Category Archives: Fundamentals

The basic building blocks.

5G Data Rates and Shannon Capacity

Recently I came across a post from T-Mobile in which they claim to have achieved a download speed of 5.6 Gbps over a 100 MHz channel resulting in a Spectral Efficiency of more than 50 bps/Hz. This was achieved in an MU-MIMO configuration with eight connected devices having an aggregate of 16 parallel streams i.e. two parallel streams per device. The channel used for this experiment was the mid-band frequency of 2.5 GHz.

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5G Rollout in the USA: Long Way to Go

There is a 3 way race for 5G leadership in the US between T-Mobile(+Sprint), Verizon and AT&T. There are competing claims for the number of 5G subscribers, coverage area and download speeds. But let us look where the 5G industry stands today compared to the expectations a few years back. More than 80% of US population lives in urban areas which comprise of 2% of the total land area of about 10 million squared kilometers. That is 80% of the population lives in an area of about 200,000 squared kilometers.

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Near Field of an Antenna

The Electromagnetic Radiation from an antenna, particularly dipole antenna, has been studied in great detail. The mathematical framework proposed by Maxwell has stood the test of time and theoretical concepts have been verified through physical measurements. But the behavior of Electromagnetic (EM) waves close to the radiating antenna is not that well understood. This region that extends to about a wavelength from the antenna is called Near Field, as opposed to Far Field, which extends further out. The Near Field is further divided into Reactive Near Field and Radiative Near Field.

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Phase Lock Loop – Explained

Phase Lock Loops (PLLs) are an important component of communication systems, where they are used for carrier phase and frequency synchronization. They are also used in test and measurement equipment such as in Signal Generators and Vector Network Analyzers (VNAs) for frequency synthesis. Although not discussed here in detail but PLLs are also quite adept at generating multiples of a base frequency e.g. if you have a reference signal at 10MHz then a PLL can be used to generate a 100MHz signal (X=10) or even a 1GHz signal (X=100). In fact, you can also divide the frequency to get low frequency signals. In the first case the feedback frequency is divided by X and in the second case the reference or input frequency is divided by X.

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KAY’s Single Frequency Estimator

As previously discussed, finding the frequency of a complex sinusoid embedded in noise is a classical problem in Signal Processing. The problem is compounded by the fact that number of samples available is usually quite small. So far, we have discussed Zero Crossing, FFT, MUSIC and ESPRIT methods of frequency estimation. Zero Crossing method is simplest of the above four but it can detect only one sinusoid at a time. Advantage of Zero Crossing method is that it is computationally not that complex. It does not require complex matrix manipulations as some of the other methods do.

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A Comparison of FFT, MUSIC and ESPRIT Methods of Frequency Estimation

As discussed in previous posts it is frequently required in communications and signal processing to estimate the frequency of a signal embedded in noise and interference. The problem becomes more complicated when the number of observations (samples) is quite limited. Typically, the resolution in the frequency domain is inversely proportional to the window size in the time domain. Sometimes the signal is composed of multiple sinusoids where the frequency of each needs to be estimated separately. Simple techniques such as Zero Crossing Estimator fail in such a scenario.  Even some advanced techniques such as MATLAB function “pwelch” fail to distinguish closely spaced sinusoids.

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Frequency Estimation Using Zero Crossing Method

A sinusoidal signal is the most fundamental type of signal that exists in communication systems, power systems, navigation systems etc. It is controlled by three parameters which are the amplitude, phase and frequency. The last two, that is phase and frequency, are interconnected. As discussed in my previous post Instantaneous Frequency (IF) is nothing but the rate of change of phase. This can be mathematically described as:


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What is Energy Harvesting

Conventional battery powered systems can be impractical, expensive, or have negative environmental impacts. Energy harvesting (EH) offers a potential solution to these problems. Through ambient sources such as solar, vibrational, thermal, and RF, self-sustaining IoT devices can be designed. These devices can be easily implemented in wearables, medical implants, and infrastructure. Companies such as TI and ADI have developed power management systems for EH and consumer products already exist. These products continue to increase in efficiency and practicality every year.  

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Pulse Amplitude Modulation Symbol Error Rate in AWGN

Pulse Amplitude Modulation (PAM) is a one dimensional or in other words real modulation. Simply put it is an extension of BPSK with M amplitude levels instead of two. This can be a bit confusing because BPSK can be looked at as a phase modulation and its natural extension must be QPSK or 8-PSK modulations. To remove this ambiguity lets call M-PAM an extension of simple amplitude modulation but with M levels. In the discussion below we consider M=4 but then extend it to the general case of M=2k (k=1,2,3…).

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Beyond Massive MIMO

Recently Björnson and Marzetta in their publication on Antenna Arrays [1] discussed five possible future research directions. In their opinion Massive MIMO is no longer a theoretical concept and it is already being adopted in the industry. It is not uncommon to find 64 element antenna arrays being deployed in wireless communication systems. So we now need to look beyond Massive MIMO or MaMIMO as it is popularly referred to. Here are three possible future research directions that we find most interesting.

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