A generalization of digital transmultiplexer technology is presented. The proposed method can realize transmultiplexer (TMUX) and transdemultiplexer (TDUX) filter banks whose element filters have bandwidths greater than the channel spacing frequency. This feature is useful in many communications applications. As an example, a satellite switched (SS) Frequency Division Multiple Access (FDMA) system is proposed for spot beam satellite communications, particularly for mobile satellite communications

Ichiyoshi, Osamu

English

NASA Technical Reports Server

o N 9 2 - 2 4 1 3 8
A Generalized Transmultiplexer and
its Application to Mobile Satellite
Communications
Osamu Ichiyoshi
NEC Corporation
4035 IKEBE-CHO, MIDORI-KU
YOKOHAMA, 229 Japan
Tel: 045-939-2215
Fax: 045-933-9768
ABSTRACT
This paper presents a generalization
of the digital transmultiplexer techno-
logy. The proposed method can realize
a transmultiplexer (TMUX) and a trans-
Demultiplexer (TDUX) filter banks whose
element filters can have bandwidths
greater than the channel spacing fre-
quency. This feature is useful for
many applications in communications
fields. As an example, a satellite
switched (SS) FDMA system is proposed
for spot beams satellite communications
in particular for mobile satellite
communications.
i. INTRODUCTION
The transmultiplexer based on FFT
and Digital polyphase concept was pro-
posed in 1974 l Since then extensive
applications have been made to FDM/TDM
transmultiplexers for General Switched
Telephone Networks 2'3 Another inter-
esting area of its application is to
the onboard processing circuit for
satellite switched (SS) FDMA systems 4,
which will be quite effective for
mobile satellite communications. An
exhaustive summary and prospect of the
technology is given in the literature 5.
The conventional transmultiplexer
method has an inherent limitation that
the bandwidth of the element filter of
the filter bank is bounded by the
channel spacing frequency. This limi-
tation is too restrictive for general
SS/FDMA systems which must be able to
provide transparent transmission paths
for any pcrtion of the assigned fre-
quency ranges.
This paper presents a generalization
of the transmultiplexer which can pro-
vide such filter banks.
2. CONVENTIONAL TRANSMULTIPLEXER
A block diagram of the trans multi-
plexer is given in Figure i. In the
figure (A) shows a multiplexer (TMUX)
and (B) a demultiplexer (TDUX). The
TMUX output Y (Z) is given by
N-I N-I 2Tlki
Y(Z) = Z Z-iGi(Z N) Z eJN - Xk(ZN)
i=0 k:0
(2-i)
where
Z = e j2!<fT = e j2Tf/fs (2-2)
fs : I/T ; Sampling frequency (2-3)
= _ xk(n)z-nN (2-4)Xk(ZN) n
Those Gi(zN) (i=0,I,2 ..... N-l) in
eq(1) are the subfilters which consti-
tute the basic LPF G(Z) as
L-I
G(Z) = k g(_)Z -_
_=0
N-I
= }] Z-iG i (Z N) (2-5)
i=0
L/N-1
G i(Z N) = g(£N+i)z-_N (2-6)Z
4=0
International Mobile Satellite Conference, Ottawa, t990
417
https://ntrs.nasa.gov/search.jsp?R=19920014895 2020-03-17T12:28:47+00:00Z
x o (z N )
X 1 (Z N )
Xk(ZN)
XN_I(Z N )
(A)
N-Point
IFFT
G0 (ZN)
_ GI(ZN) _--_
G i (Z N ) _'_
P/
/
/
/
/
Y(Z]
V0(ZN
VI(ZN
Vk(Z N
VN_ 1 (Z N
(B)
N-Point _ _"
S
/
R(Z)
I
Figure 1
(A) Multiplexer (MUX)
(B) Demultiplexer (DUX)
Conventional Digital FDM Circuit
The output of the k-th channel of TDUX
is given by
N-I 2_
Vk(ZN ) = _ e-J--N--klHN_I_i(zN)Ri(Z N)
i=0
(2-7)
where the receive signal R(Z) is de-
