 orthogonality of the subcarriers. Since the carriers are all sine/cosine wave, the area under one period of the sine/cosine wave is zero. Even if a sinusoid of frequency n is multiplied by a sinusoid of frequency m/n, the area under the product is also zero. In general, for all integers m and n, sin mx, cos mx, sin nx and cos nx are all orthogonal to each other and these frequencies are called harmonics. The orthogonality allows simultaneous transmission of many subcarriers in a tight frequency space without interference from each other. Assume a signal and divide it into four groups for the four subcarriers. To transmit them individually and at the receiver end these four modulated subcarriers are added to create the OFDM symbol by using a block called the IFFT (inverse fast fourier transform) block, as can be seen in the following steps (shown in Figure 5.2). Forward FFT takes a random signal, multiplies it successively with complex exponentials Fourth Generation Mobile Networks Parallel Serial stream (IFFT) Figure 5.2 Orthogonality in OFDM over the range of frequencies, sums each product and plots the result as a coefficient of that frequency. The coefficients are called a spectrum and represent how much of that frequency is present in that signal. The results of the FFT are basically a frequency domain signal, as shown in the Figure 5.2. The inverse FFT (IFFT) takes this spectrum and converts all of it back to a time domain signal by again successively multiplying it by a range of sinusoids. The use of IFFT/FFT totally eliminates the bank of subcarrier oscillators at the transmitter/receiver. Intersymbol Interference The signal that reaches the receiving end faces attenuation during transmission. In the fading environ- ments the signal throws a splash backwards, which needs to be avoided. When the distance between the transmitted and receiving points increases, the spread of the signal is the same as the delay spread. Thus, to mitigate the effect at the front of the symbol, the symbol is moved further away f