Καθηγητής Γεώργιος Ευθύμογλου Single Carrier Transmission Systems Channel Coding & Modulation (MCS) Shannon Capacity Καθηγητής Γεώργιος Ευθύμογλου Module Title

End-to-end system model Example: code rate = 78 data bits /1024 coded bits = 0.076 Assuming QPSK modulation, one QPSK symbol is mapped to (carries ) 2 bits Efficiency = 0.076*2 = 0.152

Transmission Example 1 0 1 1 information bits 0 1 0 0 1 1 0 1 coded bits with Channel Encoder Rate ½ 0 1 0 1 1 1 punctured coded bits with puncturing pattern [1 1 0 1] Transmitted symbols in the wireless channel -1, +1, -1, +1, +1, +1 (2-PAM at baseband) Multiply 2-PAM with cos(2πfct) to obtain 2-Phase Shift Keying (PSK) signal to be transmitted by the antenna: cos(2πfct+π), cos(2πfct), cos(2πfct+π), cos(2πfct), cos(2πfct), cos(2πfct), Each symbol is transmitted for time duration Ts Transmitted symbol rate is Rs = 1/Ts symbols/sec Transmitted bandwidth is approximately BW ≈ Rs (Hz) at baseband and BW ≈ 2Rs at passband (assuming rectangular pulses)

Reception Example The received signal (assume without noise) is first multiplied by the carrier frequency cos(2πfct) for down conversion to baseband signal -1, +1, -1, +1, +1, +1 With Noise the received samples may be -0.7, +0.8, -1.2, +1.5, -0.1, +0.6 (1 channel error) Using soft decision Viterbi decoding these samples enter the Channel Decoder BUT before that they enter the de-puncturing block… The de-puncturing block output -0.7, +0.8, 0 -1.2, +1.5, -0.1, 0, +0.6 (since nothing was transmitted at the punctured bits, the de-puncturing block enter 0 values)

Reception Example These received samples -0.7, +0.8, 0, -1.2, +1.5, -0.1, 0, +0.6 enter the Viterbi decoder with rate ½ and the output is the recovered information bits 1 0 1 1 (1 channel error was corrected) Higher order modulations: M-ary modulations In the above example the bit rate Rb was equal to the symbol rate Rs in the channel. Also transmit BW ≈ 2Rs (Hz). If a system requires in the same Bandwidth to send Rb = 2 Rs , then we need to use a different mapping between bits and symbols, that is, a different modulation which will map 2 bits to 1 modulation symbol. The number of modulation symbols required will be M = 22 = 4

Bit level Monte Carlo simulation Channel Source Encoder Interleaving Decoder De-interleaving Tx Rx Modulate Demodulate Hard decision or Soft decision Random bits Estimated bits Performance Measure Encoder

Bit level end-to-end system model 0 1… ej7π/4, ejπ/4 ,… 1 0 1 1… 0 1… 1 0 1 1…

Convolutional channel encoder

Puncturing in LTE Στο LTE, ο κώδικας διόρθωσης σφαλμάτων ονομάζεται turbo code με ρυθμό 1/3. Αυτό σημαίνει ότι σε κάθε κωδικοποιημένο πακέτο, το 1/3 είναι πραγματική πληροφορία και τα 2/3 είναι επιπλέον bits.

Shannon’s capacity Σε ένα πραγματικό σύστημα μετάδοσης το σήμα λήψης θα δίνεται από το σήμα (παλμό) εκπομπής + θόρυβο Ο θόρυβος συνήθως είναι Additive White Gaussian Noise (AWGN) Για ένα σήμα λήψης με πηλίκο ισχύος σήματος προς ισχύ θορύβου SNR (Signal-to-noise ratio), η χωρητικότητα (μέγιστος ρυθμός εκπομπής bit/sec) δίνεται από τη σχέση Επομένως το bit rate αυξάνει αναλογικά με το information bandwidth ΒΤ και με το λογάριθμο του σηματοθορυβικού λόγου.

Information Bandwidth Given a symbol rate Rs = 1/Ts (assuming symbol time Ts), the transmitted bandwidth at baseband depends on the pulse shape, and is given as follows (at passband bandwidth is doubled) where α is the roll-off factor of the raised cosine transmit filter. Special Cases: α=1 : results in maximum transmit bandwidth α=0 corresponds to sinc pulses: results in minimum transmit bandwidth For rectangular pulses we have BW ≈ Rs

Example for SNR calculation We consider a communication system in which the distance between the transmitter and receiver is 10,000 m. The transmitter power is 30 dBW (GT =20 dBi; PT =10 dBW). The transmitting frequency is 1.5 GHz ( λ=0.2 m). The receiver antenna gain is 3 dBi; and total system losses are 6 dB. Assuming the receiver noise figure, Nf =5 dB and bandwidth, BW=1.25 MHz, calculate the received signal power at the receiver antenna:

Signal-to-Noise Ratio (SNR) Calculate the SNR of the received signal. Es = energy of modulation symbol Ts = time duration of modulation symbol since

Άσκηση 1 Bit rate depends on: channel bandwidth, Άσκηση 1 Bit rate depends on: channel bandwidth, channel SNR (received signal power to noise power), number of transmission levels. Example: A transmission channel has the bandwidth and SNR = 63. Find the appropriate bit rate and number of signal levels. Solution: Theoretical maximum bit rate is In practice, a smaller bit rate can be achieved. Assume that is, we need 4 transmit amplitudes of the sinc pulse (α=0).

Άσκηση 2 Μία ακολουθία δεδομένων 4 πλατών βασικής ζώνης έχει περίοδο συμβόλων 100 μsec . α) Ποιο είναι το ελάχιστο εύρος ζώνης που απαιτείται για εκπομπή, θεωρώντας ότι χρησιμοποιείται ένα φίλτρο υψωμένου συνημιτόνου (raised cosine) με α=0.3 β) Πόσος χρόνος απαιτείται για αποστολή 1 εκατομμυρίου bits? γ) Αν απαιτείται η μετάδοση πληροφορίας στο μισό χρόνο, πόσες καταστάσεις συμβόλων απαιτούνται χωρίς αύξηση του εύρους ζώνης μετάδοσης. Απαιτείται ΔΙΠΛΑΣΙΟ bit rate  4 bit / symbol  16 πλάτη συμβόλων.