Spectrum of M -FSK ∆ f ⋯ � f f f f f 1 2 3 M − 1 M In M -FSK, only one carrier is active in any given symbol duration to carry log 2 M bits. This is why it is not a spectral-efficient modulation scheme. Why not using all the carriers to carry information at the same time since they are orthogonal? This leads to OFDM (orthogonal frequency-division multiplexing) technique. EE456 – Digital Communications Ha H. Nguyen
OFDM (Orthogonal Frequency-Division Multiplexing) ∆ = f 1 T N ⋯ � f f f f f 1 2 3 1 N − N N Bandwidth ≈ ⋅ ∆ = W N f T N In OFDM the spectrum (frequency) is divided into overlapping but orthogonal subcarriers. Each sub-carrier is independently modulated by M -QAM. The minimum subcarrier separation is 1 /T N , where T N is the OFDM symbol length. OFDM can be simply looked upon as a combination of amplitude , phase and frequency modulation techniques. EE456 – Digital Communications Ha H. Nguyen
Communication Services using OFDM Wireless Wireline ADSL and VDSL broadband access IEEE 802.11a, g, n (WiFi) Wireless LANs via POTS copper wiring MoCA (Multi-media over Coax IEEE 802.15.3a Ultra Wideband (UWB) Wireless PAN Alliance) home networking IEEE 802.16d, e (WiMAX), WiBro, PLC (Power Line Communication) and HiperMAN Wireless MANs IEEE 802.20 Mobile Broadband Wireless Access (MBWA) DVB (Digital Video Broadcast) terrestrial TV systems: DVB -T, DVB -H, T-DMB, and ISDB-T DAB (Digital Audio Broadcast) systems: EUREKA 147, Digital Radio Mondiale, HD Radio, T-DMB, and ISDB-TSB Flash-OFDM cellular systems 3GPP UMTS & 3GPP@ LTE (Long-Term Evolution), and 4G OFDM is spectrally efficient, tolerates environments with high RF interference, works well in harsh multi-path environments and can be elegantly implemented with IFFT/FFT modules. EE456 – Digital Communications Ha H. Nguyen
Implementation of OFDM ( ) X [0] x [0] sin 2 π f t c [1] [1] ✶ ( ) X x x t � ✁ ✂ ✄ ☎ ✕ ✄ ✧ ✧ ✖ I ✬ ✄ ✗ ✡ ✡ ★ r bits/sec ✆ ✝ ✞ ✟ ✠ ✏ ✝ ✏ ✏ ✰ ( ) ✘ s t X b ✙ ✤ ✥ ✥ ✦ ✩ ★ ✞ ☛ ☞ ☞ ✌ ✍ ✴ ✱ ☞ ✍ ✌ ✑ ✪ ✚ ✲ ( ) ✛ x t ✎ ✡ ✧ ✫✬ ✭ ✏ ✠ ✞ ☞ ✌ ✑ ✜ ☛ ✒ Q ✬ ✄ ✢ ✣ ✔ ✜ ✯ ✒✓ ✞ ✟ ✌ ✍ ✆ ✏ ✠ ✒✮ ✌ ✍ ✌ ✍ ✰ ✢ [ 1] [ 1] X N − x N − ( ) cos 2 π f t c ( ) sin 2 π [0] Y [0] f t y c [1] y [1] Y ✗ � ✁ ✂ ✄ ☎ ✫ ✄ ✬ ✖ ✳ ✥ ✵ ✌ ✞ ✠ ✮ ✌ ✕ ✡ ✰ y n [ ] ✆ ✝ ✞ ✟ ✠ ✷ ✘ ✩ ★ Y r ( ) t ☞ ✍ ✌ ✑ ✪ ✙ ✥ ✥ ✦ ✧ ✧ ✡ ✸ ✯ ✴ ✱ ✌ ✞ ✠ ✓ ☛ ✠ ✍ ✚ ✧ ✭ ✬ ✫ ✹ ☛ ✒ ✛ ✧ ✜ ☛ ✒ ✯ ✢ ✏ ✠ ✒ ✮ ✌ ✍ ✌ ✍ ✣ ✳ ✫ ✥ ✄ ✬ ✧ ✜ ✌ ✞ ☛ ☞ ☞ ✌ ✍ ✢ ✰ [ 1] [ 1] y N − Y N − ( ) cos 2 π f t c EE456 – Digital Communications Ha H. Nguyen
Multipath Problem in High-Speed Wireless Transmission ✽ ✾ ✻ ✿ ❀ ❁ ❇ ❄ ❁ ❄ ❇ ✿ ✾ ❉ ❊ ❊ ❈ ✺ ✻ ✼ ✽ ✾ ✻ ✿ ❀ ❁ ❂ ✿ ❃ ❁ ❀ ❁ ❄ ❄ ❅ ❆ ❇ ❁ ❀ ❈ ❈ Example: Consider the symbol rate of 10 6 symbols/sec ⇒ The receiver expects a specific symbol within a window of 1 µ s. If multi-path delays the signal by more than 1 µ s (easily happen in real propagation environment), then the receiver will also receive the symbol in the next symbol period, causing inter-symbol-interference (ISI), hence severe performance degradation. EE456 – Digital Communications Ha H. Nguyen
How Does Cyclic Prefix Work in OFDM Append last symbols to the front µ x N [ − µ ], [ x N − µ + 1], , [ x N − 1] x [0], [1], [2], x x , [ x N − µ − 1] x N [ − µ ], [ x N − µ + 1], , [ x N − 1] ⋯ ⋯⋯⋯ ⋯ Cyclic prefix (CP) of length µ Original signal sequence of length N [0], , [ x N − 1] [0], , [ x N − 1] [0], , [ x N − 1] x ⋯ x ⋯ x ⋯ �� �� �� �� Data block CP Data block CP CP Data block ⋯ ⋯ [0], , [ y N − 1] [0], , [ y N − 1] [0], , [ y N − 1] ��� y ⋯ ��� y ⋯ ��� y ⋯ µ µ µ N N N An OFDM symbol is basically a super-symbol obtained by multiplexing many M -QAM symbols in a complicated manner. The length of a super-symbol ( T N ) becomes longer and hence more resistent to multipath effect. One can also use zero padding to create a guard interval between consecutive OFDM symbols, hence avoiding ISI. EE456 – Digital Communications Ha H. Nguyen
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