FUTEBOL Federated Union of Telecommunications Research Facilities for an EU-Brazil Open Laboratory Experimenting with Orthogonal Frequency-Division Multiplexing OFDM Modulation The content of these slides is based on the OFDM Chapter: Domingue, J., Mikroyannidis, A., Gomez-Goiri, A., Smith, A., Pareit, D., Gerwen, J. V.-V., Tranoris, C., Lampropoulos, K., Jourjon, G., Fourmaux, O., Rahman, M. Y., Collins, D., Marquez-Barja, J. M., Blumm, C., Kaminski, N., Dasilva, L. A., Sutton, P. & Gomez, I. (2015) Forging Online Education through FIRE: ipad Edition. ISBN: 978 1473020160.
Relevance of OFDM Wireless: Wireless Personal Area Network (WPAN): WiMEdia Wireless Local Area Network (WLAN): IEEE802.11a/g/n/ac/ad, IEEE 802.15.4g, HiperLAN/2 Broadcast: DAB, DVB-T/-T2, DVB-H, ISDB-T Wireless Metropolitan Area Network (WMAN): IEEE 802.16 WiMAX Mobile telephony: LTE (3.9G), LTE Advanced (4G) Wired: Power-Line-Communication Broadcast: DVB-C2 ADSL/-2/-2+ May 25, 2017 Some Footer Note 2
From FDM to OFDM Orthogonal signals do not interfere with each other Sub-spectra may overlap in frequency domain More efficient use of available spectrum Greater data rates achievable FDM f OFDM + Mathematical definition of orthogonal base signals: ψ p t ψ q t dt = t= 1: p = q 0: p q f 3
OFDM subcarrier functions 4 Generation of orthogonal carrier functions: Basis is a rect-function with symbol duration T 0 Spectrum of rect-function is a sinc-function 2 2 1 0,, rect 1 S S S T T T S S t t T t T -T S /2 T S /2 1/T S t S S S ft T t T sinc rect 1 f 1 Zeros at f = n/t S, n = -3, -2, -1, 1, 2, 3
OFDM subcarrier functions Generation a set of orthogonal basis functions k : Shifting sinc-functions in frequency domain by multiplication with complex carriers In frequency domain: Ψ 0 f f k Ψ 6 f j2f t 1 k t e rect TS t T S Subcarrier spacing f = 1 T S f 5
Loading data on subcarrier functions Visualization of base function for three subcarriers in time domain: 1 0.5 0-0.5-1 1 0.5 0 cos ψ 1 ψ 2 ψ 3 ψ 1 + ψ 2 + ψ 3 sin 3 2 1 0-1 -2 3 2 1 0-1 -0.5-2 -1 0 T S -3 0 T S 6
Loading data on subcarrier functions OFDM symbol for 1024 carriers loaded with random binary data symbols (+1 or -1): OFDM signals with many subcarriers in time-domain look like noise signals! 7
OFDM transmission via fading channels What happens to a continuous sine wave that is transmitted on a fading channel? TX RX s(t) h(t, τ) r(t) = s(t) h(t, τ) t t s k t Transmitted Signal Channel Impulse Response Received Signal t j2f j2f k k X e k k r k t X k k e Continuous sine waves experience only amplitude and phase variation! (applies to every carrier in the OFDM symbol) 8
Cyclic prefix against multipath distortion Amplitude and phase variations of continuous sine waves can easily be corrected at receiver by means of pilot signals and channel equalization BUT: We want to transmit data no continuous sine signals T S T S T S OFDM-Symbol 1 OFDM-Symbol 2 OFDM-Symbol 3 Discontinuities between OFDM symbols will lead to inter-symbol-interferences (ISI) inter-carrier-interferences (ICI) due to loss of sub-carrier orthogonality when transmitted on a fading channel 9
Cyclic prefix against multipath distortion Avoidance of ISI and ICI by introduction of Cyclic Prefix (CP): OFDM symbol is cyclically extended at its beginning T CP T S Frame still contains discontinuities, but system is tuned in at payload part of symbol CP gets corrupted by ISI, FFT-Payload remains intact (only constant amplitude and phase shift) CP can make OFDM transmissions completely immune against ISI created by multipath propagation when CP length T CP is longer than the delay spread: T CP στ h(t, τ) στ 10 t
Using discrete Fourier transforms Digital signal processing: time discrete signals s( t) s( n Tsample) s( n) Sample time T sample = 1/f sample Time-discrete notion of an OFDM modulator: Time-discrete notion of an OFDM demodulator: N C 1 s n = X k e j2π k n N C Y K = k=0 N C 1 n=0 s(n) e j2π k N C n N C IDFT X k DFT s n OFDM modulation / de-modulation equals the IDFT transformation / DFT transformation! If number of sub-carriers N C is chosen as a power of 2 (2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 ), the IDFT can be replaced by an IFFT, yielding a very efficient implementation of a OFDM modulator (FFT for demodulator at receiver) 11
Using discrete Fourier transforms Block Diagram of OFDM Modulator and Demodulator based on IFFT / FFT X 0,m Y 0,m X k,m Serial to Parallel X 1,m... IFFT Parallel to Serial... s(n) D A s(t) r(t) A D r(n) Serial to Parallel... FFT Y 1,m... Parallel to Serial Y k,m X NC 1,m Y NC 1,m Modulat or Demodulator 12
Using discrete Fourier transforms Up-conversion to carrier frequency (using quadrature modulator) X 0 X 1 X 2 IFFT R s(n) = I cos 2πf c t sin 2πf c t X 15 I s(n) = Q f f c 1 2 f s f c f c + 1 2 f s 13
