Multiple access techniques for wideband upstream powerline communications: CAP-CDMA and DMT-FDMA Th. Sartenaer, F. Horlin, L. Vandendorpe
∗
COST 262 - 4th MCM - November 22-23, 1999, Barcelona, Spain
Abstract This paper compares two multiuser transmission techniques in the context of wideband upstream powerline communications. The first one is based on the combination of CAP and CDMA, the second one is based on DMT and relies on a share of the different carriers among the users. The issue of reception under ideal synchronisation assumptions and a simplified noise environment is addressed. Fractional FIR linear and decision feedback joint detectors are derived. A heuristic resource (code/tone) allocation algorithm is proposed.
1
Introduction
Powerline communications that is to say communication over power distribution networks is receiving much attention nowadays. The part of the network under consideration in the present paper is that located between the medium voltage/low voltage transformer and the meter in the home. This type of access network presents a number of technical challenges. First of all the cable between the line termination located at the transformer and the network termination located at the customer premises is of the multiconductor type. Most of the cables contain three conductors. Hence transmission over two out of the three conductors may be corrupted by reflections due to other propagation modes that are not properly terminated. Next, there is a lot of non white background noise coupling onto the cable. Finally the transmission may also be corrupted by impulsive noise, but the purpose of this analysis is only to take into account the effect of stationary noise sources. This access network has to be shared among different users possibly requesting different bit rates. Besides the frequencies below a certain limit cannot be used. The upper frequency will depend on how much capacity can be found. Because of its inherent frequency diversity and its multiuser and multirate capabilities, DS/SS CDMA [1, 2] is a potential candidate for a transmission technique. In the present paper we propose to associate DS/SS with CAP (carrierless/amplitude phase modulation) [3] in order to locate the transmitted signal in the appropriate band. CAP has been known for many years in xDSL transmission as the competitor of DMT (discrete multi-tone) [4] . On the other hand, the DMT scheme can be directly extended to the multiuser configuration thanks to its multicarrier ∗
The authors are with the Communications and Remote Sensing Laboratory of the Universit´e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. Email:
[email protected].
1
Th. Sartenaer - MA techniques for wideband upstream powerline communications nature [5]. Each user will be provided with a given subset of carriers, in a so-called ’DMT-FDMA’ technique. In the present paper we propose and compare CAP-CDMA and DMT-FDMA schemes for multiuser transmission over a powerline network. Depending on the chosen multiple access technique, a set of resources (codes or tones) will be allocated to each user. A simple algorithm is proposed for the allocation of those resources to the different users, depending on their respective channels. We derive FIR fractional linear and decision-feedback receivers for both transmission techniques and show their performance.
2
The channel model
International standards and restrictions concerning the use of high bandwidths in powerline cables for high speed communication purposes are under development. The available bandwidth will be down-limited as the lower part of the spectrum is dedicated to the existing low speed services and the power distribution itself. We assume a free bandwith Bu of several MHz starting from a lower limit fmin arbitrarily fixed to 1 MHz. In wired communications [6] , the restriction on the emitted power usually consists of a transmission mask giving the upper limits of the signal power spectral density γ x (ω). We assume a flat mask γmax of -60 dBm/Hz along the bandwidth Bu (the same limit as in VDSL, a wired system with similar bandwidths). Powerline networks can vary in a wide range, depending on the number of users, the actual topology, the cables nature, the lines termination, the noise environment, etc. We chose a typical network model with Ku = 5 user-modems (Network Terminations, NT1 to NT5 ) located along the main distribution cable at increasing distances from the Line Termination (LT). Multiple reflections of the signals at cables transitions and on ill-terminated cables derivations give rise to frequencydispersive channel transmittances, as illustrated on Figure 1. Powerful equalization will be needed to counteract these effects. Both NT’s and LT will be provided with an analog front end consisting of at least a line-driver for tuning the signal to the right power level, a high-pass service-splitter and a low-pass filter designed to reduce out-of-band signal components. We consider the case of an uplink, namely transmission between NT’s and the LT. The problem of duplexing will not be considered in this paper. The signal xk (t) of user k ∈ [1, Ku ] is transmitted over an analog channel with impulse response ck (t) comprising both the channel itself, the line driver and the transmit analog filters. The signal received at the LT is given by ra (t) =
Ku X
k=1
xk (t) ⊗ ck (t) + na (t)
(1)
where ⊗ denotes the convolution operator.
