Multicarrier Access and Routing for
Wireless Networking
Diakoumis Gerakoulis
General Dynamics Advanced Information Systems, Bloomington, MN 55431, USA Email:[email protected]
Received 28 February 2005; Recommended for Publication by Fary Z. Ghassemlooy
A multicarrier access and routing system has been proposed for use in wireless networks. Users within each cell access a radio port (RP). All RPs are connected to a radio exchange node (REN) which routes the calls or packets. The uplink access is orthogonal multicarrier code-division multiple access (MC-CDMA) and the downlink transmission is multicarrier orthogonal code-division multiplexing (MC-OCDM). The REN contains a switch module which provides continuous routes between wireless terminals without demodulation/remodulation or channel decoding/reencoding. The switch module is nonblocking and has complexity and speed linearly proportional to its size. Also, the switch module does not introduce interference into the network. Any existing interference or noise in its input port is transferred to its output port. The input-output switch connections are assigned on demand by a control unit. A random input/output port assignment process can achieve maximum switch throughput.
Keywords and phrases:multicarrier access, multicarrier routing, multicarrier CDMA, radio exchange node, switch module.
1. INTRODUCTION
Multicarrier transmission methods have been widely ac-cepted and used because of their advantages over single-carrier transmission in broadband wireless links. The ex-isting multicarrier systems however, such as the orthogonal frequency-division multiplexing (OFDM), are only defined for the physical layer, while wireless networks also require a method for multiuser access and routing. This paper focuses on the development of a multicarrier system that operates at physical, multiple access and routing level. The transmission and access is based on orthogonal multicarrier (MC) code-division multiple access (CDMA), see [1,2,3,4,5]; while the routing scheme on code-division multiplexing [6].
The wireless network is assumed to have the configu-ration shown in Figure 1. It consists of a radio exchange node (REN) connected to a number of radio ports (RPs). All RPs are connected to the radio exchange node (REN) which routes packets or calls between RPs. Users within each cell access the corresponding radio port (RP) by an orthogonal multicarrier CDMA described in [5]. All up-link transmissions require synchronization. The downup-link transmission is multicarrier orthogonal code-division mul-tiplexing (OCDM) described in [4]. The REN contains the
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
switch module which routes packets and calls between ra-dio ports without demodulation/remodulation or channel decoding/reencoding. Such a wireless network then provides a continuous mobile-to-mobile route that achieves high net-work throughput and spectral efficiency.
InSection 2we present the system description and verify its functional correctness. InSection 3we examine the net-work capacity and performance which includes the routing capacity and the network interference.
2. SYSTEM DESCRIPTION
The wireless access and routing system is shown inFigure 2. Wireless terminals within each cell access the corresponding radio port by orthogonal multicarrier code-division multiple access (MC-CDMA) [5]. The uplink transmission and recep-tion is described below, in Section 2.1. The received signal at the REN is routed by the switch module to the destina-tion output port. The source-destinadestina-tion informadestina-tion is sup-plied by the control unit. The switch module is anM-input, M-output, nonblocking, routing fabric which is described inSection 2.2. The output port signal is transmitted in the downlink and received by the wireless terminal as described inSection 2.3.
2.1. The uplink
RP RP
RP RP
RP
RP REN
RP: radio port
REN: radio exchange node
Figure1: The wireless access and routing network.
spread by the Hadamard sequencew with rateLR.
Assum-ing that x(,m) represents a complex-valued signaling point,
that is,x(,m)=α(,m)+jβ(,m), the spread signal is
¯
Yk(,m)=x(,m)w,k
=α(,m)w,k+jβ(,m)w,k fork=0, 1,. . .,L−1.
