Wireless/SDR Archives | Page 6 of 22

Linear interpolation between pilot subcarriers

July 18, 2022 Wireless/SDR

Channel Estimation in OFDM Systems

Channel estimation in single-carrier systems has been described in a previous article. In OFDM systems, each subcarrier acts as an independent channel as long as there is no Inter-Carrier Interference (ICI) left in the synchronized signal. The options of both a training sequence and individual pilots are available for channel estimation and the choice between the two depends on time variation rate of the channel as well as the computational complexity. Many systems acquire the channel through the preamble while employ the pilots for channel tracking. The discussion in this article is mostly based on Ref. [1]. For a simplified

Error Vector Magnitude (EVM) for 1 symbol

May 30, 2022 Wireless/SDR

What is Error Vector Magnitude (EVM)?

Measuring the performance of a digital communication system is not a straightforward task as different impairments have different impacts on the final bit error rate. Error Vector Magnitude (EVM) is a useful metric that helps gauge the impact of all impairments simultaneously from a single value. A Single Modulation Symbol We start with observing a single modulation point at the receive end. Once we establish the baseline error in this scenario, we will combine the effect of all such symbol points into a single number. Assume that a modulation symbol S is represented by a blue constellation point in the

January 25, 2021 Wireless/SDR

On the Link Between Gardner Timing Error Detector and Early-Late Timing Error Detector

This post is written on an advanced topic mainly for practitioners and researchers in the design of wireless systems. For learning about wireless communication systems from a DSP perspective (the idea behind SDRs), I recommend you have a look at my book. F. M. Gardner described his well known Timing Error Detector (TED) — known as Gardner TED — in his often cited article [1]. Gardner was a pioneer in the area of synchronization and Phase Locked Loops (PLL). Later, M. Oerder (a student of Heinrich Meyr) derived this scheme from the maximum likelihood principle in [2]. Heinrich Meyr is

An intuitive way to understand the maximum ratio transmission

November 24, 2021 Wireless/SDR

Maximum Ratio Transmission (MRT)

In Maximum Ratio Combination (MRC), our focus was on combining the signals from multiple antennas at the Rx side. Here, we will see how a similar system can be developed with multiple antennas at the Tx side. As our first consideration, we attempt to replicate the results of Rx diversity in a scenario where there are multiple Tx antennas and a single Rx antenna. This is commonly known as a Multiple-Input Single Output (MISO) system. Assume that there are $N_T$ Tx antennas available and only a single Rx antenna as shown in the figure below. This is a dual problem

Generating multivariate normal random numbers without statistics and machine learning toolbox

April 15, 2025 Wireless/SDR

How to Generate Multivariate Normal Random Numbers in Matlab without Statistics and Machine Learning Toolbox

Generating Additive White Gaussian Noise (AWGN) is an indispensable for simulating communication systems. In some cases, we need to produce sequences from a multivariate normal distribution. The standard way to generate such random sequences in Matlab is to use the function mvnrnd( ). But we need the Statistics and Machine Learning Toolbox for this purpose. However, there is another way of producing multivariate normal random numbers in Matlab without this toolbox. One alternative is to use the randn( ) function along with the Cholesky decomposition of the covariance matrix. The main idea is that when generating multivariate normal random numbers,