## A Quadrature Signals Tutorial: Complex, But Not Complicated

Introduction Quadrature signals are based on the notion of complex numbers and perhaps no other topic causes more heartache for newcomers to DSP than these numbers and their strange terminology of j operator, complex, imaginary, real, and orthogonal. If you're a little unsure of the physical meaning of complex numbers and the j = √-1 operator, don't feel bad because you're in good company. Why even Karl Gauss, one the world's greatest mathematicians, called the j-operator the "shadow of...

## Understanding the 'Phasing Method' of Single Sideband Demodulation

There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are:

- synchronous detection,
- phasing method,
- Weaver method, and
- filtering method.

Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION'...

## Understanding and Relating E_{b}/N_{o}, SNR, and other Power Efficiency Metrics

Introduction

Evaluating the performance of communication systems, and wireless systems in particular, usually involves quantifying some performance metric as a function of Signal-to-Noise-Ratio (SNR) or some similar measurement. Many systems require performance evaluation in multipath channels, some in Doppler conditions and other impairments related to mobility. Some have interference metrics to measure against, but nearly all include noise power as an impairment. Not all systems are...

## Some Observations on Comparing Efficiency in Communication Systems

IntroductionEngineering is usually about managing efficiencies of one sort or another. One of my favorite working definitions of an engineer says, "An engineer is somebody who can do for a nickel what any damn fool can do for a dollar." In that case, the implication is that the cost is one of the characteristics being optimized. But cost isn't always the main efficiency metric, or at least the only one. Consider how a common transportation appliance, the automobile, is optimized...

## Implementing a full-duplex UART using the TMS320VC33 serial port

Although the TMS320VC33 serial port was designed to be used as a synchronous port, it can also be used as an asynchronous port under software control. This post describes the hardware and software needed to use a TMS320VC33 serial port as a full-duplex UART port. A schematic diagram and a lengthy code listing are provided to illustrate the solution. This note discusses the implementation of an interrupt-driven, full-duplex, asynchronous serial interface, 9600-baud UART with 8 data bits, 1...

## A multiuser waterfilling algorithm

Hello,this blog entry documents a code snippet for a multi-user waterfilling algorithm. It's heuristic and relatively straightforward, making it easy to implement additional constraints or rules.I rewrote parts of it to improve readability, but no extensive testing took place afterwards. Please double-check that it does what it promises.

Introduction to multiuser waterfilling.Background information can be found for example in the presentation from Yosia Hadisusanto,

## Radio Frequency Distortion Part II: A power spectrum model

SummaryThis article presents a ready-to-use model for nonlinear distortion caused by radio frequenfcy components in wireless receivers and linear transmitters. Compared to the similar model presented in my earlier blog entry, it operates on expectation values of the the power spectrum instead of the signal itself: Use the signal-based model to generate distortion on a signal, and the one from this article to directly obtain the power spectrum much more efficiently.In...

## Understanding Radio Frequency Distortion

OverviewThe topic of this article are the effects of radio frequency distortions on a baseband signal, and how to model them at baseband. Typical applications are use as a simulation model or in digital predistortion algorithms.

IntroductionTransmitting and receiving wireless signals usually involves analog radio frequency circuits, such as power amplifiers in a transmitter or low-noise amplifiers in a receiver.Signal distortion in those circuits deteriorates the link quality. When...

## Frequency Dependence in Free Space Propagation

Introduction

It seems to be fairly common knowledge, even among practicing professionals, that the efficiency of propagation of wireless signals is frequency dependent. Generally it is believed that lower frequencies are desirable since pathloss effects will be less than they would be at higher frequencies. As evidence of this, the Friis Transmission Equation[i] is often cited, the general form of which is usually written as:

Pr = Pt Gt Gr ( λ / 4πd )2 (1)

where the...

## Pulse Shaping in Single-Carrier Communication Systems

Some common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral shaping", etc. Some of the confusion comes from the use of terms like "matched filter" which has a broader meaning in the more general field of signal processing or detection theory. Likewise "Raised Cosine" has a different meaning or application in this...

## Amplitude modulation and the sampling theorem

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.

Convolution...

## Some Observations on Comparing Efficiency in Communication Systems

IntroductionEngineering is usually about managing efficiencies of one sort or another. One of my favorite working definitions of an engineer says, "An engineer is somebody who can do for a nickel what any damn fool can do for a dollar." In that case, the implication is that the cost is one of the characteristics being optimized. But cost isn't always the main efficiency metric, or at least the only one. Consider how a common transportation appliance, the automobile, is optimized...

## There and Back Again: Time of Flight Ranging between Two Wireless Nodes

With the growth in the Internet of Things (IoT) products, the number of applications requiring an estimate of range between two wireless nodes in indoor channels is growing very quickly as well. Therefore, localization is becoming a red hot market today and will remain so in the coming years.

One question that is perplexing is that many companies now a days are offering cm level accurate solutions using RF signals. The conventional wireless nodes usually implement synchronization...

## Simulink simulation of SSB modulation and demodulation

Simulink simulation of SSB modulation and demodulation

## Polar Coding Notes: A Simple Proof

For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.

Mrs. Gerber’s Lemma

Mrs. Gerber’s Lemma provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...