(1) The spread signal ¯Yk(,m) is also encoded (multiplied) with
pseudorandon noise (PN) sequence gm = [gm,k] in order
to suppress interference from other uplink microcells with the same carrier frequency. gm is the same for all uplink
transmissions in microcellm, has the same rate (LR) as the sequence w, and thus gm does not spread the signal
fur-ther. The resulting signalYk(,m)=Y¯
(,m)
k gm,kis then encoded
by a multicarrier encoder which in this case is an orthogo-nal frequency-division multiplexor (OFDM) havingL sub-carriers. TheLparallel pointsYk(,m)then enter an IFFT given
by
y(,m)
n =
1 L
L−1
k=0
Yk(,m)ej2π(kn/L). (2)
The parallel outputs yn(,m)forn=0, 1,. . .,L−1 then enter
a P/S converter where a guard time or cyclic prefix is added. The P/S converter outputs(,m)(n) is converted into an analog
signals(,m)(t) which is up-converted into the uplink carrier
fu(m)and then transmitted to the radio port (RP). At the REN
the received signal at input portmis given by
r(m)
u (t)= L−1
=0
r(,m)
u (t)= L−1
=0
h(,m)
u (t)∗s(u,m)(t)
, (3)
where ru(,m)(t) is the received uplink signal from terminal
in microcell m, h(u,m)(t) is the impulse response of the
corresponding uplink channel, and (∗) denotes convolution (the channel is assumed noiseless at the moment). The ana-log signal ru(m)(t) enters the uplink receiver (or recovery
circuit) shown inFigure 4, where is down-converted to base-band, digitized into signal zu(m)(n), and then decoded by
the a MC-decoder (i.e., an decoder). In the OFDM-decoderz(um)(n) is S/P converted intoLparallel data points
z(um;n)forn=0, 1,. . .,L−1, which enter an FFT given by
¯ Zu(m;k)=
L−1
n=0
zu(m;n)e−j2π(kn/L) fork=0, 1,. . .,L−1. (4)
The post-FFT signal is given by
¯ Z(um;k)=
L
=1
Hu(;k,m)Y¯
(,m)
k
=gm,k L
=1
Hu(;k,m)x(,m)w,k fork=0, 1,. . .,L−1,
(5)
whereHu(;k,m)is the uplink channel transfer function (CTF)
of user in microcell mat subcarrier k. In the above we have used the assumption of perfect synchronization be-tween transmitting signals in order to verify the functional correctness of the process. The Lparallel ¯Zk(m) points then
enter a P/S converter, the output of which is first despread by gm,kto provide the signal
Zu(m;k)= L
=1
Hu(;k,m)x(,m)w,k fork=0, 1,. . .,L−1. (6)
The signal Zu(m;k) is then despread by the L Hadamard
se-quencesw = [w,0,w,2,. . .,w,L−1] in parallel in order to
recover the data of each uplink transmission in microcellm. In particular, the output signal of despreader-1 is given by
L−1
k=0
Zu(m,k)w1,k= L−1
k=0
L
=1
Hu(;k,m)X
(,m)
k
w1,k
=
L−1
k=0
L
=1
Hu(;k,m)x(,m)w,k
w1,k
=
L
=1
H(,m)
u x(,m) L−1
k=0
w,kw1,k
=
LHu(1,m)x(1,m) for=1,
0 for=1.
(7)
In the above we have made the assumption of frequency-flat channel, that is,Hu(;k,m)=H
(,m)
u for allk.
2.2. The switch module
LetG(u,m)denote the recovered signal of userat input port
m; then
G(,m)
u =LHu(,m)x(,m). (8)
Tx . . . Tx Wireless terminals
(1) (i) (N)
. . .
Rv Rv Rv
MXM switch module
Control unit
Tx Tx Tx
. . .
(1) (j)
(N) Rv
. . . Rv Wireless terminals Radio exchange node
Figure2: The wireless access and routing system.
User (,m)
w gm
S/P YL(−,m1)
. . . Y0(,m)
IFFT yL(−,m1)
. . . y0(,m)
P/S Add prefix
D/A
∼ fu(m)
Multicarrier encoder (by OFDM)
Figure3: The wireless terminal transmitter.
fu(m)
∼
A/D Multicarrier decoder
gm
w0
. . .
wL−1
L−1
q=0
L−1
q=0
0 . . . L−1 Uplink recovery circuit-m
Figure4: The uplink receiver (uplink recovery circuit-m).
circuit-m where each signal is then encoded by its corre-sponding destination encoder-(,m), shown inFigure 5. Let the destination of channelat input port mbe the output port m and channel , then the function of destination encoder (,m) is denoted as (,m) → (,m) for , = 0, 1,. . .,L−1 andm,m = 0, 1,. . .,M−1, whereM is the number of input or output ports of the switch module andL the number of channels per input or output port.
The signal at the output of the destination encoder-(,m) then isG(u,m)wwm, wherew =[w,k] andwm =[wm,n] are the destination channel and destination port orthogonal sequences, respectively. If the rate ofG(u,m)isR, then the rate
of the destination channel spread signalG(u,m)wisRL=LR and the rate of the destination channel and port spread sig-nalG(u,m)wwm isRM = LRL =LMR. Hence,T =LTc =
LMTcc, whereTis the symbol length,Tcis the chip length of
sequencew, andTccis the chip length of sequencewm. The signals at the outputs of the destination encoders are then summed up over all channels in each port and over all
ports to provide the signal
Gk,n= M−1
m=0 L−1
=0
G(u,m)w,kwm,n. (9)
Each destination port m then recovers its corresponding channels from the signalGk,n(taking it from the switch bus)
by using the port decoder (shown in Figure 5), which de-spreads Gk,n with the port destination sequence wm. The output of the port decoder-1 is then given by
G(dm;k=1)= M−1
n=0
Gk,nwm=1,n
=
M−1
m=0 L−1
=0 G(,m)
u w,k M−1
n=0
wm,nw1,n
=
L−1
=0 G(,1)
u w,k.