In this paper, we restrict ourselves to the case of an additive white gaussian noise n a (t) with twosided power spectral density γ(ω) = N0 /2 equal to -140 dBm/Hz. It has to be underlined that more complex additive noise configurations should be taken into account in realistic situations, including colored and non-stationary noises. This simplified configuration, however, is convenient for the study of multiple access techniques.
3
The CAP-CDMA transmission scheme
A subset Ck of kc (k) codes is allocated to each user from the set of Kc codes thanks to a code allocation algorithm in the LT. The impulse responses associated with the spreading codes of user 2
Th. Sartenaer - MA techniques for wideband upstream powerline communications Low voltage channels from LT to NTi (1≤ i ≤ 5) − unused taps are left open
0
−10
Channel Transmittance (dB)
−20
−30
−40
−50
−60
−70
−80
−90
0
5
10
15
20
25 30 Frequency (MHz)
35
40
45
50
Figure 1: Powerline channels transmittance k are denoted by ac (m) with c ∈ Ck . They are assumed to be of length Nc . We denote by Ica (n) and Icb (n) the sequences of real symbols of duration Tb spread with the code c allocated to user k. The signal xk (t) transmitted by user k is given by xk (t) =
∞ X X
l=−∞ c∈Ck
Ica (l) uc (t − lTb ) −
∞ X X
l=−∞ c∈Ck
Icb (l) u ˜c (t − lTb )
(2)
where uc (t) = u ˜c (t) =
c −1 1 NX √ ac (n) p(t − nTc ) Nc n=0
c −1 1 NX √ ac (n) p˜(t − nTc ) Nc n=0
(3)
and p(t) = g(t) cos(ωc t)
(4)
p˜(t) = g(t) sin(ωc t)
(5)
and g(t) is a half root Nyquist filter with roll-off factor α. The two shaping filters p(t) and p˜(t) constitute a Hilbert pair and hence p˜(t) denotes a Hilbert transform. The central frequency fc = fmin + Bu /2 corresponds to the center of the signal banwidth. Tc = Tb /Nc = 1/Bu denotes the chip duration.
4
The DMT-FDMA transmission scheme
DMT signals synthesis relies on the separation of the emitted complex symbols into N p /2−1 parallel streams (called tones) at rate Tb through the use of an order-Np Inverse Fast Fourier Transform 3
Th. Sartenaer - MA techniques for wideband upstream powerline communications operator (IFFT). The DC and Nyquist components are supposed to be left unused. In the set of Np /2 − 1 tones, only Kp ones are available as the lower ones correspond to the unused part of the spectrum. This set of Kp tones is divided among the Ku users in subsets Pk thanks to a tone allocation algorithm in the LT. The signal xk (t) transmitted by user k is given by xk (t) =
∞ X X
Ip (l) Φp (t − lTb ) +
l=−∞ p∈Pk
∞ X X
l=−∞ p∈Pk
Ip∗ (l) Φ∗p (t − lTb )
(6)
where Φp (t) =
Np −1 X 2πj np 1 p e Np g(t − nTp ) Np n=−ν
(7)
and g(t) is an interpolation filter. The second term in (6) is necessary to make the signal real. Defining Φp (t) = Φap (t) + jΦbp (t)
(8)
Ipa
(9)
Ip =
+
jIpb ,
we have the equivalent real expression for the DMT signal: xk (t) = 2
∞ X X
Ipa (l) Φap (t
l=−∞ p∈Pk
− lTb ) − 2
∞ X X
l=−∞ p∈Pk
Ipb (l) Φbp (t − lTb ) .
