OFDM found optimal for certain signal timing patterns in communications
On the Optimality of OFDM for Aperiodic Ranging
Information Theory
Summary
The paper looks at how to best arrange signals in communication systems so that overlapping signals don’t interfere much with one another, focusing on something called autocorrelation sidelobes. The researchers find that a popular method called OFDM works perfectly only when certain timing conditions related to the signal length are met. They also prove that no single arrangement can minimize interference for all timing shifts when the signal length is three or more. This helps reveal exactly when OFDM is the best choice and when it is not for reducing signal interference.
What this means in practice
- •For wireless communication engineers: Design signaling schemes to minimize signal interference when the signal length and timing lags meet specific divisibility conditions.
- •For radar system designers: Apply the OFDM modulation to optimize signal clarity in ranging systems for particular timing setups where lags divide signal length.
A theory result. No direct application yet.
Authors
Yifeng Xiong, Fan Liu, Ya-Feng Liu, Shi Jin, Jianhua Zhang
Abstract
We study the expected aperiodic autocorrelation sidelobes of random communication symbols transmitted through a unitary modulation matrix. We consider proper sub-Gaussian constellations, namely those with fourth absolute moment $μ_4<2$ and zero pseudo-variance, including the commonly used uniform square quadrature amplitude modulation (QAM) and uniform phase-shift keying (PSK) constellations. For every prescribed lag, we determine the exact minimum expected sidelobe level (ESL) and a unitary modulation attaining it by applying a normalized inverse discrete Fourier transform (IDFT) separately on each chain of sample indices spaced by that lag. The full orthogonal frequency division modulation (OFDM) modulation attains this minimum if and only if the lag divides the block length $N$. Combining this criterion with the complete characterization of the minimizers at lag one, we show that a unitary modulation minimizes the ESL simultaneously over the first $r$ positive lags, called the prefix $\{1,\ldots,r\}$ with $1\le r<N$, if and only if every lag in that prefix divides $N$. In particular, simultaneous optimality over all positive lags is impossible for $N\ge 3$. We also prove that OFDM globally minimizes the partial expected integrated sidelobe level (EISL), defined as the sum of the ESLs over a selected subset of positive lags, for every such prefix. This also resolves the full EISL conjecture when $r=N-1$.