In previous posts, we have discussed convolutional codes with Viterbi decoding (hard decision, soft decision and with finite traceback). Let us know discuss a block coding scheme where a group of information bits is mapped into coded bits. Such codes are referred to as codes. We will restrict the discussion to Hamming codes, where 4…
In the post on Viterbi decoder and soft input Viterbi decoder, we discussed a convolutional encoding scheme with rate 1/2, constraint length and having generator polynomial and having generator polynomial . If the number of uncoded bits is , then the number of coded bits at the output of the convolutional encoder is . Decoding…
Considering a typical scenario where there might exist a small phase offset between local oscillator between the transmitter and receiver. Figure 1 : Transmitter receiver with constant phase offset In such cases, it might be desirable to estimate and track the phase offset such that the performance of the receiver does not degrade.
Following a brief discussion with my friend Mr. Rethnakaran Pulikkoonattu on phase noise profiles, he pointed me to his write up on Oscillator Phase Noise and Sampling Clock Jitter . In this post, we will discuss the math behind integrating the phase noise power spectral density (in dBc/Hz) to find the root mean square jitter value.
Those who are regular visitors to dsplog.com might have noticed the small FeedBurner chicklet on the side showing subscriber count showing 1000+ subscribers. Its a nice milestone to reach, one that looked so distant when I wrote the first post stating the objective of this blog on 26th February 2007. We now have around 86…
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 post on OFDM (here), we have understood that an OFDM waveform is made of sum of multiple sinusoidals (also called subcarriers) each modulated independently. In this post, let us try to understand the estimation of frequency offset in a typical OFDM receiver (using the short preamble specified per IEEE 802.11a specification as…
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…
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…
Post describes about the need for I-Q modulation by comparing the spectral efficiency of passband PAM and passband QAM.
The IEEE 802.11a specifications are used by many to understand a wireless communication link built using OFDM. In this post, I have put together a set of 10 multiple choice questions based on 802.11a specifications. The questions are on the building blocks in 802.11a specifications, preamble structure and so on. Upon completion of the quiz,…
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,…
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 simulation scripts show good agreement with the derived theoretical results. With Binary Phase Shift Keying (BPSK), the binary digits 1…
The post on MIMO with Zero Forcing equalizer discussed a probable way of equalizing a 2×2 MIMO channel. The simulated results with the 2×2 MIMO system with zero forcing equalizer showed matching results as obtained in for a 1×1 system for BPSK modulation in Rayleigh channel. In this post, we will try to improve the…