# Exercise 2 Common Fundamentals: Multiple Access

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1 Exercise 2 Common Fundamentals: Multiple Access Problem 1: TDMA, guard time. To set up a GSM-connection, the base station (BTS) and the mobile station (MS) use the following short access burst in a TDMA-slot for synchronisation and initial information exchange. Tail Training Sequenz Information Tail guard-time 7 Bit 41 Bit 36 Bit 3 Bit 63 Bit Time-Slot 577 μs a) Determine the guard-time, if the bit-period is 3.7 μs. b) The transmission delay between BTS and MS is unknown at the time of sending the access-burst. Determine the maximum GSM cell radius such that the access burst do not interfere with the next time-slot. Problem 2: Cellular radio coverage. Assume that a certain mobile radio system needs a carrier-to-interference-ratio C/I of at least 9 db to guaranty an acceptable link quality. a) Determine the normalized co-channel reuse distance q = D/R in an environment with a propagation loss of 40 db per decade. b) Determine the custer-size N to build a homogeneous, cellular radio network. c) Please sketch the resulting homogeneous cellular radio network with the hexagonal cells. Problem 3: Erlang capacity. a) A GSM-operator gets 1/4 of the GSM900-spectrum for radio coverage in an area, where a cluster size of N=7 must be used. How many GSM-frequency carriers and how many traffic channels per cell for voice communication can be used on the average? b) How many GSM-subscribers per cell can be served if they accept a blocking probability of 2% and call 90s in a busy hour on the average? 1/6

3 Problem 7: OFDM (DAB). Digital Audio Broadcasting (DAB) is a broadcast standard for terrestrial digital radio. Transmission mode 1 uses OFDM with N=1536 DQPSK-modulated subchannels in a 1 khz grid. The guard interval is Δ = 246 μs. a) How long lasts an OFDM symbol without cyclic suffix and with cyclic suffix? b) How many bits carries a single OFDM symbol? c) How large can the maximum (multipath-) channel delay τ max be? And how large can the maximum path-distance-difference Δd max be? d) How large is the (I)FFT block length N in the sender and in the digital radio? Problem 8: OFDM (DVB-T). DVB-T is an OFDM-based standard for terrestrial Digital-TV. A DVB-T-channel is typically 8 MHz wide and used for the transmission one or more video streams. There are 2 operation modes, namely a 2K-mode with 2048-point (I)FFT and a 8K-mode with a 8192-point (I)FFT. In the 2K-mode there are N 2K =1512 subchannels and in the 8K-mode N 8K =6048 subchannels. For modulation, QPSK, 16QAM or 64QAM can be used. a) Please complete the missing parameter in the white fields of the following table: DVB-T width 8 MHz bandwidth 2K mode 8K mode Number of subchannels Subchannel spacing Symbol period without prefix b) Which mode is better suited for setting up simulcast networks with large distances between the senders (that all use the same Tx-frequency)? c) Which mode is more robust against Doppler effects at mobile reception? d) Determine for both modes the maximum netto data rate R max under the following Txconditions: - Guard Intervall = 1/4 of the symbol period - FEC coding rate = 3/4-64QAM on all subchannels (pilot channels are neglected) 3/6

4 Solution Problem 1 a) guard-time = = 233 μs. b) 2 times the BTS-MS-distance = guard-time times speed of light c = 70 km => maximum GSM-cell-radius = 35 km Problem 2 a) propagation loss = 40 db per decade => γ=4. normalized co-channel reuse distance q = D/R = ( ) 0.25 = b) Cluster-size q 2 /3 = 2.31 The smallest number N of the form N = I 2 +IJ+J 2 = 3, where I=J=1. c) A co-channel cell is in the origin, another co-channel cell at distance D has the coordinates (I=1,J=1). The co-channel reuse distance D = 3 3 R = 3R. j-axis D i-axis Problem 3: Erlang capacity. a) in total 124/4 = 31 frequency carriers => 31/7 4 frequency carriers per cell => 32 time slots per cell (about K = 30 traffic channels and 2 slots for control data) b) Erlang B table with K = 30 and P b =0.02 => traffic V = Erlang traffic per user in busy hour : 90s / 3600s = E = 25 me The operator can serve / = 880 subscribers per cell in a busy hour 4/6

5 Problem 4 The data bit d k sent by user k can be determined by correlating r with s k and taking the sign of the result, i.e. d 1 = sign(r T s 1 ) = sign(4) = 1 d 2 = sign(r T s 2 ) = sign(4) = 1 d 3 = sign(r T s 3 ) = sign(4) = 1 d 4 = sign(r T s 4 ) = sign(-4) = -1 Problem 5 a) user 1 data rate R 1 = 1/(2T c ) user 2 data rate R 2 = 1/(4T c ) => R 1 = 2R 2 b) E b = P 1 /R 1 = P 2 /R 2 => P 1 = 2 P 2 c) Downlink 1 with the higher data rate R 1 produces more interference because the Tx-power is P 1 higher than P 2. Problem 6 a) in the maximum there are 3/e 1 successful access request per second b) the maximum successful access requests result when there is 1 access request per slot on the average, i.e. 3 access requests per second. Problem 7 Digital Audio Broadcasting (DAB) is a broadcast standard for terrestrial digital radio. Transmission mode 1 uses OFDM with N=1536 DQPSK-modulated subchannels in a 1 khz grid. The guard interval is Δ = 246 μs. a) OFDM symbol without cyclic suffix: 1 ms OFDM symbol with cyclic suffix: ms b) a single OFDM symbol carries 3072 bits c) τ max 246 µs => Δd max = 246 µs c = m = 73.8 km d) (I)FFT block length N = 2048 > N 5/6

6 Problem 8 a) DVB-T width 8 MHz bandwidth 2K mode 8K mode Number of subchannels Subchannel spacing 8 MHz / 2K 4 khz 8 MHz / 8K 1 khz Symbol period without prefix 1 / 4 khz = 250 µs 1 / 1 khz = 1 ms b) large radio propagation differences when receiving from 2 senders transmitting at the same frequency that are a long way away from each other => 8K mode is better suited because the symbol period is larger c) 2K-mode is more robust against Doppler effects because subchannel spacing is larger d) R 2K mode = (3/4) Bits / (5/4 250 µs) = Mbps => R 8K mode = R 2K mode 6/6

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