GLOBECOM’95, SINGAPORE, NOV. 1995
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Performance of Capture-Division Packetized Access (CDPA) with Partial Frequency Reuse and Power Control Flaminio Borgonovo, Michele Zorzi, Luigi Fratta Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy Piazza leonardo Da Vinci, 32 - 20133 Milano, ITALY fax: +39-2-2399-3413; e-mail: last
[email protected]
Abstract
— Recently, a new method for achieving spectrum reuse in cellular systems, called Capture-Division Packetized Access (CDPA), has been introduced. The method uses a single frequency in all cells but, unlike CDMA, allows each transmitter to access the full bandwidth. Practically, the CDPA’s way of operation can be seen as an S-ALOHA scheme among different cells in which the Mobile Terminals belonging to the same cell transmit using a collision-free mechanism, which is easily obtained due to the very short intra-cell propagation delay. Parallel transmission in different cells is achieved through the “capture” capability. Packets that are not captured are almost immediately retransmitted, thus assuring that packets are eventually correctly received. In this paper we analyze an extension of the CDPA that uses partial frequency reuse. In fact, in this case, a trade-off exists between the bandwidth wasted by retransmissions and the bandwidth wasted by subdividing spectrum usage in K parts. It is shown that, depending on the capture threshold ratio b at receivers, an optimal choice exists. In all cases, the spectrum efficiency obtained almost doubles the efficiency of systems, like GSM, with K = 7. The gain offered by power-control techniques is also investigated. I. INTRODUCTION Recently, a new method for achieving spectrum reuse in cellular systems, called Capture-Division Packetized Access (CDPA), has been introduced [1, 2, 3]. CDPA is, in fact, a novel cellular architecture for wireless communications between Mobile Stations (MS) and Base Stations (BS), which exploits at three different levels the benefits of packet switching. The first level is the channel reuse technique, which is the method by which the same channel can be reused in different cells. The second level concerns the channel transmission scheme within a cell and the third level is the type of wireless-channel procedure to connect to the Base Stations. Two different approaches to channel reuse are currently proposed. The first one is adopted in narrowband systems, e.g., GSM [4], where the system bandwidth is divided into a number of channels, and the same channel is assigned for use to a fraction of cells in such a way that the distance between cells that use the same channel is maximized and the interference is reduced to a tolerable level. The second solution is CDMA, where interference from adjacent cells is dealt with by Spread-Spectrum techniques. The price to be paid is a bandwidth subdivision in the first case, and the need for a bandwidth spreading in the second. The CDPA channel reuse technique is based on packetized transmission and the receiver capture, which is the ability of the receiver to detect a signal in the presence of interference noise. The same channel is used in all cells and transmissions in each cell occur This work has been partially supported by CNR and MURST, Italy.
independently of those in other cells. Since the interference from other cells changes rapidly with time because of changes in traffic conditions, transmitters and channel attenuation, packet transmission can statistically take advantage of periods in which the interference is low and the capture of packets is possible. When this happens, packets are correctly received, and parallel transmission is achieved. Otherwise, packets are retransmitted. In practice, an ALOHA retransmission scheme is used to solve “contentions” among transmissions of different cells. If the traffic is adequately low, and a retransmission scheme is implemented, a complete reuse of the bandwidth does not inhibit system operation [5]. The advantage of this approach is that the bandwidth is wasted only when necessary (i.e., to retransmit erroneous packets), as opposed to an “a priori” protection strategy, where the waste of bandwidth is always incurred. As a matter of fact, the analytical models presented in [1, 2] show that the CDPA presents a throughput gain over classic schemes as FDMA with a 7 cell reuse pattern. The channel transmission scheme used by CDPA within the cell, is a polling-like mechanism, C-PRMA [6], which is very efficient because of the short propagation delays and can easily integrate different types of traffic. This access method, if coupled with a smart scheduling strategy, allows a prompt retransmission of erroneous packets, so that the total packet delay can be kept within acceptable values. This feature makes CDPA an attractive system even for delay-sensitive traffic, such as voice. Finally, the packet switching technology allows to use connection-less communication between MSs and BSs. This, combined with the use of the same frequency in all cells, is expected to drastically reduce the hand-over traffic on the radio links. The analysis appeared in [1, 2] refers to the case in which the frequency reuse is complete, i.e., the full bandwidth is allocated to each cell, as in CDMA. In this paper, we extend the analysis to the more general case in which CDPA is used in conjunction with partial frequency reuse. This framework leads to the assessment of a trade-off between the probability of successful transmission and the spectrum efficiency. Our results, limited to the throughput analysis, indicate the existence of an optimum cell-cluster size, which depends on the capture ratio assumed at the receivers. We also consider the use of power control and provide the corresponding throughput performance. In Section II the CDPA architecture is briefly described, and in Section III the throughput analysis is presented. Numerical results are given in Section IV, and the Conclusions are drawn in Section V. II. CDPA BASICS The Capture-Division Packetized Access is a cellular access architecture that operates on a packet switching basis [1, 2]. Transmissions from Mobile Stations (MS) to Base Stations (BS) use
GLOBECOM’95, SINGAPORE, NOV. 1995
Fig. 1. Uplink and downlink-channel time relationship.
