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Transport aspects 2
Appendix III
Definition of transmitter PSD (TXPSD) for non-continuous transmissions
(This appendix does not form an integral part of this Recommendation.)
This appendix provides a formal definition for transmitter power spectral density (TXPSD) for signals
comprising a stream of symbols including quiet periods, such as those produced by time division duplexed
DMT systems.
This appendix defines TXPSD that is applicable to a stream of transmitted symbols, a punctured stream of
symbols, or a continuous stream of symbols. Transmitted symbols are all symbols transmitted in the
transmission period for the transmission direction. The quiet symbol positions in the transmission period
are excluded. It does not define a measurement technique.
This appendix defines TXPSD in terms of an intermediate variable, "Transmitter Symbol PSD" (TXSPSD).
TXSPSD is defined in relation to the Expectation of the energy spectral density (ESD) of symbols transmitted
in a particular direction.
The ESD of a symbol voltage waveform Vs(t) is derived into a reference impedance of 100 Ω.
2
( , ) = 1 |∫ ∞ ( ). − 2π | ( / )
0 −∞
= 100
0
TXSPSD is derived from the Expectation of the ESD over a set of transmitted symbols.
( ) = . E[ ( ( ), ); ∈ ] (in unit of W/Hz)
S = {S0,S1...SN}
S0,S1...SN is a valid sequence of transmitted symbols
E[x] is the statistical expectation of x.
This normalization by the period of the symbol ensures that in the limit an infinite sequence of symbols has
TXSPSD that converges to the classical PSD derived from the Fourier transform of the autocorrelation
function.
The verifiable TXPSD is defined in a particular bandwidth bw as follows:
1 +
∫
2
( , ) = 30 + 10 × ( − ( ) ) (in unit of dBm/Hz)
10
2
TXPSDM(f) is the maximum permitted level for TXPSD(bw,f) of a long symbol sequence.
Methods for compliance verification are out of the scope of this Recommendation.
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