Single-Carrier Block Transmission With Frequency-Domain Equalisation

Transcription

1 ELEC6014 RCNSs: Additional Topic Notes Single-Carrier Block Transmission With Frequency-Domain Equalisation Professor Sheng Chen School of Electronics and Computer Science University of Southampton Southampton SO17 1BJ, UK sqc/ez / 1

2 Motivations For 4G and B4G high-speed broadband applications, data rate of tens Mbps over wireless channel of typical delay spread in microseconds ISI spanning tens or even hundreds of symbols Nightmare for time-domain equalisation: impractically long equaliser, excessively slow convergence poor performance Orthogonal frequency division multiplexing, a multi-carrier technique, offers a viable low-complexity high-performance solution for ISI mitigation High peak-to-average power ratio, intolerance to amplifier nonlinearity, and high sensitivity to carrier frequency offsets Alternative solution for ISI mitigation is single-carrier modulation with frequencydomain equalisation Similar low-complexity and performance, but avoiding OFDM s drawbacks Not as flexible as OFDM in managing bandwidth and energy resources 2

3 Quick Comparison Symbol mapping S/P N Cyclic prefix insertion N+M P/S Wireless channel P/S Symbol detection mapping S/P IFFT N IFFT Frequency domain equalisation Cyclic prefix insertion N+M FFT P/S N S/P Wireless channel prefix removal SC FDE P/S equalisation and detection FFT N S/P prefix removal OFDM Both transceivers have similar implementation complexity, but SC-FDE transmitter is simpler and hence better for uplink handset 3

4 Block Transmission Data symbols {s n } are transmitted in blocks of N symbols with cyclic prefix of length M block length of N + M M is chosen to be larger than channel impulse response length Cyclic prefix insertion M CP block of Ndata symbols last M symbols copied M symbols copying Last M symbols may be training symbols, eg known PN sequence Spot difference SC-FDE: data symbols are time-domain quantity and transmitted directly OFDM: data symbols are frequency-domain quantity (and are IDFT into time-domain for transmission) 4

5 OFDM Cyclic prefix at beginning of each block has two main functions Prevent contamination of a block by ISI from previous block, by simply dropping first M time-domain samples of received block of length N + M Make received block periodic with period N, essential for DFT to lead single-tap equalisation in frequency domain Received block has cyclicity property r m = N h 1 X k=0 h k s m (k mod N), 0 m N 1 where N h M is length of CIR, and h k, 0 k N h 1, CIR taps Process received block {r m } N 1 m=0 by DFT: R l = N 1 X m=0 r m e j2πlm N = H l S l + V l, 0 l N 1 CFR {H l } N 1 is N-point DFT of CIR {h k } N h 1 k=0, V l is noise term One-tap equalisation Y l = W l R l, 0 l N 1 {Y l } N 1 provides sufficient statistics for detection of transmitted data symbols {S l } N 1 5

6 Cyclic Prefix and Cyclicity Transmitted time-domain OFDM signal: s N+M = ˆs N 1 s N 2 s N M s 1 s 0 s 1 s 2 s M T N data symbols s N = ˆs N 1 s 1 s 0 T, and M-length cyclic prefix ˆs 1 s 2 s M T = ˆsN 1 s N 2 s N M T M CIR length, and for convenience, let CIR be: ˆh 0 h 1 h M T Received block of length N + M: r N+M = ˆr N 1 r 1 r 0 r 1 r 2 r M T Dropping ˆr 1 r 2 r M T removes ISI from previous block N-length received block r N = ˆr N 1 r 1 r 0 T has cyclicity property Linear convolution r N = H L s N+M, H L : N (N + M) r N 1 = h 0 s N 1 + h 1 s N h M s N M+1 r M = h 0 s M + h 1 s M h M s 0 r M 1 = h 0 s M 1 + h 1 s M h M 1 s 0 + s M s 1 r 1 = h 0 s 1 + h 1 s 0 + h 2 s h M s M+1 r 0 = h 0 s 0 + s 1 s h M s M 6

7 2 6 4 r N 1 r M r M 1 r 1 r 0 Cyclicity (continue) = s N 1 s N 2 s N M s 0 s 1 s 2 s M Circular convolution r N = H C s N, H C : N N r N 1 r M r M 1 = r r 0 h M h 0 h 1 h M 1 h 2 h M h 0 h 1 h 1 h M 1 h M h s N 1 s N 2 s

8 Block Processing in SC-FDE Cyclic prefix at beginning of each block has two main functions Prevent contamination of a block by intersymbol interference from previous block, by simply dropping first M samples of received block of length N + M Make received block periodic with period N, essential for DFT to lead singletap equalisation in frequency domain Received block has cyclicity property r m = N h 1 X k=0 h k s m (k mod N), 0 m N 1 where N h M is length of CIR, and h k, 0 k N h 1, CIR taps Process received block {r m } N 1 m=0 R l = N 1 X m=0 by DFT: r m e j2πlm N = H l S l + V l, 0 l N 1 CFR {H l } N 1 is N-point DFT of CIR {h k } N h 1 k=0, V l is noise term 8

9 One-Tap Equalisation In frequency-domain, equalisation can be achieved by one-tap linear equaliser Y l = W l R l, 0 l N 1 Zero-forcing: W l = H l H l 2, 0 l N 1 Minimum mean square error: W l = H l H l 2 + σ2 v σ 2 s, 0 l N 1 where σ 2 v is noise power and σ 2 s = E[ s n 2 ] signal power SC-FDE with decision feedback equaliser {y n } N 1 n=0, IDFT of {Y l} N 1 y n = 1 N N 1 X Y l e j2πln N, 0 n N 1 provides sufficient statistics for detection of transmitted data symbols {s n } N 1 n=0 9

10 OFDMA / SC-FDMA Multi-carrier system to support multi users: orthogonal frequency division multiple access OFDMA N subcarriers to support K users Carrier assignment scheme CAS assigns N/K subcarriers to each user User 1 User 2 User 3 User 4 4 users 16 subcarriers Each user assigns its data symbols to subcarriers it occupies, and assigns zero to unoccupied subcarriers Single-carrier system to support multi users: frequency division multiple access SC-FDMA user 3 user 2 user 4 user 1 Total bandwidth For MC systems, such as OFDMA, flexible for resource allocation, such as power allocation to subcarriers 10

11 References 1 D Falconer, SL Ariyavisitakul, A Benyamin-Seeyar and B Eidson, Frequency domain equalization for single carrier broadband wireless systems, IEEE Communications Magazine, vol40, no4, pp58 66, April F Pancaldi, GM Vitetta, R Kalbasi, N Al-Dhahir, M Uysal and H Mheidat, Single-carrier frequency domain equalization, IEEE Signal Processing Magazine, vol25, no5, pp37 56, Sept N Benvenuto and S Tomasin, Iterative design and detection of a DFE in the frequency domain, IEEE Trans Communications, vol53, no11, pp , Nov C Zhang, Z Wang, C Pan, and L Hanzo, Low-complexity iterative frequency domain decision feedback equalization, submitted to IEEE Trans Vehicular Technology,