Chirp-based Multicarrier Communication
Motivations
The motivation is a simple one, what are the tradeoffs associated with using chirp-based multicarrier systems as supposed to sinusoidal ones like OFDM. What do we gain at the cost of linearity?
For instance, when there is narrow band interference, OFDM on principle will suffer great BER loss due to decoding errors dominated by subcarriers of a certain frequency band. However, chirps do not have such concern as all subchirps occupy the entire bandwidth and theoretically errors caused by narrow band interference are propogated across subchirps, thereby significantly improving performance.
Model
There are a number of chirp models in literature. We restrict the scope of chirp signals to the action of a special linear group
Each matrix uniquely defines an integral transform in the following way:
After some algebra and assumptions, the resulting generalizing transform is in optics referred to as linear canonical transform, in communication it’s called discrete affine Fourier transform. Assume
Problems
From now, the research problems branch into many directions. A number of transforms commonly used in wireless and optical communication can be represented accordingly. DFT, used as the transform basis for OFDM, is characterized by the
My research focus majorly on OCDM-based systems with
- Demonstration that the peak-to-average power ratio (PAPR) and capacity of DAFT-based multicarrier equivalent channels are independent of the basis used. The capacity and probability distribution of PAPR are both derived and simulated.(Thesis)
- Detailed analysis of the bit error rate (BER) performance of chirp multicarrier systems through diversity and piece-wise error probability (PEP) analysis. Our study reveals that the chirp rate significantly influences multipath diversity, coding gains, and error performance under different equalization schemes. We characterize diversity in relation to the chirp basis and propose algorithms to enhance BER performance and reduce equalization complexity.((Guo et al., 2024))
- Impact of carrier frequency offset (CFO) on chirp multicarrier systems. Our analysis includes the derivation of mutual information and BER performance under CFO. Additionally, we study CFO estimation, compensation, and related identifiability issues for chirp systems. We propose algorithms to mitigate these challenges effectively.((Guo et al., 2024))
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