(10)
Tp = Tb /(N + ν) denotes the nominal DMT sample duration. An optional cyclic prefix of length ν can be added to the signal in order to provide an easier equalization, the so-called ’guard-time’ equalization technique, which is specific to the DMT basis functions. As the sample duration T p is fixed to 0.5/(fmin + Bu ), the use of the cyclic prefix adds a penalty of Np /(Np + ν) to the baud rate 1/Tb and the resulting capacity.
5
The CAP-CDMA receiver
The spectrum of the transmitted signals will extend up to fc + 0.5(1 + α)/Tc . Let us assume that Ts = Tc /Mc is a sampling period fulfilling the sampling theorem, namely Mc /Tc ≥ (2fc +(1+α)/Tc ). There is no loss of information if the received signal is sampled at the M c /Tc rate after presampling filtering f (t) with cutoff 0.5Mc /Tc . We call this a chip fractional description of the received signal. Let ra (t) ⊗ f (t) =
Ku X X
∞ X
k=1 c∈Ck l=−∞
Ica (l) hc (t − lTb ) −
Ku X X
∞ X
k=1 c∈Ck l=−∞
˜ c (t − lTb ) + nf (t) Icb (l) h
(11)
˜ c (t) = u where hc (t) = uc (t) ⊗ ck (t) ⊗ f (t), h ˜c (t) ⊗ ck (t) ⊗ f (t) and nf (t) = na (t) ⊗ f (t). We define r(l) = ra (lTs ) ⊗ f (lTs ). Besides we use a polyphase notation so that all sequences be defined at the same rate 1/Tb . We define Mc Nc polyphase components rk1 (n) (k1 = 0, Mc Nc − 1) as follows: rk1 (n) = r(nTb + k1 Ts ) =
Ku X X
∞ X
k=1 c∈Ck l=−∞
Ica (l) hc (nTb + k1 Ts − lTb ) 4
Th. Sartenaer - MA techniques for wideband upstream powerline communications
−
Ku X X
∞ X
˜ c (nTb + k1 Ts − lTb ) Icb (l) h
Ku X X
∞ X
Ica (l) hc,k1 (n − l) −
Ku X X
L2 X
Ica (n − l) hc,k1 (l) −
k=1 c∈Ck l=−∞
+ nf (nTb + k1 Ts ) =
k=1 c∈Ck l=−∞
+ nk1 (n) =
k=1 c∈Ck l=−L1
+ nk1 (n).
Ku X X
∞ X
Ku X X
L2 X
k=1 c∈Ck l=−∞
˜ c,k (n − l) Icb (l) h 1
k=1 c∈Ck l=−L1
˜ c,k (l) Icb (n − l) h 1 (12)
where it has been assumed in the last equality that the polyphase components of the channel impulse responses are of length L1 + L2 + 1 = L + 1. Using a matrix formalism, we can write:
r(n) =
h
H(L2 ) · · · H(0) · · · H(−L1 )
= Hr Ir (n) + n(n)
I(n − L2 ) .. .
i
I(n) .. .
I(n + L1 )
+ n(n)
(13)
where r(n) and n(n) are vectors of Mc Nc polyphase components, H(l) with l ∈ [−L1 , L2 ] are matrices of size Mc Nc × 2Kc and I(n) is the vector of 2Kc real symbols transmitted by the users at time n. It should be understood that this equation is a matrix formulation of a continuous transmission process, not a block based transmission scheme. From this representation, we will investigate FIR linear and decision-feedback receiver structures.
