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 this post lets discuss a closed-loop transmit diversity scheme, where the transmitter has the knowledge of the channel. As there is a feedback path required from the receiver, to communicate the channel seen by the receiver to the transmitter, the scheme is called closed-loop transmit diversity scheme. Recall that the transmit diversity using Space…
In TETRA specifications, one of the modulation technique used is Differential 8 Phase Shift Keying (D8PSK). We will discuss the bit error rate with non-coherent demodulation of D8PSK in Additive White Gaussian Noise (AWGN) channel.
In the previous post on Binary to Gray code conversion for PSK, I had claimed that “for a general M-QAM modulation the binary to Gray code conversion is bit more complicated“. However following a closer look, I realize that this is not so complicated. 🙂 The QAM scenario can be treated as independent PAM modulation…
Equivalence of Moving Average and CIC filter Let me briefly share my understanding on the cascaded integrator comb (CIC) filter, thanks to the nice article. For understanding the cascaded integrator comb (CIC) filter, firstly let us understand the moving average filter, which is accumulation latest samples of an input sequence .
Following discussion of bit error rate (BER) for BPSK and bit error rate for FSK, it may be interesting to move on to discuss a higher order constellation such as Pulse Amplitude Modulation (PAM). Consider that the alphabets used for a 4-PAM is (Refer example 5-34 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]).
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,…
Given that we have discussed symbol error rate probability for a 4-PAM modulation, let us know focus on finding the symbol error probability for a QPSK (4-QAM) modulation scheme. Background Consider that the alphabets used for a QPSK (4-QAM) is (Refer example 5-35 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]). Download free e-Book discussing theoretical and simulated error rates for…
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…
On July30th, 2008 I had sent a request for feedback to 93 subscribers who have opted to receive articles over email. As on 3rd August, I received the response from around 8 persons. Not bad, around 8.5% response. Thanks a lot for the feedback. I will summarize the response from the group and note down…
While browsing through the web for materials on the wireless communication and implementation, found this rich set of articles as part of MIT OPEN COURSEWARE program. The course is from Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
The article gives a quick overview of a simple statistical multipath channel model called Rayleigh fading channel model. Multipath environment In a multipath environment, it is reasonably intuitive to visualize that an impulse transmitted from transmitter will reach the receiver as a train of impulses.
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.