composed into subsequences Ri(Z N) as
follows
N-I
R(Z) = Xr(n)Z -n= Y_ Z-iRi(Z N) (2-8)
n i=0
Ri(Z N) = Er(n-N+i)Z -Nn (2-9)
n
It is apparent from Figure 1 that the
TMUX and TDUX are mutualy inverse
operations.
It should be noted that because sampl-
ing frequencies for the signals Xk(ZN)
or Vk(ZN) are
1 fs
Af = - (2-10)
NT N
the bandwidth of each multiplex or de-
multiplex filter can not exceed Af.
3. GENERALIZED TRANSMULTIPLEXER
The structure of the generalized
TMUX and TDUX is given in Figure 2.
418
International Mobile Satellite Conference, Ottawa, 1990
rx0 (z)
I
Xl(Z]
Xk(Z)
XN_ 1 (Z)_
(A) MUM
N-Point
IFFT
G° (ZN) _ A
p _
I • /
/
Y(z)
v0 (z)
vI [z) _{_--
Vk(Z) __ -
VN_ 1 (Z)_ -
N-Point
FFT
(B) DUX
!
!
P/
!
/s
!
R(z)
Figure 2 Generalized Digital FDM Circuit
3.1 TMUX
In general the k-th input Xk(Z) is
expressed as
-n
Xk(Z ) = nZ xk(n)Z (3-1)
This signal is to be frequency con-
verted to fk;
fs
fk = k. Af = k.--_-- (3-2)
The conversion is made by the variable
transform;
_j2_fkTz . _--2_Z + e = e-3k-- Z (3-3)
Hence ;
2z
Xk(Z;k ) = Ze3_--knx(n)Z -n (3-4)
n
In the same manner the original LPF
G(Z) is also frequency converted to fk
in order to select Xk(Z;k);
N-I 2_
G(Z;k) = Z e3-N-kIz-iGi (zN) (3-5)
i=0
Thus the output of the TMUX will be
N-I
Y(Z) = Z G(Z;k)'Xk(Z;k)
k=0
.2_
= N-Iz Z-iG i(ZN)N_le3N-kl'xk(z;k)
i=0 k=0
(3-6)
InternationalMobile SatelliteConference, Ottawa, 1990
419
Eq (3-6) is depicted in (A) of Figure
2. The figure and eq (3-6) tell that
the generalized TMUX is basically of
the same structure as the conventional
TMUX including it as a special case as
shown below. From eq (3-4)
Xk(Z;k) = Ee3k-N--nxk(n)z-n
n
If the input signal Xk(Z) has data only
for every N samples, then
-n'N
Xk(Z;k) = _ xk(n'N)Z = Xk(Z N)
n'
Thus the generalized TMUX reduces to
the conventional TMUX.
If the input Xk(Z) has data for every
N/2 samples, then
N
Xk(Z;k ) = _(-l)knxk(n2)z-n2_ (3-7)
n
Eq (3-7) can be expressed in another
form;
Xk(Z;k) = Xk(ZN;e)+(-I)kz-N/2xk(ZN; 0)
(3-8)
where
-nN
Xk(ZN;e) = Zxk(nN)Z (3-9)
n
N -nN
Xk(ZN;O) = Ix (nN+__)Z (3-10)
n k z
Because the sampling frequency is 2Af,
the bandwidth of the input signal can
be greater than hf up to 2Af.
3.2 TDUX
The receive signal R(Z) is first
frequency converted from fk to 0(Hz),
and then selected by the LPF H(Z).
The frequency conversion is made by the
variable transform
Z + eJ_ k • Z (3-11)
Hence;
R(Z;-k)= Er(n)e -3-j-knz-n (3-12)
n
Then the low pass filter output is
given by
Vk(Z ) = H(Z)R(Z;-k)
N-I
= Z-( N-1 ) Z ZZ (i-n)
i=0 n HN-I-i ( )-ZN"
.2_. n
•e-3_ -K r(n)
2_
z-(N-1)_z-me-J-_-km N-I -j2_ki
= Z e N
m i=0
HN_I_i (zN) r (re+i) (3-13)
The equation gives the structure (B) of
Figure 2.
If we select one of every N samples,
then we put m=nN to obtain
N-I 2_
-(N-I).zz-nN. X e-3--N-ki
Vk(ZN) = Z
n i=0
HN_I_ i (ZN) r (nN+i)
z-(N-I)N-I -j2_kiN
= Z e HN_I_i(zNj'Ri(ZN,__
i=0
(3-14)
Thus the generalized TDUX includes the
conventional TDUX as a special case.
If we select one of every N/2 samples,
then we put m=nN/2 to obtain
Vk(Z N/2) = z-(N-I)Ez-nN/2(-1)kn"
n
_ 2_
"Nxle-3N-kli=0 HN-I- i (ZN) r (nN/2+i)
= Z- (N-I) {Vk (zN;e)
+Z -N/2(-1)k'Vk(ZN;O) } (3-15)
where for even samples
2z •
N-I _j-N-kl
Vk(ZN;e) = E e __I_i(zN)Ri (ZN)
i=0
(3-16)
and for odd samples
N-I .2_ki
Vk(ZN;O) = I e-3 N HN_I_i(zN)R'i(zN)
i=0
(3-17)
where
R' i (zN) = Z r (nN+i) Z -nN
n
(3-18)