6
The DMT-FDMA receiver
The conventional detection mechanism in the DMT scheme implies the use of a direct Fast Fourier Transform (FFT) operator, after removal of the cyclic prefix. If we make use of the guard time technique, it would be helpful to use a time domain equalizer (TEQ) in order to shorten the main energy of the channel impulse response down to the cyclic prefix duration. In the multiuser case, however, different subcarriers are affected by different channels and the TEQ method is not directly applicable. If we want to keep the guard time duration below a reasonable value or if we don’t make use of the TEQ technique, the use of an equalizer in the frequency domain (FEQ) will be needed. Because of the sidelobes of the DMT basis functions, the transmitted signals are not strictly bandlimited to 0.5/Tp . It is possible to gain some information about the transmitted symbols by sampling the received signal at a rate 1/Ts = Mp /Tp with Mp > 1. In that case, we propose to use an order-Mp Np FFT operator whose Np /2 first complex analysis filters are oversampled versions of the complex synthesis filters, and the (Mp − 1)Np /2 remaining complex analysis filters provide some extra-information about the received signals to the equalizer input. Again, we can write: 5
Th. Sartenaer - MA techniques for wideband upstream powerline communications
ra (t) ⊗ f (t) =
Ku X X
∞ X
Ipa (l) hap (t
k=1 p∈Pk l=−∞
− lTb ) +
Ku X X
∞ X
k=1 p∈Pk l=−∞
Ipb (l) hbp (t − lTb ) + nf (t)
(14)
where hap (t) = 2Φap (t) ⊗ ck (t) ⊗ f (t) and hbp (t) = −2Φbp (t) ⊗ ck (t) ⊗ f (t). We define s(l) = ra (lTs ) ⊗ f (lTs ). Using the polyphase notation, we define Mp (Np + ν) real polyphase components sk1 (n) (k1 ∈ [−Mp ν, Mp (Np − 1)]) as follows: sk1 (n) = s(nTb + k1 Ts ) .
(15)
The analysis stage transforms them into Mp Np real frequency-domain components according to: rpa (n) rpb (n)
=
1 p M p Np
Mp Np −1
1 = −p M p Np
X
k1 =0
k1 p sk1 (n) cos 2πj Np
Mp Np −1
X
k1 =0
!
k1 p sk1 (n) sin 2πj Np
!
(16)
with p ∈ [0, Mp Np /2 − 1]. Combining equations (7), (14) and (16), we can combine the sampled transmittances hp (l) with the Mp Np analysis filters to get Mp Np transmittances at rate Tb . Again, we assume these transmittances are limited to a length L1 + L2 + 1 = L + 1. The optional presence of the cyclic prefix makes this manipulation sligthly more difficult than equation (12). The result is a straigthforward matrix expression equivalent to equation (13), where r(n) and n(n) are vectors of Mp Np frequency-domain components, H(l) with l ∈ [−L1 , L2 ] are matrices of size Mp Np × 2Kp and I(n) is the vector of 2Kp real symbols transmitted by the users at time n.
7 7.1
FIR joint detection FIR linear joint detection
In both schemes, FIR linear joint detector will build estimates of the 2K r symbols streams (Kr = Kc or Kp ) from the M N received samples streams (M N = Mc Nc or Mp Np ) in the following way:
ˆI(n) =
h
C(K2 ) · · · C(0) · · · C(−K1 )
= Ct rt (n)
r(n − K2 ) .. .
i
r(n) .. .
r(n + K1 )
(17)
where C(l) with l ∈ [−K1 , K2 ] are matrices of size 2Kr × M N . About the processed samples one can also write rt (n) = Ht It (n) + nt (n)
(18)
where Ht is a M N (K1 + K2 + 1) × 2Kr (K1 + K2 + L + 1) matrix built as follows:
H(−L1 ) 0 H(L2 ) H(L2 − 1) · · · H(L2 ) · · · H(−L1 + 1) H(−L1 ) .. .. .. .. . . . . H(L2 ) ··· · · · H(−L1 ) 0 6
.
(19)
Th. Sartenaer - MA techniques for wideband upstream powerline communications We have that
I(n − K2 − L2 ) .. .
It (n) =
I(n) .. .
I(n + K1 + L1 )
n(n − K2 ) .. .
nt (n) =
n(n) .. .
n(n + K1 )
.
