Operating Manual Vol 1 - ES Documentation

Digital ModulationSMIQTable 2-9Coding algorithmsCODING Coding algorithm Applicable for K bit/symbolNONE dc n = d n K = 1 to 8DIFF dc n = (d n + dc n-1) modulo 2k K = 1 to 7GRAY+DIFF Gray coding with additional differential coding K = 1 to 7GSM dc n = not (d n exor d n-1 K = 1VDL VDL standard K = 3Example 1:Differential coding for QPSK modulation with K = 2 bit/symbolDecimal display; value range for modulation symbolsdn ∈ 0123 ;; ;{ }Recursive coding is defined as follows: dc n = (d n + d cn -1) modulo 4.Depending on the state of a preceding modulation symbol dc n-1 the coded modulationsymbol dc n is obtained for example from a modulation symbol d n = 2 as follows:d n = 2 dc n-1 dc n0 21 32 03 1By means of differential coding, the assignment between modulation symbols andphase differences shown in the following table is generated:Modulation symbol d n(binary, MSB, LSB)00 01 10 11Phase difference ∆ϕ 0° 90° 180° 270°Example 2:Gray and differential coding for 8PSK modulationFirst, a gray coding is performed according to the gray code. Afterwards, a differentialcoding is performed according to the recursive coding algorithm quoted above. Bymeans of the mapping rule shown in the figure in Section 'PSK and QAM Modulation'above, IQ values are assigned to the re-coded modulation symbols. In summary, theassignment between modulation symbols and phase differences shown in the followingtable is generated:Modulation symbol d n(binary, MSB, LSB)000 001 010 011 100 101 110 111Phase difference ∆ϕ 0° 45° 135° 90° 270° 315° 225° 180°1125.5555.03 2.90E-9