Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Multi-Carrier FDMA 111RectangularshapingNyquistshapingfrequencytime(a) Rectangular shaping(b) Nyquist shapingFigure 3-2Example of OFDMA with band-limited spectraThe Nyquist shaping function g(t) can be implemented with a time-limited square rootraised cosine pulse with a roll-off factor α,⎧ [ ] πtsin⎪⎨ T ′ (1 − α)4αt [ ] πt+sT s′ cosT ′ (1 − α)[s( ) ]g(t) =πt 4αt 2for t ∈{−4T s ′,4T s ′}. (3.8)T s⎪⎩′ 1 −T s′0 otherwiseThe relationship between T s ′,Ts,andα (roll-off factor) provides the property of the individualseparated spectra, where T s ′ = (1 + α)T s.3.2.1.4 Frequency Hopping OFDMAThe application of frequency hopping (FH) in an OFDMA system is straightforward.Rather than assigning a fixed particular frequency to a given user, the base station assignsa hopping pattern [2, 12, 28, 36]. In the following it is assumed that N c sub-carriers areavailable and that the frequency hopping sequence is periodic and uniformly distributedover the signal bandwidth.Suppose that the frequency sequence (f 0 ,f 7 ,f 14 ,...) is assigned to the first user, thesequence (f 1 ,f 8 ,f 15 ,...) to the second user, and so on. The frequency assignment to N cusers can be written asf(n,k)= f k+(7n mod Nc ), k = 0,...,N c − 1, (3.9)where f(n,k) designates the sub-carrier frequency assigned to user k at symbol time n.