(20)
i
(21)
ˆ of estimates is of size 2Kr . The corresponding vector of correct symbols can be The vector I(n) obtained from the vector I t (n) by means of a matrix F which extracts the right subblock: I(n) = F I t (n) F =
h
02K
r ×2Kr (K2 +L2)
E2K
02K
r
r ×2Kr (K1 +L1 )
where 0X stands for a matrix of zeros of size X and EX stands for an identity matrix of size X. The vector of estimation errors can be computed as = Iˆ − F I t .
(22)
We can use the orthogonality principle and the matrix inversion lemma to design the joint detector according to the MMSE criterion. We denote by RXY the correlation matrix between vectors X and Y . We obtain that
−1
Ct = F RI I + t t
HH R−1 n t nt t
Ht
H −1 R = F R−1 It It + Ht Rnt nt Ht
7.2
−1 −1
HH R−1 t nn
(23)
FT .
(24)
t
t
DF joint detection
In a DF receiver, one also uses the decisions on a number K3 of previous blocks of symbols. Furthermore, we assume that each time a new symbol is detected in the current block, it is used for the next estimation to be performed. Hence, the estimation is computed as follows (perfect past decisions are assumed): i h ˆ I(n) = Ct rt (n) − B − F I t (n) (25) where B is a matrix with ’1’s in the same positions as matrix F and non zero values only at the left of this diagonal of ’1’s. This makes the feedback causal.
We can again use the orthogonality principle. It comes Rr
= 0 t
C = B RI r R−1 rt rt . t t
(26)
Then the correlation matrix of estimation errors is given by
−1
R = B RI I + t t
R−1 HH t nt nt
Ht
−1
BT .
(27)
Matrix B is made, from the left, of a number of null columns (the number depends on how many past decisions are used), then a number of non zero values bounded at the right by the diagonal of ’1’s, and then again ’0’s corresponding to the future symbols. It appears that the non-zero part of 7
Th. Sartenaer - MA techniques for wideband upstream powerline communications matrix B, denoted by B’, can be seen as a lower triangular matrix with ’1’s on the main diagonal, and of which some upper lines have been removed. We can also write the correlation matrix of prediction errors as (28) R = B’ Rgg B’T where Rgg is that part of the inverse matrix affected by non zero values of matrix B’. That matrix will also be a correlation matrix and hence has an Lg Λ LTg decomposition where Lg is lower triangular and Λ is diagonal. On another hand the inverse of a lower (resp. upper) triangular matrix is also lower (resp. upper) triangular. Then we can select for B’ to be the lower part of the lower triangular matrix which is inverse of Lg . The prediction errors will be corresponding eigenvalues.
8
Bit rates estimation
In both systems, every user is provided with a number of pairs of parallel data streams consisting of PAM symbols at a baud rate 1/Tb . The constellation size of a specific stream can be adapted to the reception quality. Considering a target symbol error probability P s , and assuming that the decision variable is approximately gaussian, the maximum number of bits per PAM symbol is given by the well-known formula: SNIR 1 ) (29) b = log2 (1 + 2 Γ where Γ, the ’SNIR-gap’, is a function of Ps , and the SNIR is defined as the ’Signal to Noise plus Interference ratio’ on the symbols stream. Interference comes from adjacent symbols on the same stream (Inter Symbol Interference) and from symbols on the other streams (Inter Carrier Interference, Inter Code Interference, or more generally Multiple Access Interference). The total system bit rate is given by the following expressions: CCAP = γduplex Bu log2
2K Yc
c=1
CDMT = γduplex
SNIRc Γ
! 2N1
c
2Kp
(30)
Y SNIRp Np Kp (fmin + Bu ) log2 Np + ν Np /2 Γ p=1
1 2Kp
(31)
where the effect of the Nyquist filter rolloff α has been neglected in (30) (assume the effective bandwidth goes below fmin and upon fmin + Bu because of α). γduplex is introduced to take into account the duplexing scheme, supposed here to be Time Division Duplexing (TDD). It is the ratio between the time dedicated to the uplink transmission and the total time for both transmissions (uplink and downlink). A useful bound on the attainable equalizer performance is the ’Matched Filter Bound’ (MFB) defined as the best reachable SNR in the absence of interfering streams, when a single symbol is sent on the useful stream. This best SNR is given by 2Es /N0 , where Es is the PAM symbol energy at the receiver. By properly tuning the choice of the parameters, the coefficients in front of the log function in (30) and (31) can be made equal if ν = 0. In the case of ideal channels ck (t) = A δ(t − T∆ ), all the Es are the same in both modulations and the geometrical means in (30) and (31) are also equal if we consider the MFB and if Kc = Nc . This shows us that both techniques have the same potentialities in terms of bit rates. With non-ideal channels, all the tones or all the codes won’t have the same potentialities for a given user. Considering the Ku different channels, an important problem to solve is the partitioning of the resource set in order to maximize the resulting bit rate. 8
