OFDM

The use of OFDM in wireless applications can be traced back to the 1960s, when it was used for several high frequency military systems such as KINEPLEX [22], ANDEFT [26] and KATHRYN [27]. In the 1980s, OFDM was studied for high-speed modems [28], digital mobile communications and high-density recording and in the 1990s, OFDM was investigated for wideband data communications over mobile radio channels [29], high bit rate digital subscriber lines'* [30, 31 ] and digital broadcasting [32, 33].

OFDM has now been employed in numerous wireless systems such as indoor wireless LANS (HIPERLAN/2 [34], IEEE 802.11a [35]), broadband WLLs (IEEE 802.16 [36]) and digital audio and video broadcasting (DAB and DVB [32, 33]).

The basic idea of OFDM is to modulate a number of parallel data streams using orthogonal subcarriers such that they satisfy the condition given in Equation 2.2.

T

0 forfl5Éf2 (2.2)

where T is the OFDM symbol duration and fi and f2 are two subcarrier frequencies.

The orthogonality condition in Equation 2.2 is satisfied by making the subcarrier spacing equal to an integer multiple of the symbol rate, i.e., for an OFDM signal with symbol duration T, the spacing between each subcarrier should be equal to Njnt(1/T), where N^t is an integer. In the frequency domain this results in the spectrum of each carrier having a null at the centre frequency of each of the other subcarriers in the system (Figure 2.9(a))®. Maximum spectral efficiency can be achieved by making the spacing between each subcarrier equal to 1/T (as shown in Figure 2.9(b)). Note that in this case there is considerable overlapping between the spectra of the individual subcarriers, however, the information can be reliably recovered due to the fact that the subcarriers are made orthogonal to one another.

* In this case, O FD M is referred to as Discrete Muiti-Tone (DMT).

® The spectrum of the O FD M signal is said to fuifii the Nyquist criterion for an ISI free pulse shape, where the pulse is present in the frequency domain and not the time domain [19].

Chapter 2: Multi-carrier CDMA 34

(a)

(b)

Figure 2.9: OFDM spectrum (a) Orthogonal subcarriers; (b) Orthogonal subcarriers with maximum spectral overlap

In the time domain this can be interpreted as having an integer number of cycles during the symbol period (as shown in Figure 2.10).

<■

Figure 2.10: OFDM symbol with 4 subcarriers

Unlike the direct sequence spread spectrum or frequency hopping systems described in Section 2.1, OFDM does not provide any spectral spreading. The bandwidth of the OFDM signal is the same as that of the original signal. The overall system bandwidth is merely divided between the different subchannels.

Figure 2.11 shows the transmitter model for OFDM. At the input of the transmitter, the data is first Serial-to-Parallel (S/P) converted into a number of low rate data streams. The parallel outputs from the S/P converter are then modulated onto a set of orthogonal subcarriers and summed together. In order to completely eliminate the effects of ISI caused by multipath, a Guard Period (GP) is generally added at the beginning of each OFDM symbol before up- conversion and transmission.

Input data : OFDM : Signal Re{.} Add GP S/P

Chapter 2; Multi-carrier CDMA 35

In most OFDM based systems, the guard period is a cyclic extension of the OFDM symbol (Figure 2.12) and is referred to as the Cyclic Prefix (CP). The cyclic prefix not only eliminates the ISI but also eliminates Inter Carrier Interference (ICI) in the presence of multipath®.

Figure 2.12: Guard perlod/CyclIc prefix

The insertion of the GP to the beginning of each OFDM symbol increases the spacing between the individual subcarriers from N m t/T to Njnt / ( T - Tq p) (This is illustrated in Figure 2.13 for the maximum overlap case). The spectrum of the transmitted OFDM signal no longer satisfies the orthogonality condition discussed above. However, at the receiver, the GP is removed from the beginning of each OFDM symbol before demodulation. Hence, the spectrum of the signal at the input of the dem odulator is similar to that shown in Figure 2.9(b).

1 /(T -Tgp)

1/T

Figure 2.13: Spectrum of OFDM signal with the insertion of the guard period

Figure 2.14 shows the receiver model for OFDM. At the input, the signal is first down- converted to baseband. The GP is then removed and the signal is demodulated by multiplying it with the complex conjugate of the orthogonal subcarriers and integrating over the symbol duration. LPF OFDM Signal Recovered data Remove G P _ P/S

Figure 2.14: OFDM receiver

Chapter 2: Multi-carrier CDM A 36

The OFDM transmitter and receiver model presented in Figure 2.11 and Figure 2.14 require banks of oscillators at the transmitter and receiver. This results in a complex system, particularly if the number of subcarriers is large. Weinstein and Ebert [25] have shown that OFDM signals can be generated and detected using an IDFT and a DFT, which greatly reduces the complexity of the system. The availability of F FT algorithms and cheap F FT chips reduces the cost and complexity of OFDM systems even further. The structure of the F FT based OFDM transmitter and receiver is shown in Figure 2.15. In this implementation the banks of oscillators at the transmitter and receiver are replaced by the IFFT and F FT, respectively. The guard period operates in the same manner as before. At the transmitter, the signal has to be converted to analogue format before transmission and at the receiver the received symbol has to be converted to digital format before demodulation. (Note that in this figure the up-conversion and down-conversion blocks have been omitted, however, in a typical system the OFDM signal at the output of the transmitter is up-converted before transmission and consequently, the received signal is down-converted before the A/D conversion.)

Input data

S/P IFFT P/S

O FD M O FD M

Add _D/A Signal Signal_A/D Remove

UP GP S/P FFT P/S

Recovered data

Figure 2.15: Discrete time representation of OFDM transmitter and receiver

In a practical system, the length of the IFFT/FFT is chosen to be greater than the number of subcarriers [37]. Figure 2.16 shows the spectrum of the IFFT output with the length of the IFFT set equal to the number of subcarriers. In this case, a filter with realistic passband-to- stopband transition cannot be used to recover the OFDM symbol. Hence, the length of the IFFT is increased in order to introduce a separation between the symbol spectrum and its copies. Figure 2.17 shows the spectrum of the IFFT output with the length of the IFFT set equal to N’ (where N’> Nsubcamers)- In this case, a filter with realistic passband-to-stopband characteristics can be used to recover the OFDM symbol.

► f

Nsubcamere/T 2N gijbcarriei» / T

Chapter 2: Multi-carrier CDMA 37

0 NTT

Figure 2.17: OFDM spectrum with iFFT/FFT size=N’(>N*ubcarriers)

The following section introduces the concept of combining OFDM with CDMA (referred to as multi-carrier CDMA).