the uplink channel, while transmissions from BSs to MSs use the downlink channel. For sake of simplicity, in the following we assume that two disjoint frequency bands are assigned to these channels for narrowband transmission. The implementation of each channel uses the same frequency in all cells. The transmissions on both channels are temporally and logically driven by the BS, which periodically releases commands on the downlink channel. The time between consecutive commands is constant and defines the channel slot as a logical entity that can be usefully referred to in the sequel. Uplink packet transmissions occur as depicted in Figure 1, where all signals are observed by three MSs, assumed at the same distance from the BS. Commands, like in polling systems, trigger the immediate response of the polled station (processing times are ignored). The time between two consecutive commands is set equal to the packet transmission time plus the maximum round trip delay, 2 . This guard time is needed, in order to allow the complete reception of uplink packets before a new command is issued. An unsuccessful MS transmission is promptly recognized by the BS, which can reschedule a new attempt by issuing the appropriate command. In the downlink channel, packets are transmitted by the BS after the command. This transmission, however, requires an explicit acknowledgment, which is transmitted by the MS starting 2 seconds after the BS packet has been received, to avoid overlapping with the packet transmission from another MS. The above procedure, which manages the packet transmissions on the radio channel, allows the immediate retransmission of corrupted packets. It is used in CDPA, together with a scheduling algorithm, to overcome the packet errors due to collisions among transmissions in different cells. A key role in accomplishing prompt retransmissions is played by the scheduling algorithm, which must be flexible enough to efficiently integrate transmissions and retransmissions, according to the specific needs of each source. In particular, it must be able to support constant rate traffic, such as voice with or without silence suppression, and data traffic with different constraints. We remark that an algorithm with these features will make possible packet voice transmission with retransmission recovery, a technique usually not considered due to delay constraints. A possible implementation of such an algorithm is C-PRMA, described in [6]. However, in this paper we will refer to a simplified versions of the algorithm, suitable for constant rate traffic only. The effective multiplexing of discontinuous sources requires an MS to be polled only when ready to transmit. While the polling mechanism can be interrupted simply by a flag in the MS packet header, the polling resume requires a further signaling channel from MS to BS to transmit a connection request (CR). Such a signal is also used to start a new connection set up. Therefore, besides
2 uplink reserved slots, i.e. slots dedicated to packet transmissions, some uplink slots are dedicated to the transmission of CRs. These slots, signaling slots, are declared by appropriate commands in the downlink channel and can be used by all MSs willing to send CRs. A possibility is to subdivide the signalling slot into several mini-slots that can be used by MSs according to some random access technique. As in this paper we are only interested in the performance evaluation of the channel reuse technique, this issue will no longer be considered. In this paper, we ignore the errors in ACK and command transmissions, caused by cochannel interference. As these errors drastically reduce the system throughput, the adequate protection of ACKs and commands is to be accomplished by means of specific transmission techniques. The effectiveness of specific coding techniques and the impact on system performance are discussed in [7]. In this paper, we also assume that the transmissions of commands at different BSs are synchronized. This assumption, although not strictly required for system operation, positively affects the system performance, as in the case of Pure and Slotted Aloha, and simplifies the performance analysis. III. THROUGHPUT ANALYSIS To derive the average throughput on the uplink and downlink channels of a cellular system operating under the CDPA technique with complete or partial frequency reuse, the total bandwidth is subdivided into K sub-bands. Each cell is assigned a sub-bandwidth, according to a regular pattern. As a result, the cells are grouped into clusters, i.e., groups of K cells which use different sub-bands. Clusters are repeated to cover the whole plane. Due to geometric requirements related to the possibility of covering the plane with symmetric clusters of hexagonal cells, only some values of K are possible [8]. In the following, we consider K = 1; 3 and 7. Note that K = 1 corresponds to the complete frequency reuse of pure CDPA. To carry out the analysis we make the following assumptions. The base