Th. Sartenaer - MA techniques for wideband upstream powerline communications
9
A simple resource allocation algorithm
Assuming an initial set of Kr resources to be shared among the Ku users, there are (Ku + 1)Kr possible allocations if we consider the possibility of leaving some resources unused. The choice of the optimal allocation is a problem of best assignment that can be solved by a long and systematic search. We could analyze the contribution of each resource at the output of an analysis device (matched filter or FFT operator), when assigned to every of the Ku users. This contribution would consist of one useful signal on the right output and Kr − 1 interference components on the Kr − 1 other outputs. With Ku matrices of size Kr × Kr representing this information, plus a vector of Kr noise components, the choice of a specific allocation scheme would come down to the selection of the right subsets of columns in the matrices and the calculation of the resulting bit rate would be straigthforward. A difficulty at this point comes from the use of equalizers to obtain the final SNIR that will decide for the bit rate. Indeed, the equalizers coefficients depend on the chosen resource allocation, and recomputation of the equalizer would be needed for every considered allocation. To overcome this problem, we remind that the MFB is a good indicator of the reachable bit rate for a specific resource on a specific channel, especially if the joint detection process is efficient. We propose to select the allocation of the available resources on that simplified criterion. The basis for that work is just the computation of Ku size-Kr vectors giving the metrics Ck,r =
1 2Tb
log2 (1 +
2EsI (k,r) N0 Γ )
+ log2 (1 +
2EsQ (k,r) N0 Γ )
with k ∈ [1, Ku ] and r ∈ [1, Kr ].
To select the best allocation, we still need a criterion of optimality. A possible choice would be the maximization of the total system bit rate, but the corresponding optimum could be the allocation of all resources to the user with the best channel, which is of course not acceptable. Some constraints have to be defined that guarantee a fair share between the users. In real systems, these would depend on the effective needs of the users. As an example, we assume all users request an access to the same type of service. The optimisation criterion will be the total bit rate C tot under a fairness constraint on the ’users imbalance index’ ∆users defined as: ∆users = where C¯ =
1 Ku
P
k
Ck =
1 Ku Ctot
maxk (Ck ) − mink (Ck ) ≤δ C¯
(32)
is the average user bit rate and δ is a small tolerance coefficient.
It is assumed that some allocation schemes satisfying (32) exist. This will be true if the imbalance between the channels is not too large and if the number of available resources is high enough to compensate for that imbalance by the allocation of a different amount of resources to the users. The following algorithm is proposed: Step 1 Compute an initial allocation. Every user is provided with the same amount of Ku /Kr resources. The weakest user, i.e. P the user with the smallest r (Ck,r ), is given the priority. He gets his best resource. After each allocation, the identity of the weakest user is recomputed on the basis of the remaining resources. After this step, weak users got the preference but this could be insufficient to meet condition (32). Step 2 Swap resources to get a fair bit rates distribution. Select the user k1 with the smallest bit rate. That user will be provided with one resource r from another user k2 in order to get closer to condition (32). From all possible swaps, select the one that maximizes the bit rate increase Ck1 ,r − Ck2 ,r (or, more probably, that minimizes the bit rate decrease). Continue until the condition is met. 9
Th. Sartenaer - MA techniques for wideband upstream powerline communications Step 3 Swap resources to maximize the total bit rate under the fairness constraint. Once we reached the region of allocations satisfying (32), it could be possible to increase C tot by single swaps as in the last step, under the condition that (32) remains valid. Consider every user and every resource not allocated to that user. If that resource comes to that user, verify that (32) remains valid and that the bit rate increase is positive. Stop when all potential bit rate increases are negative. The algorithm proposed here is not optimal in the sense that it is based on the MFB. As the effective SNIR obtained at the output of the detector could be quite smaller, a new iterative procedure should follow in order to reach condition (32) on the user bit rates.
