Signal Processing for Communication Systems
Mathuranathan If squares of k independent standard normal random variables are added, it gives rise to central Chi-squared distribution with ‘k’ degrees of freedom. Instead, if squares of k independent normal random variables with non-zero means are added, it gives rise to non-central Chi-squared distribution. Non-central Chi-square distribution is related to Ricean distribution, whereas the central … Read more
A random variable is always associated with a probability distribution. When the random variable undergoes mathematical transformation the underlying probability distribution no longer remains the same. Consider a random variable whose probability distribution function (PDF) is a standard normal distribution ( and ). Now, if the random variable is squared (a mathematical transformation), then the … Read more
Uniform random variables are used to model scenarios where the expected outcomes are equi-probable. For example, in a communication system design, the set of all possible source symbols are considered equally probable and therefore modeled as a uniform random variable. The uniform distribution is the underlying distribution for an uniform random variable. A continuous uniform … Read more
As discussed in the introduction to estimation theory, the goal of an estimation algorithm is to give an estimate of random variable(s) that is unbiased and has minimum variance. This criteria is reproduced here for reference In the above equations f0 is the transmitted carrier frequency and is the estimated frequency based on a set … Read more
A generic complex baseband simulation technique, to simulate all M-ary phase shift keying (M-PSK) modulation techniques is given here. The given simulation code is very generic, and it plots both simulated and theoretical symbol error rates for all MPSK modulation techniques. M-ary phase shift keying (M-PSK) modulation In phase shift keying, all the information gets … Read more
Key focus: Derive BPSK BER (bit error rate) for optimum receiver in AWGN channel. Explained intuitively step by step. BPSK modulation is the simplest of all the M-PSK techniques. An insight into the derivation of error rate performance of an optimum BPSK receiver is essential as it serves as a stepping stone to understand the … Read more
In simple words, The Q-function gives the probability that a random variable from a normal distribution will exceed a certain threshold value. The erf function gives the probability that a normally distributed variable will fall within a certain range. Q function Q functions are often encountered in the theoretical equations for Bit Error Rate (BER) … Read more
Key focus: Understand the basics of estimation theory with a simple example in communication systems. Know how to assess the performance of an estimator. A simple estimation problem : DSB-AM receiver In Double Side Band – Amplitude Modulation (DSB-AM), the desired message is amplitude modulated over a carrier of frequency f0. The following discussion is … Read more
In GMSK modulation (used in GSM and DECT standard), a GMSK signal is generated by shaping the information bits in NRZ format through a Gaussian Filter. The filtered pulses are then frequency modulated to yield the GMSK signal. GMSK modulation is quite insensitive to non-linearities of power amplifier and is robust to fading effects. But … Read more
Prerequisite: Sampling theorem – baseband sampling Intermediate Sampling or Under-Sampling A signal is a bandpass signal if we can fit all its frequency content inside a bandwidth . Bandwidth is simply the difference between the lowest and the highest frequency present in the signal. “In order for a faithful reproduction and reconstruction of a bandpass … Read more