In an earlier post, it was mentioned that delta modulator without the quantizer is identical to convolving an input sequence with . Let us first try to validate that thought using a small MATLAB example and using the delta modulator circuit shown in Figure 9.13a of DSP-Proakis [1]. % delta modulation xn = sin(2*pi*1/64*[0:63]); xhatn…
Long back in time we discussed the BER (bit error rate) for BPSK modulation in a simple AWGN channel (time stamps states August 2007). Almost an year back! It high time we discuss the BER for BPSK in a Rayleigh multipath channel. In a brief discussion on Rayleigh channel, wherein we stated that a circularly…
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
We have discussed quite a few receiver structures for a 2×2 MIMO channel namely, (a) Zero Forcing (ZF) equalization (b) Minimum Mean Square Error (MMSE) equalization (c) Zero Forcing equalization with Successive Interference Cancellation (ZF-SIC) (d) ZF-SIC with optimal ordering and (e) MIMO with MMSE SIC and optimal ordering From the above receiver structures, we…
In a previous post (here), we looked at using CORDIC (Co-ordinate Rotation by DIgital Computer) for understanding how a complex number can be rotated by an angle without using actual multipliers. Let us know try to understand how we can use CORDIC for finding the phase and magnitude of a complex number. Basics The CORDIC…
In this post, let us evaluate the impact of frequency offset resulting in Inter Carrier Interference (ICI) while receiving an OFDM modulated symbol. We will first discuss the OFDM transmission and reception, the effect of frequency offset and later we will define the loss of orthogonality and resulting signal to noise ratio (SNR) loss due…
Question 39 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q39. The signal as shown is applied both to a phase modulator (with as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency. The ratio for the same maximum phase deviation is,…
An earlier post we discussed hard decision decoding for a Hamming (7,4) code and simulated the the bit error rate. In this post, let us focus on the soft decision decoding for the Hamming (7,4) code, and quantify the bounds in the performance gain.
From the previous posts on Linear Regression (using Batch Gradient descent, Stochastic Gradient Descent, Closed form solution), we discussed couple of different ways to estimate the parameter vector in the least square error sense for the given training set. However, how does the least square error criterion work when the training set is corrupted by…
In problem 9.14 of DSP-Proakis, the objective is to analyze the effect of zero-order interpolation and first-order interpolation to double the number of samples in the sinusoidal while keeping the sampling frequency unchanged. My take: The first part of the problem (a) is to generate the sequence having half the frequency of . For zero-order…
In signal processing blocks like power estimation used in digital communication, it may be required to represent the estimate in log scale. This post explains a simple linear to log conversion scheme proposed in the DSP Guru column on DSP Trick: Quick-and-Dirty Logarithms. The scheme makes implementation of a linear to log conversion simple and…
This is the second post in the series aimed at developing a better understanding of Shannon’s capacity equation. In this post let us discuss the bounds on communication given the signal power and bandwidth constraint. Further, the following writeup is based on Section 12.6 from Fundamentals of Communication Systems by John G. Proakis, Masoud Salehi
In May 2008, we derived the theoretical symbol error rate for a general M-QAM modulation (in Embedded.com, DSPDesignLine.com and dsplog.com) under Additive White Gaussian Noise. While re-reading that post, felt that the article is nice and warrants a re-run, using OFDM as the underlying physical layer. This post discuss the derivation of symbol error rate for a general…
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…