## How Multiple Antennas Sample the Signal

Once upon a time, an antenna was viewed as a simple device to transmit and receive an electromagnetic wave, much like a battery the sole purpose of which is to provide electrical power. A set of antennas, however, can be viewed from a new angle as follows. Sampling in Time Domain An Analog-to-Digital Converter (ADC) is a device that samples an analog signal in time domain to create a corresponding sequence of numbers. Similarly, a Digital-to-Analog Converter (DAC) gets a sequence of numbers as an input to generate a reconstructed analog signal. As an example, a rectangular pulse shape is

## Quadrature Amplitude Modulation (QAM)

Quadrature Amplitude Modulation (QAM) is a spectrally efficient modulation scheme used in most of the high-speed wireless networks today. We discussed earlier that Pulse Amplitude Modulation (PAM) transmits information through amplitude scaling of the pulse $p(nT_S)$ according to the symbol value. To understand QAM, two routes need to be traversed. Route 1 We start the first route with differentiating between baseband and passband signals. A baseband signal has a spectral magnitude that is nonzero only for frequencies around origin ($F=0$) and negligible elsewhere. An example spectral plot for a PAM waveform is shown below for 500 2-PAM symbols shaped by

One of the drawbacks of an OFDM waveform is its high Peak to Average Power Ratio (PAPR). This high PAPR arises from the fact that a set of $N$ QAM symbols are taken into time domain through an inverse Fourier Transform (iFFT) operation that basically generates a combination of complex sinusoids scaled by those symbols. Due to the variations between the symbol values and the sinusoids with different frequencies, the output waveform can have a large variance in amplitudes. This reduces the power amplifier efficiency that results in faster battery drainage in a mobile terminal. The effect on base station