This is the second post in the series discussing receiver diversity in a wireless link. Receiver diversity is a form of space diversity, where there are multiple antennas at the receiver. The presence of receiver diversity poses an interesting problem – how do we use ‘effectively‘ the information from all the antennas to demodulate the…
We have discussed about probable transmit pulse shaping filter and have observed that raised cosine filtering filtering allows a simpler implementation, albeit at the cost of increased bandwidth. Let us know understand the eye diagram, which is a useful graphical tool to quantify the degradation of the signal due to filtering. Eye diagram An eye…
From the post on Closed Form Solution for Linear regression, we computed the parameter vector which minimizes the square of the error between the predicted value and the actual output for all values in the training set. In that model all the values in the training set is given equal importance. Let us consider the case where it is known…
Some of us would have used Newton’s method (also known as Newton-Raphson method) in some form or other. The method has quite a bit of history, starting with the Babylonian way of finding the square root and later over centuries reaching the present recursive way of finding the solution. In this post, we will describe…
In this post, let us try to understand Gray codes and their usage in digital communication. Quoting from Wiki entry on Gray code [Gray-Wiki], The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit. In a digital communication system,…
Being not too happy with the speed of the shared hosting, decided to move the blog to an Amazon Elastic Compute Cloud (Amazon EC2) instance. Given this is a baby step, picked up a micro instance running an Ubuntu server and installed Apache web server, MySQL, PHP . After doing a bit of tweaking with this new…
A friend called me up couple of days back with the question – How white is AWGN? I gave him an answer over phone, which he was not too happy about. That got me thinking bit more on the topic and the result is this post – brief write up on thermal noise and it’s…
In this post, we will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER results obtained using Matlab/Octave & Python simulation scripts show good agreement with the derived theoretical results. System Model Transmitter With Binary Phase Shift Keying…
In a previous post (here), we discussed in brief, Orthogonal Frequency Division Multiplexing (OFDM) transmission. Let us know probe bit more into the motivation of cyclic prefix (aka guard interval) associated with each OFDM symbol. What is cyclic prefix? Let us consider one subcarrier (subcarrier +1 specified in IEEE 802.11a specification) alone. In the figure…
The post on thermal noise described the noise produced by resistor ohms over bandwidth at temperature Kelvin. In this post, let us define the noise voltage at the input and output of a resistor network and further use it to define the Noise Figure of such a network.
This post attempts to build further on the MIMO equalization schemes which we have discussed – (a) Minimum Mean Square Error (MMSE) equalization, (b) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) and (c) ZF-SIC with optimal ordering. We have learned that successive interference cancellation with optimal ordering improves the performance with Zero Forcing equalization….
Mr. Lealem Tamirat, in a comment on BER for BPSK in Rayleigh channel, wondered about the performance of an OFDM modulated system in a frequency selective Rayeligh fading channel. My response was that, Though the total channel is a frequency selective channel, the channel experienced by each subcarrier in an OFDM system is a flat…
In DSP-Proakis, I found the problem 2.56 interesting as it provides insight into delta modulation. The task is to show that, where is any discrete time signal and is the unit step function.
Question 24 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q24. Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max[X,Y] is less than 1/2 is (A) 3/4 (B) 9/16 (C) 1/4 (D) 2/3