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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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