Design of Truncated Maximum Length Ternary Signals Where Their Squared Versions Have Uniform Even Harmonics

Abstract

The design of pseudo-random maximum length (PRML) ternary signals with properties suitable for identification of generalized quadratic Hammerstein models is considered. For such an application, it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed, with its squared version having odd harmonics suppressed and even harmonics uniform. To date, the only class of signal known to possess such harmonic properties comprises of PRML ternary signals based on Galois field GF(3), and its extension fields. In this note, theoretical conditions for a PRML signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated PRML signals that fulfill the required specifications.Index Terms-Frequency domain design, Hammerstein models, maximum length signals, perturbation signals, pseudo-random signals, system identification.

Iterative channel estimation for multiuser fibre‐wireless uplink exploiting semi‐correlated ternary signals

“…This allows the spectral properties of x(n) to be designed based on those of d(n) since all relevant harmonic properties of x(n) can be determined from the discrete Fourier transform of d(n), provided that j(0) = 0. By designing d(n) to have g subperiods within a single period, a much larger number of actual periods N act = (N TPRS /g) becomes available since x(n) will also have g subperiods within the period N TPRS [21]. The essence of this approach lies in the design of j.…”

“…Similar to the field element conversion in (10), a PRML sequence y q , ψ ( n ) with ψ > 1 can be converted to a PRML signal x ( n ) such that This allows the spectral properties of x ( n ) to be designed based on those of d ( n ) since all relevant harmonic properties of x ( n ) can be determined from the discrete Fourier transform of d ( n ), provided that ξ (0) = 0. By designing d ( n ) to have γ subperiods within a single period, a much larger number of actual periods N act = ( N TPRS / γ ) becomes available since x ( n ) will also have γ subperiods within the period N TPRS [21].…”