Digital modulation and mobile radio (VII)

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Digital modulation and mobile radio (VII)
3.2.4 Architecture of GMSK modulator                 1 0 0 0 1 1 1 0 1 0 0                                            -0.5          2

Before the data stream is fed to the
modulator, it is differentially encoded
                                                                             T
using the rule d(k) = a(k) ⊕ a(k – 1)
where d(k) ∈ {0; 1}. Adding –0.5 and
                                                                    1 1 0 0 1 0 0 1 1 1 0
then multiplying by a factor of 2 gives
a sequence of bipolar delta functions
δ(k) ∈{–1; +1}. The rest of the modula-                                                                                                             D
                                                                                                                                                                                        c I(t)
                                                                                                                                                        A
tion process depends on the structure of                                          sin x/x              Gaussian
                                                                                                                             Calculation
                                                                                                                              of ϕ, sinϕ
the hardware and firmware used for                                               lowpass                filter
                                                                                                                              and cosϕ
                                                                                                                                                    D
the modulators, the only proviso being                                                                                                                  A
                                                                                                                                                                                       c Q(t)
                                                     1 1 -1 -1 1 -1 -1 1 1 1 -1 Oversampling
that the tolerances stated in TABLE 5
must be met for bursts lasting 562 µs.
                                                    FIG 21 Generating modulation signals cI(t) and cQ(t)



  Max. frequency          Max. phase error          how complexity can be reduced drasti-                                      resulting direction of rotation of the RF
      error                 peak/rms
                                                    cally. With this approach, differential                                    vector, it can be verified that this form
      1 x 10 –7                20°/ 5°
                                                    encoding need not be performed as a                                        of modulation and the modulation
                                                    separate operation and the tables for                                      produced by the original, differentially
TABLE 5     Tolerances for modulated carrier
                                                    calculating cos[ϕ fil(t)] and sin[ϕ fil(t)]                                encoded signal are identical (FIG 22).
                                                    can be dispensed with entirely – a
These parameters depend on the                      major improvement. To do this, the
accuracy of the modulating signals                  original data sequence that has been                                       3.2.5 Demodulating MSK
cI(t) and cQ(t), on the frequency and               converted into a bipolar signal is multi-                                        and GMSK signals
phase stability of the oscillator and               plied by a phasor e –jkπ /2. The complex                                   As equation (20) shows, MSK signals
the exact orthogonality of the I and Q              coefficients c(k) that result are fed to a                                 are frequency-modulated RF signals. In
carrier components. The exact solution              filter with Gaussian-like characteristics.                                 the case of GMSK signals, only the
involves finding the convolution of                 A complex function appears at the                                          baseband function, which is propor-
pc(t) · hGauss(t). The δ(k) are interpolat-         output of the filter. Its real part approxi-                               tional to the output frequency, is filtered.
ed using a bipolar NRZ function in                  mates the modulation signal c I(t), while                                  The RF signal can also be thought of
a digital filter with an oversampling               its imaginary part approximates the                                        as being frequency-modulated. Con-
rate of up to x16, before they are                  modulation signal c Q(t). From the                                         sequently, simple frequency demod-
transformed into the function c fil (t) by
a further filter with Gaussian character-
istics. The next part of the modulator is                                                                   1 0 1 0 1 0 -1 0 1 0 1
                                                                                                   -jkπ
the same as the MSK modulator that                              -0.5              2
                                                                                                 --------
                                                                                                e 2
                                                                                                                                                D
has already been described. In other                                                                                                                A
                                                                                                                                                                                        c I(t)

words, the instantaneous phase is                                                                                            Digital
                                                                                                                              filter
calculated by integrating c fil (t) to                                                                                                          D
                                                                                                                                                                                   c Q(t)
obtain ϕ fil(t), cos[ϕ fil(t)] and sin[ϕ fil(t)]     1 0 0 0 1 1 1 0 1 0 0                                                                          A

are calculated and these functions are                                                                      0 1 0 -1 0 -1 0 -1 0 1 0
multiplied by the two orthogonal carrier
components (FIG 21).                                               c I (t)

                                                                                                                                                            t
In practice, however, there is no need
to follow the exact sequence of opera-                            c Q (t)

tions that flow from the theory. As there                                                                                                                   t
are a large number of mobile stations,                                                                                                                  Direction of rotation
it is essential to adopt a cost-effective                                                                                                               of RF vector

approach while at the same time meet-                                                                                                                   Reconstructed differentially
                                                                                   1        0      0        1     0      0      1       1   1       0   encoded data sequence
ing the requirements listed above. A
concept developed by Philips shows                  FIG 22      Efficient implementation of GMSK modulator