(i=0,1,2, .... N-I)
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International Mobile Satellite Conference, Ottawa, f1990
The generalized TDUX above gives
the output with sample frequency 2Af.
Therefore the bandwidth of the filter
H(Z) can be greater than Af up to 2Af.
It is apparent from Figure 2 that
the TMUX and TDUX are mutually inverse
operations. If the output of TDUX is
fed to the corresponding input of TMUX,
then the total frequency response is
given as follows.
N-I
Y(Z) = _ G(Z;k)Vk(Z;k)
k=0
N-I
= E G (Z;k)H(Z;k)R(Z)
k=0
N-I
= R(Z) Z G(Z;k)H(Z;k)
k=0
(3-19)
Thus the whole transmission path is
transparent if
N-I
Z G(Z;k)H(Z;k) = 1 (3-20)
k=0
4. SATELLITE SWITCHED (SS) FDMA
SYSTEM
The block diagram of a SS/FDMA
system for mobile satellite system is
given in Figure 3. The SS/FDMA system
is very effective for mobile satellite
communications systems with a number
of spot beams. For example mobile to
mobile links can be easily set up to
avoid the double delay which would be
incurred by double hops via feeder
links. By adoption of spot beams for
feeder links Very Small Aperture
Stations (VSATs) can be easily set
close to customer facilities and can
reduce utility cost for terrestrial
networks.
The proposed SS/FDMA system uses
the generalized TDUX to divide incoming
signals from each beam, put them into
the Base Band Switch Matrix (BBSM)
which executes the inter-beam switch-
ing.
The output of the BBSM is frequency
multiplexed by the generalized TMUX to
be sent to each downlink.
The total frequency response of the
proposed system is depicted in Figure
4. The filters for TMUX and TDUX are
designed to satisfy eq (3-20). Thus
the proposed system can provide adap-
tive bandwidth SS/FDMA system with
perfectly transparent transmission
paths.
5. ACKNOWLEDGEMENT
The author wishes to thank
T. Furukawa and other colleagues of
him for guidances and useful discus-
sions.
REFERENCES
i. M.Bellanger and J.L.Daguet, 1974
"TDM-FDM transmultiplexer; Digital
Polyphase and FFT"
IEEE trans, vol. COM-22, pp.i199-
1204, Sept. 1974.
2. R.Maruta and A.Tomozawa, 1978
"An improved method for digital
SSB-FDM modulation and demodulation
IEEE trans, vol. COM-26, pp.720-
725, May, 1978.
3. F.Takahata, Y.Hirata, A.Ogawa and
K.Inagaki, 1978
"Development of a TDM/FDM trans-
multiplexer"
IEEE trans, vol. COM-26, pp.726-
733, May, 1978
4. W.H.YIM, C.C.D.KWAN, F.P.COAKLEY
and B.G.EVANS, 1988
"Multi-Carrier Demodulators For
ON-BOARD Processing Satellites"
International Journal of Satellite
Communications Vol. 6, pp.243-251
(1988).
5. H.Scheuermann and H.Gockler, 1981
"A Comprehensive Survey of Digital
Transmultiplexing Method"
Proceedings of the IEEE, Vol. 69,
No.ll, November, 1981.
International Mobile Satellite Conference, Ottawa, 1990
421
I I
" ° ° ° I
TE UX I 'M[ X 1
L-Band
Spot Beam 1
Base Band Switch Matrix
• o
TMUX
I'L
A
L-Band
Spot Beam m
..t ,
L
!
l J
A
Ku-Band
Spot Beam 1
If
TMUX
Ku-Band
Spot Beam n
Figure 3 Satellite Switched FDMA System
(A)
I/CT --
CHN_ 2 CHN_ 1 CH0 CHI CH2
-2_f -Sf 0 _f 2Af
_f
(B)
-2_f -_f 0 Af 25f
_f
(c)
i--
i/2 ....
CHN_ 2 CHN_ 1 CHO CHI CH2
-25f -Sf 0 Af 2Af
Figure 4
(A) TDUX Filter Bank
(B) TMUX Filter Bank
(C) TDUX-TMUX Filter Bank
Satellite Switch Frequency Characteristics
422
International Mobile Satellite Conference, Ottawa, 1990


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