OFDM Presented by Md. Imdadul Islam

Fig.1 Single carrier vs. multi-carrier transmission Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation scheme that transmits data over a number of orthogonal subcarriers. A conventional transmission uses only a single carrier modulated with all the data to be sent. OFDM breaks the data to be sent into small chunks, allocating each sub-data stream to a sub-carrier and the data is sent in parallel orthogonal sub-carriers. As illustrated in Figure 1, this can be compared with a transport company utilizing several smaller trucks (multi-carrier) instead of one large truck (single carrier). Fig.1 Single carrier vs. multi-carrier transmission

OFDM is actually a special case of Frequency Division Multiplexing (FDM). In general, for FDM, there is no special relationship between the carrier frequencies, f1, f2 and f3. Guard bands have to be inserted to avoid Adjacent Channel Interference (ACI). For OFDM on the other hand, there must be a strict relation between the frequency of the sub-carriers, i.e. fn = f1 + n⋅Δf where Δf = 1/TU and TU is the symbol time. Carriers are orthogonal to each other and can be packed tight as shown in Figure 2. Splitting the channel into narrowband channels enables significant simplification of equalizer design in multipath environments. Flexible bandwidths are enabled through scalable number of sub-carriers. Effective implementation is further possible by applying the Fast Fourier Transform (FFT). Dividing the channel into parallel narrowband sub-channels makes coding over the frequency band possible (COFDM). Moreover, it is possible to exploit both time and frequency domain variations, i.e. time and frequency domain adaptation. Fig.2

S/P Σ x(t) x0(t) x1(t) xNc-1(t) Channel r(t) ……… Fig.3 A baseband OFDM transmission model is shown in Figure 3. It basically consists of a transmitter (modulator, multiplexer and transmitter), the wireless channel, and a receiver (demodulator).

is a set of complex orthogonal waveforms In Figure 3, a bank of modulators and correlators is used to describe the basic principles of OFDM modulation and demodulation. This is not practically feasible, and the specific choice of sub-carrier spacing being equal to the per carrier symbol rate 1/TU makes a simple and low complexity implementation using Fast Fourier Transform (FFT) processing possible as shown in Figure 4. For more details on the FFT implementation

Fig.4 Transmitter and receiver by using FFT processing r(t) x(t) S/P IDFT …… A0 A1 AN-1 P/S ……… ……………… D/A Channel DFT A/D r0 r1 rN-1 Useless Fig.4 Transmitter and receiver by using FFT processing r(t) x(t)

Practical Implementation Orthogonal Frequency Division Multiplexing (OFDM) shows better spectral efficiency than that of Frequency Division Multiplexing (FDM) technique due to orthogonal relationship between sub-carriers. Orthogonal frequency division multiplexing (OFDM) introduces the concept of allocating more traffic channel within limited spectral width compared to Frequency Division Multiplexing (FDM). Here spectrums of adjacent channels are overlapped which resembles to adjacent channel interferences but interferences are avoided maintaining orthogonal relation between sub-carriers.

First of all high speed serial data is converted to low speed parallel data based. Output of each parallel line is modulated; two widely used modulation schemes are QPSK and 16-QAM. Parallel waves are again converted to an instantaneous serial waves prior transmission. This phenomenon resembles to Inverse First Fourier Transform (IFFT) mentioned. At receiving end signals are detected by coherent or envelope detection. Entire communication system is shown in fig.1.

Fig. 1: OFDM communication system Serial data input m(t) OFDM signal v(t) Im(g(t)) Re(g(t)) ……………………… S/P converter IFFT P/S converter Re(ej2πfct) Im(ej2πfct) Σ Modulator Serial data output m(t) Channel AWGN n(t) D-Modulator …… FFT Fig. 1: OFDM communication system

K=0,1,2……..Nc-1; Nc is the number of sub carrier Kth sub carrier signal is defined as K=0,1,2……..Nc-1; Nc is the number of sub carrier Δf is the frequency separation between carriers

Where amk are the constellation vector mth OFDM block Total Continuous-time signal of OFDM Where amk are the constellation vector

OFDM is a block modulation scheme OFDM is a block modulation scheme. Let Ts be the symbol intervals of the input source sequence. A block of N serial symbols is converted into a block of N parallel modulation symbols, each of duration T = NTs.

For simplicity, m=0, The set of complex orthogonal waveform, Now,

Sampling S(t) at t = lTs, The term is independent of k and can be combined with carrier Therefore the complex envelope can be written as, Where, l = 0, 1, 2 ,…, N-1

the carrier which produce the OFDM signal, The samples are then passed through a D/A converter and are used to modulate the carrier which produce the OFDM signal,

IDFT ak0 ak1 … … … akN-1 Ak0 Ak1 AkN-1 aK Transmitter Carrier DMOD DFT D/A Carrier MOD OFDM signal x(t) ak0 ak1 … … … akN-1 Ak0 Ak1 AkN-1 aK Transmitter Received OFDM signal r(t) = x(t) + n(t) A/D Carrier DMOD DFT rk0 rk1 … … … rkN-1 Rk0 Rk1 RkN-1 Decision device rK Transmitter

Modulation symbol amk is recovered by correlation

Received signal and n(t) is AWGN of environment and A maximum likelihood sequence estimator would have to choose one out of all possibly transmitted symbol sequence μ. The sequence estimator determines an estimated <Sm,k> according to the following criterion, Where μ is the types of possible modulation symbols and Hmk is the transfer function of channel during mth block