30        News from Rohde & Schwarz      Number 156 (1997/IV)
                                                                                                                                  Refresher topic

ulation using conventional frequency                  T = 1/fIF subsampling: TA = (n+1/4)T
                                                                                                                                    xI(2i)
discriminators or an indirect approach
using FM to pulse frequency modula-                         IF    D                              (-1)i
tion conversion would be sufficient to                    stage       A                          (-1)
recover the transmitted data. Never-                                                                        Inter-                xQ(2i)
                                                                                                           polation
theless, the considerably more complex                                             xQ(2i-1)

route of coherent demodulation, de-
                                                                                                                                             FIG 24
scribed in chapter 2.6, is taken. There           cI(t)                                                                                      Top: demodulation
are two main reasons for this:                                                                                                               with A/D converter.
                                                                                                                                             Bottom: signals c I(t)
                                                                                                                                             and cQ(t) recovered
1. Under the same transmission con-
                                                  cQ(t)                                                                                      by IF sampling
ditions, coherently demodulated RF                                                                                                           ( l sample,
signals exhibit lower bit error rates                                                                                                            interpolated value)
than those that are not.
2. Because of the transfer function of
the mobile-radio channel, the RF signal
is altered in such a way that demodu-            RF signal is converted to an IF and                       ponent samples. The delay between
lating the received signals without              fed to the two mixers. The frequency of                   the two components is equalized by
equalization would in most cases lead            the superheterodyne oscillator is syn-                    an interpolation filter.
to unacceptably high error rates. How-           chronized by means of a frequency-cor-                                             Peter Hatzold
ever, equalization is only possible if the       rection burst transmitted at regular inter-
characteristics of the radio channel             vals by the base station. This oscillator                 REFERENCES
over time are known, in other words its          provides the two orthogonal signals                       Mäusl, R.: Digitale Modulationsverfahren. Hüthig
transfer function must be continuously           cos(ωt) and –sin(ωt). After passing                       Verlag, Heidelberg, 1988

estimated.                                       through the mixers and lowpasses, the                     Proakis, J. G.: Digital Communications. McGraw
                                                                                                           Hill, New York, 1989
                                                                                                           Schöffel, P. et al.: Architektur eines Mobilfunkge-
                cos t
                                                                                                           rätes für das Netz D. Philips Innovation (1/1991)

                             A       xI(t)                                                                 Picken, D.: The GSM mobile-telephone network:
                                          Digital signal
                                 D        processor for    To                                              technical features and measurement require-
                                       channel estimation, decoder                                         ments. News from Rohde & Schwarz Nos. 136,
       IF
                                       channel correction
     stage                                                                                                 137, 138
                                 xQ(t) and deriving data
                             A          most likely to be
                               D               sent                                                        Lüttich, F., Hecht, A.: Testing digital radio re-
   Frequency
                                                                                FIG 23                     ceivers with Signal Generator SMHU58. News
synchronization sin t                                                           GMSK demodulator           from Rohde & Schwarz Nos. 136, 137



As described in chapter 2.6, coherent            two components of the equivalent
demodulation gives the complex                   baseband signal undergo D/A conver-
envelope of the RF signal, which is also         sion and are fed to a digital signal pro-
modified by the radio channel. If the            cessor that, from the distorted complex
undistorted baseband signal is known             envelope, reconstructs the sequence that
as well, the transfer function of the            is most likely to have been transmitted.
channel can be calculated. A sequence
of 26 bits, referred to as the training se-      For the demodulator too there are
quence and a copy of which is stored             less involved solutions. FIG 24 shows
in the receiver, is transmitted in the           a concept that uses just one A/D
middle of every burst of 156 bits.               converter. The received signal that                                  Digital modulation and mobile radio
By finding the cross-correlation of the          has been converted to an IF is under-                                Refresher topic



received equivalent baseband signal              sampled using a sampling period of
and the complex envelope that the                Ts = (n + 1/4 )T, where T is the IF period.
training sequence would generate if              The samples xi are multiplied by (–1)i,
reception were ideal, the characteristics        in other words the samples with odd
of the radio channel can be estimated.           indices have their signs inverted. Sam-
                                                 ples with indices of the form 2i are the
                                                                                                           Reader service card 156/13 for a copy of the
The block diagram of the demodulator             I-component samples of the received                       complete refresher topic (available in English and
is shown in FIG 23. After reception, the         signal, those with (2i – 1) the Q-com-                    German)


                                                                                              News from Rohde & Schwarz            Number 156 (1997/IV)         31