Input ports (1)
. . .
(M) L Destination encoder-M
L L Destination
encoder-1 L
. .
. G
BUS L
L . . .
Port decoder-M
Port decoder-1 L
L
Output ports
(1) . . .
(M)
(a)
RateR w
RateLMR wm
Destination channel Destination port Destination encoder (,m) (,m)
RateLMR wm
L−1
0 RateLR
Port decoder
(b)
Figure5: The switch module.
gm
D/A Multicarrier
encoder
∼ fd(m)
Downlink encoder-m
Figure6: The downlink transmitter (downlink encoder).
Hence, the signal at the output of port decoder-m(output port-m) is given by
¯ G(dm;k)=
L−1
=0 G(,m)
u w,k. (11)
The above indicates that each output port is a sum of up toL channels which may originate in different input ports.
2.3. The downlink
The signal ¯G(dm;k) then enters the downlink transmitter (or
downlink encoder) shown inFigure 6, where it is encoded (multiplied) with the PN-sequence gm = [gm,k] of the downlink microcell-mto provide the signal
G(dm;k)=gm,kG¯(m ) d;k =gm,k
L−1
=0
G(u,m)w,k. (12)
Then,G(dm;k)is encoded by a MC-encoderm(i.e., an OFDM
encoder) by taking its IFFT:
y(m)
n =
1 L
L−1
k=0
G(dm;k)ej2π(kn/L) forn=0, 1,. . .,L−1. (13)
After the P/S converter, the digital signaly(m)
(n) is converted into an analog signals(m)
(t) which is then up-converted to the downlink carrier of microcellm, fd(m). The receiver of
wireless terminalin microcellmis shown inFigure 7. The received downlink signal from the REN is given by
rd(m)(t)= L−1
=0
rd(,m)(t)=h
(m)
d (t)∗s
(m)
d (t), (14)
wheres(dm)(t) is the sum of all downlink signals, that is,
s(dm)(t)=
L−1
=0s(,m
)
d (t), ands
(,m)
d (t) is the downlink signal
of a terminal.s(d,m)(t) are orthogonal to each other. Also,
h(dm)(t) is the impulse response of the downlink channel in
microcellm. The received signalrd(m)(t) is down-converted
to baseband and then an A/D converter provides the digital signalrd(n) which enters the OFDM decoder. At the decoder after the cyclic prefix is removed, an S/P corverter provides L parallel data pointszd(m;n). The Lparallel pointsz
(m) d;n , for
n = 0, 1,. . .,L−1, then enter an FFT which provides the signal
¯ Zd(m;k)=
L−1
k=0
r(m)(t)
∼ fd(m) A/D r
(m)(n) S/P Remove
prefix z(0m)
. . . z(Lm−1)
FFT Z0(m)
. . . ZL(m−1)
P/S
gm w L−1
k=0
x(,m)
Multicarrier decoder (by OFDM)
Figure7: The wireless terminal receiver.
The post-FFT signal ¯Zd(m;k)is given by
¯
Z(dm;k)=H
(m) d;k G
(m) d;k =H
(m) d;k gm,k
L−1
=0 G(,m)
u w,k
=Hd(m;k)gm,kL L−1
=0 H(,m)
u x(,m)w,k,
(16)
whereHd(m;k) is the transfer function of the downlink chan-nel in microcellmat subcarrierkandHu(,m)is the transfer
function of the uplink channel of terminalin microcellm, (which has been assumed to be constant at all subcarriers). In the above we have used (8) and (12). ¯Zd(m;k)is then despread with the PN-sequencegm,kto provide the signal
Zd(m;k)=LHd(m;k)
L−1
=0 H(,m)
u x(,m)w,k. (17)
The desired signal of a wireless terminalis then recovered by despreadingZ(km)with the sequencew, that is,
L−1
k=0
Zd(m;k)w,k= L−1
k=0
LHd(m;k)
L−1
=0
H(,m)
u x(,m)w,k
w,k
=
L−1
k=0
L−1
=0
LHd(m;k)Hu(,m)x(,m)w,kw,k
=
L−1
=0
LHd(m)Hu(,m)x(,m) L−1
k=0
w,kw,k
= L
2H(m)
d H
(,m)
u x(,m) for=,
0 for=.