10
Results and conclusions
Figures 2 and 3 illustrate the power spectral density of the signals emitted by NT 2 in CAP-CDMA and DMT-FDMA respectively. The available bandwidth goes from 1 to 11 MHz (B u = 10M Hz). The effective spectral occupation is sligthly higher because of the filters rolloff α. In the first scheme, the set of length-64 orthogonal Hadamard codes was used (Kc = Nc = 64). After the code allocation algorithm, user-2 was provided with 10 codes. In the second scheme, a length-128 IFFT was used, without cyclic prefix (Np = 128, ν = 0). 58 out of the 64 tones were available for the transmission (Kp = 58). After the tone allocation algorithm, user-2 was provided with 9 tones. By comparison of both figures, we can see that the signal emitted by a single user does not reach the spectral mask γmax in the CAP-CDMA case, when only a subset of the codes is allocated to that user. This is not the case in the DMT-FDMA configuration, where every tone reaches the maximum power spectral density on its center frequency. If the power constraint dictated by the standards is limited to the modem output, we could take profit of it to boost the CAP-CDMA signal by some dB’s to reach the limit. If all the modems are sufficiently far from each other, there would be no risk to overstep the bound when signals add to each other, as this would happen after a sufficient attenuation of the transmitted signals. This issue requests a thorough study of signals profile along the power cable. Figures 4 and 5 give the SNIR profiles at the output of the detectors, together with the MFB. The lower figures give the code and tone allocation schemes respectively. CAP-CDMA with joint detection (JD), which is now very popular [7], is highly efficient as can be seen from figure 4. This figure also shows the large difference between DFE or linear JD on the one hand, and detection of whitening matched filter output on the other hand. Finally, there is also a significant improvement of DF vs linear JD, but the reader should be reminded that perfect past decisions are assumed. In DMT-FDMA, for the FFT sizes considered here (up to Np = 256), no acceptable guard time duration could be found because of the channels impulse responses length. As also the TEQ technique does not work as such in a multiuser scenario, it was decided not to use any guard time and to implement a FEQ which is in fact a JD device. The global system bit rate here is summarized in table 1, with equalizers sizes K 1 = K2 = K3 = 4 (reasonable values as L1 and L2 are in the same range), γduplex left to 1 and a symbol error probability Ps = 10−7 . Please also remember the poor noise model used here. Both systems seem to have comparable potentialities if decision feedback is used. In DMT-FDMA, the joint detector could be replaced by a lower complexity detector consisting of the combination of a very large FFT and a sufficient guard time. Corresponding bit rates are 10
Th. Sartenaer - MA techniques for wideband upstream powerline communications
Linear-JD DF-JD MFB
CAP-CDMA Kc = 32 Kc = 64 67 (1.42) 69 (1.31) 97 (0.58) 102 (0.41) 119 (0.18) 119 (0.14)
DMT-FDMA Kp = 29 Kp = 58 82 (0.63) 87 (0.47) 101 (0.34) 101 (0.24) 108 (0.18) 107 (0.19)
Table 1: Bit rates (Mbits/s) and ∆users
illustrated on figure 6, for a system working with a size-4096 FFT, as a function of the cyclic prefix length ν. It appears that the best performance (85 Mbits/s) is below that of the DFJD. Furthermore, accurate users synchronisation is necessary to get such a low multiple access interference level. Another drawback is the higher system latency involved by the large FFT-size. Finally a simple scheme was proposed to share the resources among the users, based on the MFB. It has to be underlined that in the case lower complexity detectors are used, this scheme won’t be effective at all as the real bit rates calculated at the detectors output could present very large imbalances between the users. The algorithm is more efficient in the DMT-FDMA scheme as the MFB is easier to reach. A more complex allocation algorithm, taking into account the performance of practical detectors, is under investigation. The idea is to initialize the allocation procedure with the MFB-based algorithm, and to compute the joint detector corresponding to that first scheme. If the resulting bit rates distribution is too unfair, one resource should be given from the best user to the weakest one. The joint detector corresponding to that new scheme can be computed easily from the former one, as only one resource swaps from one channel to another. The iterative process goes on until we obtain a fair bit rates distribution.
