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# OFDM system characteristics. Effect of wireless channel Intersymbol interference in single carrier systems due to multipath propagation with channel delay.

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OFDM system characteristics

Effect of wireless channel Intersymbol interference in single carrier systems due to multipath propagation with channel delay spread τ > symbol time T s ( symbols overlap!!!)

Transmission with OFDM OFDM is a “block transmission system,” i.e., a group of symbols are grouped and sent after application of forward error correction codes. In the frequency domain, these are represented by Nsubcarriers, which are orthogonal. There is thus no interference within the symbols sent in a block.

4 Αναλογική Υλοποίηση OFDM Ν Σύμβολα Χ 0,Χ 1,...,Χ Ν-1 Διάρκεια πακέτου Τ: Διάρκεια αρχικών συμβόλων OFDM Σύμβολο

OFDM uses Orthogonal Subcarriers Subcarriers of time duration Ts=T OFDM =NT with T=1/BW, frequencies that differ by Δf = 1/T OFDM and N=BW/Δf

6 OFDM using N orthogonal subcarriers Διαμόρφωση (OFDM): Όλοι οι “υπο-δίαυλοι”, ταυτόχρονα, χρησιμοποιούνται από τον ίδιο χρήστη.

Orthogonal subcarriers The peak of one subcarrier falls in the nulls of all other subcarriers

OFDM example With a bandwidth of 5 MHz using QPSK modulation (2 bits per symbol) gives a symbol rate of 5 Msymbols/sec or a time per symbol of T = 1/(5M sym/sec) = 0.2 μseconds. With a bandwidth of 5 MHz, if we have an OFDM system with 1000 carriers, the OFDM symbol time is T OFDM = 1/Δf = 1/(5MHz/1000) = 200 μseconds. At the speed of light, an object in an urban environment (typically 1 Km away) generates a delay of 6.6μsec. This reflected signal would be completely out of sync with the direct signal. The delay of 6.6 μseconds is thus less than 1/30th of the OFDM symbol duration of 200 μseconds.

Number of subcarriers given BW The amount of data which is carried by each subcarrier will depend on the considerations of intersymbol interference due to multipath delay spread. For example, if the delay spread due to multipath signals is τ =10 μseconds, then the symbol time needs to be much larger than the delay spread. If we take a factor of 10 to be a reasonable factor to overcome intersymbol interference, then the OFDM symbol time will be T OFDM =10*τ=100 μseconds. This permits the subcarriers to be spaced Δf = 1/(100 μsec) =1/100 MHz apart or 10 KHz apart. A 5-MHz channel can thus accommodate 512 subcarriers.

CALCULATING THE NUMBER OF SUBCARRIERS BASED ON DELAY SPREAD The number of subcarriers can be calculated for a given bandwidth based on the delay spread of the channel. As an example, if the delay spread is 20 μseconds, in order that the subcarriers have flat fading, the OFDM symbol duration should be at least 10 times the delay spread or T OFDM =200 μseconds. The OFDM symbol duration is then 200 μseconds (including the guard band) and the bandwidth of each subcarrier is 1/200μsec = 5 KHz. If the channel bandwidth is 1 MHz, 200 subcarriers can be used for OFDM operation.

Εφαρμογή σχεδίασης συστήματος OFDM 11 Θέλουμε να σχεδιάσουμε ένα OFDM σύστημα με f c =2.5GHz, BW < 20MHz που να μεταφέρει δεδομένα με ρυθμό R b = 10.24Mbps και με ρυθμό κωδικοποίησης (FEC) ρ = 1/2. H μέγιστη ταχύτητα του δέκτη είναι v max = 216km/h και ο δίαυλος έχει τ max = 8μsec. Θέλουμε επίσης για τη χρήσιμη διάρκεια του OFDM συμβόλου να ισχύει 5τ max ≤ T sym ≤ 0.03T coh όπου Coherence time Τ coh του καναλιού είναι η χρονική διάρκεια στην οποία το κανάλι παραμένει σταθερό.

Εφαρμογή 12

Εφαρμογή 13 Χωρίς OFDM, 82 διαδοχικά σύμβολα QPSK επηρεάζονται από ISI

Fixed WiMAX standard IEEE 802.16d-2004

Fixed WiMAX In Fixed WiMAX the number of subcarriers is 256. The subcarrier spacing is given by: Subcarrier spacing, Δf =(BW/256)* OS where OS oversampling rate (e.g., 8⁄7 for guard band of 1⁄8). As an example, for a bandwidth of 3.5 MHz the subcarrier spacing is 15.625 KHz, while for a bandwidth of 7 MHz the subcarrier spacing is 31.25 KHz. Increasing the subcarrier spacing has the impact of reducing the symbol time as T OFDM =1/Δf. In the above example, at 3.5 MHz, the OFDM symbol time is 64 μseconds, while for 7 MHz it is 32 μseconds (total symbol durations are 72 and 36 μ seconds, respectively, after accounting for guard bands).

OFDM symbols in time domain with guard interval

Data Rates for Fixed WiMAX The basic resource unit in WiMAX is the OFDM symbol duration, which is defined by the subcarrier spacing. In fixed WiMAX, the useful symbol duration is The bit rate achieved by Fixed WiMAX depends on the modulation and coding scheme (MCS) used in each subcarrier and is given by

Estimating data rates For an OFDM system with 192 subcarriers, the number of bits carried by an OFDM symbol are 192 *B where B = bits/modulation symbol. Numerical example using QPSK

Data Rate with OFDM Raw Bit Rate = (OFDM symbols/sec) * (Bits/OFDM symbol) When channel coder with rate R=k/n is used Data (Information) Rate = Raw bit Rate * Channel Coding Rate

WiMAX frames OFDM symbol and guard times in WiMAX (example for 3.5 MHz bandwidth)

Data Rates for fixed WiMAX As an example with a 3.5 MHz channel bandwidth with a 5 ms frame time, the symbols per frame are 69 (each symbol is 72 μ seconds) and the OFDM symbol transmission rate is 69/0.005 = 13,800 OFDM symbols/sec. If the OFDM symbols are carried using 64 QAM (192*6 = 1152 bits/OFDM symbol), this gives a data rate of 13,800*1152 = 15.9 Mbps. The data rate available to the MAC layer will be lower; for example, if a coding rate of 5/6 is used, the data rate is 13.2 Mbps.

Data rates using frames Raw Bit Rate = (OFDM symbols/frame) * (Frames/sec) * (Coded Bits/Symbol) Data Rate for Channel = Raw Bit Rate * Error Coding Rate

Subchannels in OFDM systems Subchannelization in Fixed WiMAX is done in the uplink direction only (subscriber station to base station). In the downlink direction, all the subcarriers (i.e., 192) are assigned to the base station. In the uplink direction, 16 subchannels are defined, of which any number (1, 2, 4, 8, or 16) can be assigned to a subscriber station. Only one subscriber station can transmit on a particular subchannel at one time. As there are 192 data subcarriers, one subchannel implies 192/16 =12 subcarriers in the frequency domain. This implies that a subscriber station can transmit at bit rates which represent 1/16 of the bits carried in an OFDM symbol.

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