(18)
In the above we have made the assumption that the down-link channel in microcellmis frequency flat, that is,Hd(m;k)=
Hd(m)for allk. The purpose of the above analysis is to verify
the functional correctness of the process and therefore it does not include the effects of noise or interference. The effects of interference and noise are examined in the performance sec-tion.
3. CAPACITY AND PERFORMANCE EVALUATION
3.1. The routing capacity
We consider a switch module withM input andM output ports, andLaccess channels per port. The switch will then provide a capacityofML×MLsimultaneous connections. This capacity is achieved when the REN is fully equipped. A fully equipped REN hasMmulticarrier uplink receivers (up-link recovery circuits) andM multicarrier downlink trans-mitters. The switch module hasMLdestination encoders in the input (Lin each input) andLport decoders at the out-put (Lin each output port). Therefore the required circuitry of the switch module islinearly proportionalto the its size M (this may be compared to a crossbar switch that hasM2
crosspoints). Given the above assumptions the switch fabric isnonblockingfor any incoming call to an input port. That is, there is always a connection available to a destination output. The number of active calls at an input portior output port
jmust be less thanL, that is,Mj=0ti j ≤Land
M
i=0ti j ≤L,
whereti jis the number of calls betweeniandj. A call may be
blocked by the input- and/or output-port capacity limitL. The input-output connections are assigned on demand by the control unit (CU). That is, the CU receives an input-output call request via a demand or control channel and makes the requested connection in the switch module which is used to route the call. The assignment input-output con-nection in the switch module by the CU is made upon avail-ability (at random) without rearranging the on-going calls. This simple approach is shown to achieve maximum switch throughput for the type of code-multiplexed switch module presented here [6]. This is not the case in time-multiplexed switching which requires more complex routing control al-gorithms to achieve maximum throughput [7].
The speed or the clock rate of andM×Mswitch mod-ule isMtimes the rate of the incoming signal. This isMLR; whereLis the number of access channels per port, andRis the symbol rate per access channel (when there is no demod-ulation, i.e., no phase detection and symbol recovery at the REN). If we consider demodulation ofM-ary symbols at the REN, the speed of the switch will increase by a factor log2M (i.e., (log2M)ML).
3.2. The network interference
interference (MAI) and AWGN of cellmin frequency bink, that is,
nu(m;k)=Iu(m;k)+no, (19)
whereIu(m;k)represent the intercell interference. The intracell
interference is zero if we assume all uplink transmissions are perfectly synchronized. The received uplink signal then is
Zk(m)= L−1
=0
H(,m)
u x(,m)w,k+n(um;k). (20)
The signal at the output of the uplink recovery circuit then is
G(,m)
The signal at the switch bus is
Gk,n=
The downlink signal at the output portmin frequency bin kis given by
The received downlink signal of cellmin frequency binkis
Zd(m;k)=H
The signal at the output of the wireless terminal receiver then is
is the downlink other-cell interference in frequency bin k) and taking the variance of the total MAI plus noise in the downlink receiver, we have
σ2 MAI and noise has the following terms (in the order they ap-pear): the uplink (transferred;u/d) MAI, the downlink MAI, the cross-product of the uplink MAI and the downlink MAI, the cross-product of the uplink MAI and the downlink noise, the cross-product of the uplink noise and the downlink MAI, the uplink noise, and the downlink noise. There are seven terms of interference and noise instead of the typical two terms (MAI and AWGN) in a single-hop point-to-point sys-tem.
In the above analysis we have assumed no demodula-tion at the REN, that is, no phase detecdemodula-tion and symbol recovery and no channel decoding at the REN. If we had as-sumed demodulation, that is, making a hard decision after MC-decoding and before MC-reencoding, that is, x(,m) =
α(,m)+jβ(,m)→ {−1, 1}, then that would effectively
decou-ple the downlink from the uplink. In this case the interfer-ence transfer terms (cross-terms) will not appear. The speed of the switch however will increase by a factor log2M(i.e., (log2M)ML). Therefore the cross-terms appear as a result of coupling between uplink and downlink in the case of no de-modulation at the REN.
3.3. The signal amplitude distribution
Letxi(,m)=α
(,m)
i +jβ
(,m)
i represents theithM-ary symbol
of theth user at themth input port. Also, letw(l) be the
The signal amplitudes of the inphase (I) and quadrature (Q)
This signal will be overspread with the destination port code wm(k) at the rateLMRcorresponding to chip durationTcc=
1/LMR. The signal amplitudes of the (I) and (Q) compo-nents of theith symbol then are, respectively,
Ai=
where Ai andBi represent (I) and (Q) components of the
signal in the switch bus. Then, a port decoder will provide the signal of the output port m by despreading it with the corresponding code wm(n), that is, Mm=1Aiwm(n) =
Therefore, assuming that the chip amplitude remains constant for durationTc=1/LR, the switch does not
intro-duce any interference during the process of routing.