References [1] IEEE Journal on Selected Areas in Communications, vol. 12, No. 4, May 1994. [2] IEEE Journal on Selected Areas in Communications, vol. 12, No. 5, June 1994. [3] G. H. Im and J. J. Werner, ”Bandwidth efficient digital transmission up to 155 Mps over unshielded twisted pair wiring”, IEEE Journal on Selected Areas in Communications, vol. 13, No. 9, December 1995, pp. 1643-1655. [4] J. Cioffi, ”A Multicarrier Primer”, T1E1.4/91-157, November 11, 1991. [5] H. Sari, Y. L´evy, G. Karam, ”Orthogonal frequency-division multiple access for the return channel on CATV networks”, Proceedings ICT’96, Istanbul, Turkey, April 1996, pp. 602-607. [6] T1E1.4 VDSL Editor, ”Very high speed digital subscriber lines - system requirements”, T1E1.4/98-043R8, November 1998, Plano. [7] S. Verdu, “Multiuser Detection”, Cambridge University Press, 1998.
11
Th. Sartenaer - MA techniques for wideband upstream powerline communications
−55
Signal from NT2 Signals sum (NT1 to NT5)
−60
Transmit CAP−CDMA signals (dBm/Hz)
−65
−70
−75
−80
−85
−90
−95
−100
1
2
3
4
5
6
7 8 9 frequency (MHz)
10
11
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13
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15
Figure 2: Power Spectral Density of CAP-CDMA transmitted signals - K c = Nc = 64
−55
Signal from NT2 Signals sum (NT to NT ) 1
−60
5
Transmit DMT−FDMA signals (dBm/Hz)
−65
−70
−75
−80
−85
−90
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−100
1
2
3
4
5
6
7 8 9 frequency (MHz)
10
11
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13
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Figure 3: Power Spectral Density of DMT-FDMA transmitted signals - N p = 128, Kp = 58, ν = 0
12
Th. Sartenaer - MA techniques for wideband upstream powerline communications
MFB SNIR out of DF−JD (M=3) SNIR out of linear−JD (M=3) SNIR out of whitening matched filter
80
Signal to Noise Ratios (dB)
70 60 50 40 30 20 10 0 −10
User NT
−20 5 4 3 2 1 4
8
12
16
20
24
28
32 36 code index
40
44
48
52
56
60
64
Figure 4: SNIR on received codes (CAP-CDMA) - Mc = 3, K1 = K2 = K3 = 4
MFB SNIR out of DF−JD (M=2) SNIR out of linear−JD (M=2) SNIR out of FFT operator
80
Signal to Noise Ratios (dB)
70 60 50 40 30 20 10 0 −10
User NT
−20 5 4 3 2 1 4
8
12
16
20
24
28
32 36 tone index
40
44
48
52
56
60
64
Figure 5: SNIR on received tones (DMT-FDMA) - Mp = 2, K1 = K2 = K3 = 4
13
Th. Sartenaer - MA techniques for wideband upstream powerline communications
100 Upper bound 90 80
Bit rates sum
Bit rate (Mbits/s)
70 60 50 40 30 Bit rates NTi
20 10 0
0
40
80
120
160
200 240 280 320 Cyclic prefix length (# samples)
360
400
440
480
Figure 6: Bit rates for a size-4096 DMT-FDMA system with guard time equalization vs cyclic prefix length
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