Now we turn out attention towards a topic that causes a lot of confusion for communications and DSP learners: what is the difference between a matched filter and a correlator in a communications receiver? Let us start with the definition of a correlator: A correlator is a device that performs correlation of a received signal with its template within a given window of time. In our context, that window of time is the symbol duration, $T_M$. So a correlator performs the following operations. It takes this sample-by-sample product and sums them together. Next, it samples the output of this accumulation
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Wireless communications and Software Defined Radio (SDR)
Pulse Shaping Filter
In digital logic, a stream of 1s and 0s forms a sequence of rectangular pulses, which can be easily identified at the receiver side by a threshold. In time domain, everything looks nice and perfect. Let us investigate the system characteristics in frequency domain. In a Pulse Amplitude Modulation (PAM) system, the main component that defines the spectral contents of the signal is the pulse shape $p(nT_S)$ at the Tx. We start with our attention towards a simple rectangular pulse shape. Here is a brief outline of what we cover in this article. Table of Contents 1. Spectrum of a
Continue readingComputing Error Rates
Having built a simple digital communication system, it is necessary to know how to measure its performance. As the names say, Symbol Error Rate (SER) and Bit Error Rate (BER) are the probabilities of receiving a symbol and bit in error, respectively. SER and BER can be approximated through simulating a complete digital communication system involving a large number of bits and comparing the ratio of symbols or bits received in error to the total number of bits. Hence, \begin{equation}\label{eqCommSystemSER} \text{SER} = \frac{\text{No. of symbols in error}}{\text{Total no. of transmitted symbols}} \end{equation} and \begin{equation}\label{eqCommSystemBER} \text{BER} = \frac{\text{No. of bits in
Continue readingHow a Frequency Locked Loop (FLL) Works
We saw before how a carrier frequency offset distorts the received signal. Later, we also described the classification of frequency synchronization techniques according to the availability of the symbol timing. Today, we will learn about the workings of a frequency locked loop. Background A Phase Locked Loop (PLL) is a device used to synchronize a periodic waveform with a reference periodic waveform. It is an automatic control system in which the phase of the output signal is locked to the phase of the input reference signal. In the article referred above, we also discussed that for a very small frequency
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