Simplified method for the construction of an orthonormal base for CPFSK signals

Bossert, Martin; Hautle, A.; Shavgulidze, Sergo; Ugrelidze, Nodar

doi:10.1049/el:19961524

Cited by 6 publications

(1 citation statement)

References 1 publication

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“…Later on, we consider the cases M 1 = M 2 if M is even, and M 1 = M 2 + 1, otherwise. For such constellations formula (2) will be

d_{\min}^{2} \leq d_{\min ()(, M 1 PSK)}^{2} .

On the basis Gram–Schmidt orthonormalisation procedure, similar to the cases considered in [22, 23], we can construct basic vectors of 4D space and for our situation (see formula (1)) we obtain

\begin{matrix} right leftthickmathspace.5em \\ ψ_{1} (t) & = \sqrt{2 / T_{normals}} \cos (ω_{c} t + π h t / T_{s}), \\ ψ_{2} (t) & = - \sqrt{2 / T_{normals}} \sin (ω_{c} t + π h t / T_{s}), \\ ψ_{3} (t) & = (1 / \sqrt{D}) [\begin{matrix} \sqrt{2 / T_{normals}} \cos (ω_{c} t - π h t / T_{s}) - a \end{matrix}], \\ ψ_{4} (t) & = - (1 / \sqrt{D}) [\begin{matrix} \sqrt{2 / T_{normals}} \end{matrix}] \end{matrix}

…”

Section: Signal Constellations Designmentioning

confidence: 99%

New four‐dimensional signal constellations construction

Ugrelidze¹,

Shavgulidze

Sordia³

2020

IET Communications

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“…Later on, we consider the cases M 1 = M 2 if M is even, and M 1 = M 2 + 1, otherwise. For such constellations formula (2) will be

d_{\min}^{2} \leq d_{\min ()(, M 1 PSK)}^{2} .

On the basis Gram–Schmidt orthonormalisation procedure, similar to the cases considered in [22, 23], we can construct basic vectors of 4D space and for our situation (see formula (1)) we obtain

\begin{matrix} right leftthickmathspace.5em \\ ψ_{1} (t) & = \sqrt{2 / T_{normals}} \cos (ω_{c} t + π h t / T_{s}), \\ ψ_{2} (t) & = - \sqrt{2 / T_{normals}} \sin (ω_{c} t + π h t / T_{s}), \\ ψ_{3} (t) & = (1 / \sqrt{D}) [\begin{matrix} \sqrt{2 / T_{normals}} \cos (ω_{c} t - π h t / T_{s}) - a \end{matrix}], \\ ψ_{4} (t) & = - (1 / \sqrt{D}) [\begin{matrix} \sqrt{2 / T_{normals}} \end{matrix}] \end{matrix}

…”

Section: Signal Constellations Designmentioning

confidence: 99%

New four‐dimensional signal constellations construction

Ugrelidze¹,

Shavgulidze

Sordia³

2020

IET Communications

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Generalized Concatenation of Encoded CPFSK Modulation

Hautle

Bossert

Shavgulidze

et al. 2000

Trans Emerging Tel Tech

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Abstract. Using the principles of generalized concatenation we introduce a new design for coded M-ary CPFSK systems with modulation index h = l/M. This technique is based on a set partitioning method of inner CPFSK into nested subsystems with increasing free Euclidean distance which are combined with several outer convolutional codes having different error-correcting capabilities. In other words, we construct multilevel codes on the basis of inner modulation with memory, namely CPFSK. The new generalized concatenated constructions were simulated in an additive white Gaussian noise channel. The multistep decoding algoritm is described where for soft output decoding the well-known symbol-by-symbol maximum n posteriori probability (MAP) algorithm is applied to the inner CPFSK. A comparison of the generalized concatenated codes with the best known trellis-coded CPFSK schemes is also presented.

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Energy efficient simplified MIMO with spatial four-dimensional modulated signals

Ugrelidze,

Shavgulidze

2024

AEU - International Journal of Electronics and Communications

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Simplified method for the construction of an orthonormal base for CPFSK signals

Cited by 6 publications

References 1 publication

New four‐dimensional signal constellations construction

New four‐dimensional signal constellations construction

Generalized Concatenation of Encoded CPFSK Modulation

Energy efficient simplified MIMO with spatial four-dimensional modulated signals

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