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Data symbols riding on the subcarriers experience a rotation due to residual carrier frequency offset and sampling frequency offset

August 29, 2022 Wireless/SDR

Effect of a Sampling Clock Offset on an OFDM Waveform

In an earlier article on the impact of a sampling clock offset on a single-carrier waveform, we explained the nature of a Sampling Clock Offset (SCO), i.e., a difference in sampling clock frequency between the Tx and the Rx. This is also known as a symbol timing frequency offset. The meaning of a sampling clock offset for a slow Rx clock that skips some samples within an interval is visually demonstrated in the figure below. In the context of OFDM systems, a previous article describes how the normalized Carrier Frequency Offset (CFO) and the normalized Symbol Timing Offset (STO) affect

August 1, 2022 DSP

Spectral Shift without any Multiplications

One of the great advantages of Digital Signal Processing (DSP) is an unexpected simplification of operations in seemingly complicated scenarios. See the Cascade Integrator Comb (CIC) filters for how to accomplish the task of sample rate conversion along with filtering with minimal resources. As another example, in wireless communications and many other applications, a frequency translation is often required in which the spectrum of a signal centered at a particular frequency needs to be moved to another frequency. From the properties of Fourier Transform, a shift by frequency $\omega_0=2\pi F_0$ requires sample-by-sample multiplication with a complex sinusoid $e^{j\omega_0 t}$. \[

Reconfigurable Intelligent Surfaces (RIS) concept

July 25, 2022 DSP / Wireless/SDR

Reconfigurable Intelligent Surfaces (RIS) – A Tutorial

For each generation of cellular networks, there is a significant jump in data rates due to the rising demand and novel use cases from emerging applications and associated ecosystems. Some examples in 6G networks are driverless and collaborative transportation, joint communication, localization and sensing, e-health and tactile Internet. Therefore, at the start of each concept-to-deployment cycle, engineers and researchers propose, evaluate and experiment with new ideas, preferably one or two disruptive technologies that can help them meet their targets. For 5G systems, these technologies appeared in the form of a large number of antennas (massive MIMO) and usage of higher

Discrete Fourier Transform (DFT) of a DFT-even sequence

July 11, 2022 DSP

The Beauty of Symmetry in Fourier Transform

In 1978, Fred Harris was a relatively unknown faculty member at the San Diego State University when he published his landmark paper titled On the use of windows for harmonic analysis with the discrete Fourier transform. That paper made him a superstar in DSP community. It presented a brief overview of signal windows and their impact on the detection of harmonic signals in the presence of broad-band noise and nearby harmonic interference. More importantly, he pointed out several common errors in the application of windows when used in the context of Discrete Fourier Transform (DFT). Today I am going to

Computation of the metric involves a correlation sum at a time difference of half symbol duration

June 13, 2022 Wireless/SDR

Timing Synchronization in OFDM Systems

Orthogonal Frequency Division Multiplexing (OFDM) has been the vehicle driving most high rate wireless communication systems in the world today. Some of the notable examples are our WiFi, 4G and 5G technologies. See the interesting LoRa PHY for modulation techniques based on frequency shift – chirp spread spectrum that utilize many of the concepts from OFDM for algorithm design. As a background, we have also discussed before the impact of a timing error on an OFDM signal. It was observed that an integer timing offset does have affect the performance as long as it within certain boundaries. A fractional timing