In the previous post on transmit filtering using Nyquist pulse, we had briefly learned that the information symbol with a symbol period can be transmitted without inter symbol interference (ISI) by using Nyquist pulse, . The resultant waveform is ideally bandlimited to frequencies from Hz to Hz. However, in typical transmission schemes, we do not…
For handling class imbalance, multiple stratetgies have emerged. Post covers Weighted Cross Entropy, Focal Loss, Assymetric Loss, Class Balanced Loss and Logit Adjusted Loss.
In previous posts, we had discussed equalization of a 2×2 MIMO channel with Zero Forcing (ZF) equalization and later, Zero Forcing equalization with successive interference cancellation (ZF-SIC). In this post, we will explore a variant of ZF-SIC called Zero Forcing Successive Interference Cancellation with optimal ordering. We will assume that the channel is a flat…
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…
Last week, I received an email from Mr. Kishore. He was wondering about the physical significance of negative frequency. Does negative frequency really exist? Though I have seen conflicting views on the net (thread in complextoreal.com, thread in comp.dsp), my perspective is that negative frequency exist. The concept of negative frequency helps me a lot…
In the previous post on I-Q modulator and de-modulator, we had briefly mentioned that the a baseband PAM transmission can be modelled as , where is the symbol period, is the symbol to transmit, is the transmit filter, is the symbol index and is the output waveform. In this post, the objective is to understand…
Wishing all the readers of dsplog.com a great year 2010 ! Its been a mixed year for dsplog. Some key milestones a) Crossing 1000 subscribers with 1100+ comments in March 2009 b) Crossing 100 posts with 2200 subscribers and 2600+ comments in October 2009 c) As I write this, we have 102 posts with 2603…
In the past, we had discussed BER for BPSK in flat fading Rayleigh channel and BER for BPSK in a frequency selective channel using Zero Forcing Equalization. In this post, lets discuss a frequency selective channel with the use of Minimum Mean Square Error (MMSE) equalization to compensate for the inter symbol interference (ISI). For…
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,…
When QAM (Quadrature Amplitude Modulation) is used, typically one may find a scaling factor associated with the constellation mapping operation. It may be reasonably obvious that this scaling factor is for normalizing the average energy to one. This post attempts to compute the average energy of the 16-QAM, 64-QAM and M-QAM constellation (where is a…
Question 47 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q47. Given that and , the value of is (A) (B) (C) (D) Solution To answer this question, we need to refer to Cayley Hamilton Theorem. This is discussed briefly in Pages 310-311 of Introduction to Linear Algebra, Glibert Strang (buy…
This is a guest post by Jose Antonio Urigüen who is an Electrical and Electronic Engineer currently studying an MSc in Communications and Signal Processing at Imperial College in London. This guest post has been created due to his own curiosity when reviewing some concepts of BER for BPSK in Rayleigh channnel published in the…
The previous post on phase noise discussed about finding the root mean square phase noise for a given phase noise profile. In this post let us discuss about the impact of phase noise on the error vector magnitude (evm) of a transmit symbol.
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…