Orthogonal signals with jointly balanced spectra: Application to cdma transmissions

Abstract

This paper presents a technique for generating orthogonal bases of signals with jointly optimized spectra, in the sense that they are made as close as possible. To this end, we propose a new criterion, the minimization of which leads to signals with close energy inside a set of prescribed subbands. Starting with the case of a single subband, we illustrate it by building orthogonal signals with maximum energy concentration in time and in frequency, with the same energy rate outside a fixed frequency interval or a fixed time interval, by resorting to Slepian sequences or Slepian functions, respectively. Then, we present spectrum balancing in a set of frequency intervals. We apply this method to Slepian sequences and Slepian functions, as well as to Walsh-Hadamard codes. On these examples, we point out a number of nice properties of the so-built orthogonal families that are of interest for signaling applications.

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

“…In [21], the author proposes a balancing algorithm that transforms a family of orthogonal signals into another orthogonal family that The low sidelobe level leads to a considerable lowering of grating lobes level. However, the limiting factor of spectrally balanced Walsh-Hadamard codes is that they can only be generated for lengths that are powers of 2 (L = 2 k ).…”

“…However, as in the case of Walsh-Hadamard signals, these sequences have poor correlation properties, which makes them poorly adapted to radar applications. Spectrally balanced versions of Slepian sequences are interesting insofar as they combine Slepian sequences properties and improved correlation properties [21]. An example of Slepian sequences and spectrally balanced ones for a t p B p = 8 is shown in Fig 10 and Using Slepian sequences to encode Costas pulses is interesting since the bandwidth of those sequences can be adapted to the t p ∆f product of the Costas signal according to Eq 10.…”

“…In [21], the author proposes a balancing algorithm that transforms a family of orthogonal signals into another orthogonal family that spans the same subspace, so that the spectra of the signals in the new basis have very close spectra. This is achieved by iteratively balancing the energy of the basis signals in a set of prescribed subbands that span the whole signal bandwidth.…”