Lower Guard Band DC Carrier Upper Guard Band Using discrete Fourier transforms Usable sub-carriers Example for 16-bin FFT 0 X 1 X 2 X 3 X 4 X 5 X 6 0 0 0 X 10 X 11 X 12 X 13 X 14 X 15 DC Carrier IFFT Upper Guard Band Lower Guard Band 14
The OFDM system model Scrambler Transmitter Receiver De-Scrambler Source Code Source De-Code Interleaving De-Interleav. Mapper De- Mapper Pilot Insertion Channel Equal. IFFT FFT CP Payload Extract. TX FE RX FE Channel 15
Symbol mapping / de-mapping Scrambler Transmitter Receiver De-Scrambler Source Code Source De-Code Interleaving De-Interleav. Mapper De- Mapper Pilot Insertion Channel Equal. IFFT FFT CP Payload Extract. TX FE RX FE Channel 16
Symbol mapping / de-mapping Loading data bits on the OFDM subcarriers IFFT accepts complex input data use complex subcarrier modulations (QAM, PSK, ) Q Q +1 1 +1 1-1 +1 I -1 +1 I 0-1 BPSK (Binary Phase Shift Keying): 1 bit per sub-carrier per symbol 0-1 17
Symbol mapping / de-mapping Gray Mapping: neighboring constellation points only differ in one bit Reduction of bit error ratio Q Q 01 +1 11 01 +1 11-1 +1 I -1 +1 I 00-1 10 00 10-1 QPSK (Quadrature Phase Shift Keying) / 4-QAM (Quadrature Amplitude Modulation): 18 2 bit per sub-carrier per symbol
Symbol mapping / de-mapping Q Q +1 0010 0110 1110 1010-1 1/3 0011 0111 1111 1011-1/3 1/3 +1-1/3 0001 0101 1101 1001 I I 0000-1 0100 1100 1000 16-QAM : 4 bit per sub-carrier per symbol 64-QAM : 6 bit per sub-carrier per symbol 19
Channel equalization Scrambler Transmitter Receiver De-Scrambler Source Code Source De-Code Interleaving De-Interleav. Mapper De- Mapper Pilot Insertion Channel Equal. IFFT FFT CP Payload Extract. TX FE RX FE Channel 20
Channel equalization Channel Equalization Insertion of known symbols (pilots) in the OFDM frame to get to know the channel impulse response Evaluating their distortions at the receiver Assuming a relatively static channel, data symbols can be equalized Zero Forcing (ZF) Equalizer equalizes phase offset and amplitude distortion in OFDM systems Easy to implement in frequency domain, assuming flat fading for each OFDM subcarrier Drawback: Amplification of noise for carriers with deep fades Approach: Y Pilot = X Pilot H Channel H Channel = Y Pilot X Pilot 1 H ZF = H Channel Y Data = X Data H Channel X Data = Y Data H ZF 21
Channel equalization Example of magnitude and phase distortion in a wireless channel Received constellation points Rel. signal power [db] Signal amplitude [V] Received signal in time domain and frequency domain t [s] f [MHz] 22
Subcarrier 8 Subcarrier 16 Phase: arg(h) Magnitude: abs(h) Channel equalization Transfer function H of wireless channel in magnitude and phase as estimated by the channel equalizer Resulting IQ vector distortion 0.69 0.42-0.26 = -14.9 1.02 =58.2 FFT Index 23
Data Rate Approximation Bits Bits per Symbol Data Rate = = Time Interval Symbol Duration N = Mod N Carr Assumption: 1 N f sample FFT + N CP 10 % of the potential carriers used for guard band (N Carr = 0.9 N FFT ) N Data Rate = N Mod f sample 0.9 FFT N FFT + N CP Example: Sampling frequency: f sample = 10 MHz 16-QAM on subcarriers: N Mod = 4 CP length: N CP = 16 samples Doubling subcarriers in used bandwidth does not double the data rate! Subcarrier spacing f = 1 T S = f sample N FFT Subcarr. Spacing FFT Size N FFT f Data Rate 8 1.25 MHz 12 Mbit/s 16 625 khz 18 Mbit/s 32 312.5 khz 24 Mbit/s 64 156.3 khz 28.8 Mbit/s 128 78.1 khz 32 Mbit/s 256 39.1 khz 33.9 Mbit/s 512 19.5 khz 34.9 Mbit/s 1024 9.8 khz 35.4 Mbit/s 24
OFDM Orthogonal Frequency Division Multiplexing (OFDM) is a high-performant modulation technology for a great number of current and next-generation communication standards Idea: Information is transmitted via an orthogonal set of subcarrier functions Benefits: High spectral efficiency Robustness in multipath channels (Cyclic prefix!) Efficient implementation based on IFFT/FFT Simple channel equalization in frequency domain Drawbacks: Time and frequency synchronization is very important Peak-to-average problem reduces the power efficiency of RF amplifier at the transmitter 25
Thank You! Questions? Comments? Presenter Name presenteremail@institution.eu http://www.institution.eu/~presentersite/ FUTEBOL has received funding from the European Union's Horizon 2020 for research, technological development, and demonstration under grant agreement no. 688941 (FUTEBOL), as well from the Brazilian Ministry of Science, Technology, Innovation, and Communication (MCTIC) through RNP and CTIC.
Running the exercises We will use FORGE tools to access the USRPs in the TCD testbed: https://ctvr-node13.scss.tcd.ie/ofdm_v2 Accounts: group02, group03, group04, group05 Password (the same for all acounts): May 25, 2017 Some Footer Note 27 one.brazil
Running at home Use http://www.forgebox.eu/fb/preview_course. php?course_id=180 Wait for the machines to be provisioned (up to 10 minutes) May 25, 2017 Some Footer Note 28