## Implementing a full-duplex UART using the TMS320VC33 serial port

Although the TMS320VC33 serial port was designed to be used as a synchronous port, it can also be used as an asynchronous port under software control. This post describes the hardware and software needed to use a TMS320VC33 serial port as a full-duplex UART port. A schematic diagram and a lengthy code listing are provided to illustrate the solution. This note discusses the implementation of an interrupt-driven, full-duplex, asynchronous serial interface, 9600-baud UART with 8 data bits, 1...

## Radio Frequency Distortion Part II: A power spectrum model

SummaryThis article presents a ready-to-use model for nonlinear distortion caused by radio frequenfcy components in wireless receivers and linear transmitters. Compared to the similar model presented in my earlier blog entry, it operates on expectation values of the the power spectrum instead of the signal itself: Use the signal-based model to generate distortion on a signal, and the one from this article to directly obtain the power spectrum much more efficiently.In...

## Analytic Signal

In communication theory and modulation theory we always deal with two phases: In-phase (I) and Quadrature-phase (Q). The question that I will discuss in this blog is that why we use two phases and not more.

Any real band-limited signal along with its Hilbert transformed pair form an analytic signal. We normally use the analytic signal for modulation. A modulated signal is actually a carrier or the sine signal that one attribute of it is changing with time which is our signal....

## A multiuser waterfilling algorithm

Hello,this blog entry documents a code snippet for a multi-user waterfilling algorithm. It's heuristic and relatively straightforward, making it easy to implement additional constraints or rules.I rewrote parts of it to improve readability, but no extensive testing took place afterwards. Please double-check that it does what it promises.

Introduction to multiuser waterfilling.Background information can be found for example in the presentation from Yosia Hadisusanto,

## Off Topic: Refraction in a Varying Medium

IntroductionThis article is another digression from a better understanding of the DFT. In fact, it is a digression from DSP altogether. However, since many of the readers here are Electrical Engineers and other folks who are very scientifically minded, I hope this article is of interest. A differential vector equation is derived for the trajectory of a point particle in a field of varying index of refraction. This applies to light, of course, but since it is a purely theoretical...

## Understanding Radio Frequency Distortion

OverviewThe topic of this article are the effects of radio frequency distortions on a baseband signal, and how to model them at baseband. Typical applications are use as a simulation model or in digital predistortion algorithms.

IntroductionTransmitting and receiving wireless signals usually involves analog radio frequency circuits, such as power amplifiers in a transmitter or low-noise amplifiers in a receiver.Signal distortion in those circuits deteriorates the link quality. When...

## Amplitude modulation and the sampling theorem

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.

Convolution...

## A multiuser waterfilling algorithm

Hello,this blog entry documents a code snippet for a multi-user waterfilling algorithm. It's heuristic and relatively straightforward, making it easy to implement additional constraints or rules.I rewrote parts of it to improve readability, but no extensive testing took place afterwards. Please double-check that it does what it promises.

Introduction to multiuser waterfilling.Background information can be found for example in the presentation from Yosia Hadisusanto,

## Radio Frequency Distortion Part II: A power spectrum model

SummaryThis article presents a ready-to-use model for nonlinear distortion caused by radio frequenfcy components in wireless receivers and linear transmitters. Compared to the similar model presented in my earlier blog entry, it operates on expectation values of the the power spectrum instead of the signal itself: Use the signal-based model to generate distortion on a signal, and the one from this article to directly obtain the power spectrum much more efficiently.In...

## There and Back Again: Time of Flight Ranging between Two Wireless Nodes

With the growth in the Internet of Things (IoT) products, the number of applications requiring an estimate of range between two wireless nodes in indoor channels is growing very quickly as well. Therefore, localization is becoming a red hot market today and will remain so in the coming years.

One question that is perplexing is that many companies now a days are offering cm level accurate solutions using RF signals. The conventional wireless nodes usually implement synchronization...

## Implementing a full-duplex UART using the TMS320VC33 serial port

Although the TMS320VC33 serial port was designed to be used as a synchronous port, it can also be used as an asynchronous port under software control. This post describes the hardware and software needed to use a TMS320VC33 serial port as a full-duplex UART port. A schematic diagram and a lengthy code listing are provided to illustrate the solution. This note discusses the implementation of an interrupt-driven, full-duplex, asynchronous serial interface, 9600-baud UART with 8 data bits, 1...

## Analytic Signal

In communication theory and modulation theory we always deal with two phases: In-phase (I) and Quadrature-phase (Q). The question that I will discuss in this blog is that why we use two phases and not more.

Any real band-limited signal along with its Hilbert transformed pair form an analytic signal. We normally use the analytic signal for modulation. A modulated signal is actually a carrier or the sine signal that one attribute of it is changing with time which is our signal....

## GPS - some terminology!

Hi!

For my first post, I will share some information about GPS - Global Positioning System. I will delve one step deeper than a basic explanation of how a GPS system works and introduce some terminology.

GPS, like we all know is the system useful for identifying one's position, velocity, & time using signals from satellites (referred to as SV or space vehicle in literature). It uses the principle of trilateration (not triangulation which is misused frequently) for...

## Polar Coding Notes: A Simple Proof

For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.

Mrs. Gerber’s Lemma

Mrs. Gerber’s Lemma provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...

## Off Topic: Refraction in a Varying Medium

IntroductionThis article is another digression from a better understanding of the DFT. In fact, it is a digression from DSP altogether. However, since many of the readers here are Electrical Engineers and other folks who are very scientifically minded, I hope this article is of interest. A differential vector equation is derived for the trajectory of a point particle in a field of varying index of refraction. This applies to light, of course, but since it is a purely theoretical...