In the recent past, we have discussed three receive diversity schemes – Selection combining, Equal Gain Combining and Maximal Ratio Combining. All the three approaches used the antenna array at the receiver to improve the demodulation performance, albeit with different levels of complexity. Time to move on to a transmit diversity scheme where the information…
This is the first 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…
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…
After a gap of around 7 months, we decided to migrate to a new template (recall, last time we changed was in May 2008). The template which we decided to use is designed by Elegant Themes. They have a wide array of themes and I chose to use the Who’s Who theme.
Oflate, I am getting frequent requests for bit error rate simulations using OFDM (Orthogonal Frequency Division Multiplexing) modulation. In this post, we will discuss a simple OFDM transmitter and receiver, find the relation between Eb/No (Bit to Noise ratio) and Es/No (Signal to Noise ratio) and compute the bit error rate with BPSK.
The post on IQ imbalance in transmitter, briefly discussed the effect of amplitude and phase imbalance and also showed that IQ imbalance results in spectrum at the image frequency. In this article, we will quantify the power of the image with respect to the desired tone (also known as IMage Rejection Ratio IMRR) for different…
The definition of Toeplitz matrix from [1] is: A matrix is said to be Toeplitz if the elements are determined completely by the difference .
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 this post, let us try to derive the symbol error rate for 16-PSK (16-Phase Shift Keying) modulation. Consider a general M-PSK modulation, where the alphabets, are used. (Refer example 5-38 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]) Figure: 16-PSK constellation plot
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 Problem 4.36 of DSP-Proakis [1], the task is to provide insights into harmonic distortion which may be present in practical sinusoidal generators. Consider the signal , where . My take: The discrete time signal of fundamental period can consist of frequency components separated by radians or cycles (Refer Section4.2 in [1]). The Fourier series…
The post covers various neural network based word embedding models. Starting from the Neural Probabilistic Language Model from Bengio et al 2003, then reduction of complexity using Hierarchical softmax and Noise Contrastive Estimation. Further works like CBoW, GlOVe, Skip Gram and Negative Sampling which helped to train on much higher data.
In a previous post, we had discussed a 2×2 MIMO transmission using BPSK modulation in Rayleigh channel with a Zero Forcing equalizer. 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…
In the post on transmit pulse shaping filter, we had discussed pulse shaping using rectangular and sinc. In this post we will discuss about optimal receiver structure when pulse shaping is used at the transmitter. The receiver structure is also called as matched filter. For the discussion, we will assume rectangular pulse shaping, the channel…