = 10 log( db k = 10 log( db 1

2 P t = (5 18 P t = 0.03 dbw 0 dbw = 1 W (correct option iv. 2. eferring to question 1, the level can P t be powered down when there is no small-sacle fading When L o = 0 db, P t can be reduced to 30 dbw = 1 mw (correct option i. 3. eferring to question 1, the processing gain, G p Processing gain, G p = ch = = db = 35 db. (correct option ii. 4. eferring to question 1, the maximum number of users per cell is approximately: E Hint: Assume the system is interference limited. i.e, b (N o+. (N o+ = S/ I/W ss = Wss/ = Gp = GpS = GpS = Gp I/S I/S I S(M 1 M 1 M G p (db / (db = 35 db 4 db = 31 db = 1258 (correct option iii. 5. Consider a CDMA direct-sequence cellular telephone system, where each user requires an of 6 db for acceptable voice quality. The chip rate ( ch is 3.68 MChips/sec, and the data rate ( is 14.4 kbit/s. Assume that the factors Nonsynchronous interference factor (γ, Voice activity factor (G v, and Outer-cell interference factor (H o are 1.5, 2.5 and 1.5 respectively, and the transmission ceases during speech pauses. The number of users per cell can be supported are: Hint: By taking γ, G v, and H o into consideration, the number of users that can be supported are M = γgvgp M = ( γgvgp = H o ( H o G p Where G p = = / 8

3 M = users/cell 4 (correct option ii. 6. eferring to question 5, if a powerful error-correcting code is used to lower the required are: by 1 db, the number of users per cell can be supported If can be lowered by 1 db (or the factor 1.259, it directly affects the user population by an increase in the same amount. Thus now, M 201 users/cell. (correct option i. 7. A direct-sequence spread-spectrum system uses QPSK modulation for transmitting data. It is required that the bit-error probability (P b be 10 5 and that chip energy-to-interference power spectral, h / 30.4 db. The processing gain, G p Hint: Processing gain, G p = / (N o+ h / Note: is bit energy-to-interference and noise power spectral density ratio. Assume that b E (N o+. Note: For QPSK, with perfect synchronization and bit-error probability, P b = Q( 2 = 10 5 requires Processing gain, G p = Let h = 30.4 db. Then G p (db = ( ( Ech of 9.6 db. (db h (db = = 40 db. < 30.4 db, then processing gain would be greater than 40 db If h (correct option iv. 8. eferring to question 7, the minimum number of chips/bit required are: Processing gain, G P is (40 db in linear scale. So, for a directsequence spread spectrum system, there must be chips/bit to meet these specifications. 3 / 8

4 (correct option i. 9. A direct-sequence spread-spectrum system with a processing gain of 20 ( db uses QPSK modulation for transmitting data. A rate 1 k 2 n errorcorrecting code is used, and the required bit-error probability is Assuming perfect synchronization, find the minimum values of the following parameters that are needed to support these requirements. Chip energy-to-interference power spectral ( h Hint: Processing gain, G p = / (N o+ h / Note: is bit energy-to-interference and noise power spectral density ratio. Assume that b E (N o+. Note: For QPSK, with perfect synchronization and bit-error probability, P b = Q( 2 = 10 5 requires of 9.6 db. Since, G p = / h / h / (db = / (db G p (db = = 10.4 db (correct option ii. 10. eferring to question 9, channel bit energy-to-interference power spectral ( Hint: Ec c = h ch = k Hint: = n c Since, Ec c = then, Ec Ec = ( c = ( k n (db = (db + k n (correct option iii. (db = 9.6 db 3 db = 6.6 db 11. There is a rich set of signaling elements used in CDMA systems that are designed to IS-95 specifications: data bits, channel bits, Walsh waveforms, Walsh chips, spread-spectrum chips, and BPSK waveforms. Consider a reverse traffic channel that is carrying full-rate digitized speech ( at 9.6 kbits/s, with a received N o+ = 7 db (assuming that N o <<. The received power-to-interference power spectral ( P r 4 / 8