The amplitudes of the I and Q components of theithM -ary symbol of thenth user in the switch bus are, respectively,
S(In)(i)=A
The terms ¯II(i) and ¯IQ(i) represent the interference from
other users and AWGN during ith symbol. The mean of the interference terms is zero and the variance is σ2
I =
var[ ¯II(i)] = var[ ¯IQ(i)].A(in) = cosφi(n) andB(in) = sinφ(in),
whereφ(in)denotes the phase angle of theithM-ary symbol
of thenth user signal, and they take values in the sets
A(in)∈
dependent and identically distributed (i.i.d.). That is, there is independence between the jsymbols and between diff er-entn(user signals) and are also identically distributed. The distribution of the phase angle φi(n) is assumed to be
uni-form in the set {π/M, 3π/M,. . ., (2M−1)π/M}and sub-sequently the phase components A(in) andB
(n)
i are i.i.d. for
differentnandiand uniformly distributed with equal prob-ability (1/M) in the above sets. For the samenandi,A(in)
andBi(n)are not independent of each other but are
uncorre-lated, since E{A(in)} = E{B
is sufficiently large (M ≥ 8), we can apply the central limit theorem (CLT) on each of the asymptotically Gaussian ran-dom variablesS(In)(i) or (S
(n)
Q (i)). Then the (unconditional)
mean and variance are E{S(n)
I (i)} = 0 and Var{S (n) I (i)} =
N(1 +σ2
I). The conditional mean is
ES(In)(i)|A The conditional variance is Var{S(n)
I (i) | A(in),n = 1, 2,. . .,
ML} =Nσ2
I (similarly for the Q component). Thus the
dy-namic amplitude range of the sum-signal in the switch bus when no interference is present is given by
terference is taken into account we must add multiples of the noise variance. For example, 3√MLσI, for 99.74%
con-fidence. That is,
The above dynamic range should be compared with the range [−1, 1] for bipolar samples for time-division multi-plexed switch modules.
4. CONCLUSION
[−MLKj,MLKj]; whereKjis the amplitude of the input
sig-nal and Lis the number of access channels per port. The input-output switch connections are assigned on demand by the control unit (upon availability of input/output ports). A random input/output port assignment process can provide maximum switch throughput.
REFERENCES
[1] V. M. DaSilva and E. S. Sousa, “Multicarrier orthogonal CDMA signals for quasi-synchronous communication systems,”IEEE J. Select. Areas Commun., vol. 12, no. 5, pp. 842–852, 1994. [2] E. A. Sourour and M. Nakagawa, “Performance of
orthogo-nal multicarrier CDMA in a multipath fading channel,”IEEE Trans. Commun., vol. 44, no. 3, pp. 356–367, 1996.
[3] M. Park, K. Ko, H. Yoo, and D. Hong, “Performance analysis of OFDMA uplink systems with symbol timing misalignment,”
IEEE Commun. Lett., vol. 7, no. 8, pp. 376–378, 2003.
[4] D. Gerakoulis and G. Efthymoglou, “A multi-carrier multiplex-ing method for very wide bandwidth transmission,” submitted toEURASIP JWCN.
[5] D. Gerakoulis, G. Efthymoglou, F. Koravos, and L. Tassiu-las, “A class of multi-carrier CDMA access method for wide-bandwidth wireless channels,” to appear inIEEE PIMRC ’05, Berlin, Germany.
[6] D. Gerakoulis and E. Geraniotis,CDMA: Access and Switching: For Terrestrial and Satellite Networks, chapter 4-5, John Wiley & Sons, Chichester, UK, 2001.
[7] C. Rose and M. Hluchyj, “The performance of random and op-timal scheduling in a time-multiplex switch,”IEEE Trans. Com-mun., vol. 35, no. 8, pp. 813–817, 1987.
Diakoumis Gerakoulisreceived his Ph.D. degree from the City University of New York in 1984, his M.S. degree from the Poly-technic Institute of New York in 1978, and his B.S. degree from New York Institute of Technology in 1976; all in electrical engi-neering. From 1984 to 1987 he was an As-sistant Professor in the Electrical Engineer-ing Department at Pratt Institute, Brooklyn, New York and, from 1987 to 1989, an