5 Hint: Pr = ( = ( Ec c = ( E w w = ( E wch = 7 db = = P r = ( = kbps = 48,000 Hz or 46.8 db-hz. (correct option iii. wch = ( h ch 12. eferring to question 11, the channel bit energy-to-interference power spectral ( Hint: For the reverse traffic channel, the code rate ( k n Hint: k n = c Since, Ec c = = ( c = ( k n = ( 1 5 = = ( 1 3 (correct option ii. = 2.2 db is eferring to questions 11 and 12, the channel bit rate ( c Since, k = n c c = n = 3 = = 28,800 channel bits/s k (correct option iv. 14. eferring to question 11, the Walsh waveform energy-to-interference power spectral ( E w Hint: Each 64-ary Walsh waveform corresponds to 6 channel bits. i.e, c w = 6 Since, Ew w = Ec E w = c w Ec c = 6 Ec (correct option i. = 6 ( 5 = 10 = 10 db eferring to questions 11 and 14, the Walsh waveform rate ( w w = ( 1 6 c = 1 28,800 = 4800 Walsh waveforms/s 6 (correct option iv. 5 / 8

6 16. eferring to question 11, the Walsh chip energy-to-interference power spectral ( E wch Hint: A Walsh waveform is composed of 64 Walsh chips. i.e, w wch = 1 64 Since, E wch E wch wch = Ew w = ( w wch Ew = ( 1 64 Ew = ( 1 64 (correct option i. 10 = = 8.1 db 17. eferring to questions 11 and 16, the Walsh chip rate ( wch wch = 64 w = = 307,200 Walsh-chips/s. (correct option ii. 18. eferring to question 11, the chip energy-to-interference power spectral ( h Hint: In IS-95, the spread-spectrum chip rate ( ch is Mchips/s. Since, Pr = ( h ch h = Pr ( 1 48,000 ch = ( = = 14.1 db (correct option iii. 19. eferring to questions 11 and 18, the number of spread spectrum (SS chips correspond to one Walsh chip ( ch wch SS-chips per walsh chip: ch wch = = ,200 (correct option ii. 20. Consider a DSSS downlink with bandwidth expansion, G p = 100. Assume the system is interference-limited and there is no multipath on any user s channel. How many users can the system support under BPSK modulation such that each user has a BE less than Hint: Assume the system is interference limited. i.e, (N o+. Hint: For BPSK, bit-error probability P b = Q( 2, and yields P b = = 6.79 db 6 / 8

7 = 6.79 db = = Gp M = 100 M 1 Solving for M (the number of users yields M = Since M must be an integer and we require P b 10 3, must be rounded down to 21 users, although typically a designer would build the system to support 22 users with a slight BE penalty. (correct option iii. 7 / 8

8 Parameter Carrier frequency Transmitter power Data (bit rate Chip rate Channel bit rate Walsh waveform rate Walsh chip rate One user s received power Spread-spectrum bandwidth Error correcting code rate Path loss Transmitting Antenna Gain eceiver figure of merit Small-scale fading loss Other losses Boltzmann s constant Link Margin The number of supported users per cell Processing Gain Bit-error probability Nonsynchronous interference factor Voice activity factor Outer-cell interference factor Interference power Interference power spectral density eceived power-to-interference power spectral density ratio Energy per bit-to-noise power spectral equired Energy per bit-to-noise power spectral Energy per bit-to-interference power spectral density ratio Energy per bit-to-noise and Interference power spectral Spread spectrum chip energy-to-interference power spectral Channel bit energy-to-interference power spectral Walsh waveform energy-to-interference power spectral Walsh chip energy-to-interference power spectral Table 1: Table of notations Notation f c P t ch c w wch S W ss k n L p G t G r T L o L o K L M M G p P b γ G v H o I P r ( N o N o reqd N o+ h E w E wch 8 / 8