stations are evenly spaced on the plane, at the center of ideal hexagonal cells, and operate with omni-directional antennas. For analytical convenience, the hexagonal cell area will be normalized to , and the cells will be approximated by circles of unit radius. Each terminal is assumed to talk to the nearest base station and to transmit using the corresponding carrier frequency, assigned according to some frequency-reuse pattern (FDMA is assumed for reference but TDMA can be used as well). MSs use slotted packet transmission and, within a cell, uplink transmissions are scheduled so that only one MS at a time can transmit, and contention is avoided (C-PRMA). Packet transmissions in different cells are also synchronized on a common slotted time basis, so that multiple transmissions overlap completely. Similarly, each BS transmits packets to the MSs within its own cell. The same frequency-reuse pattern, on a distinct band from the one used for the uplink transmissions, is assumed for the downlink communications. Due to the polling mechanism, the BS can regulate the traffic in the cell. We assume that, in a cell, a packet transmission occurs in each slot with probability G, which has the meaning of average offered traffic per slot. The power PR , received from a transmitter located at distance r, is computed assuming a propagation model that takes into account Rayleigh fading, due to multipath, log-normal shadowing, due to the terrain irregularities, and an -th power-loss law. The propagation loss exponent, , typically takes values close to 4 [9]. The
GLOBECOM’95, SINGAPORE, NOV. 1995
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received power, PR , is therefore given by [10]
PR = 2100:1 Ar? PT ;
(1)
where 2 is an exponentially distributed random variable with unit mean, is a Gaussian random variable with zero mean and variance 2 , Ar? accounts for the power-loss law, and PT is the transmitted power, which may not be the same for all terminals, if power control is used. Since is the lognormal attenuation in decibels, the shadowing parameter, , is usually given in dB. The probability, Ps , that the packet transmitted in cell “0” is successfully received at the base station when the interference contributed by N other cells is considered, is given by
Equation (5) represents a generalization of Eq. (37) in [11], which admits no general solution. Fortunately, a simple solution exists for the practical case in which a uniform throughput is required. In this case, s(}) s and S = s, where is the area of the cell. Thus, substituting in (3) g(}) obtained from (5), we have
G = s E P (G; }) ; s
? 2 0:1 0 PT >b ; (2 ) Ps = P PN 010 2 Ar 0:1i Ar ? P Ti i i=1 i i 10 where b is the capture ratio, and i is a binary random variable which takes values in f0; 1g and accounts for the fact that an interferer may or may not be present in cell i. Depending on N and on the distribution of the ri’s in (2), different situations can be taken into account, as described in detail later. Packets that have failed transmission (with probability 1 ? Ps)
S (G) = G
0
E
0
must be retransmitted. These retransmissions, along with the new packet transmissions, constitute the offered traffic, which is characterized by the average intensity, G packets per slot per cell. As the probability Ps = Ps(}) depends on the intended user’s location within the cell, }, the offered traffic density is a function of }, i.e., g(}). The total offered traffic in a cell can thus be expressed as Z Z
G=
2
0
d
1
0
rdrg(r; ) = E g(}) ;
(3 )
where } has been expressed through the polar coordinates r and . Similarly, the throughput is given by
S=
Z 2 0
d
Z
1 0
rdrs(r; ) = E s(}) ;
(4 )
where s(r; ) is the throughput density. To develop a tractable analytical model we make the following additional assumptions. Assumption I. Transmissions in the i-th interfering cell occur at the same rate (G) regardless of the location of the transmitter in cell i. Assumption II. The occurrence of transmissions in a slot are statistically independent events. Assumption III. The random variables 2i and i are assumed to be statistically independent of each other and from slot to slot. Assumption I ignores that transmissions originate within an interfering cell according to a spatial density given by g(r; ), and assumes a uniform distribution. Note, however, that the dependence of the traffic density on the location is taken into account for the intended user. This approximation is needed to make analytical evaluations possible. The impact of this assumption is negligible, as it can be seen in [3], where some simulation results with the correct transmission density have been produced. As a consequence of this assumption, we have P [ i = 1] = G, for any i and the probability Ps becomes function of G only, and not of the function g(}i ). The throughput is then evaluated as the fraction of packets correctly transmitted, i.e.,
s(}) = Ps(G; })g(});
(5 )
(6)
and therefore, the throughput of a cell as function of derived by (6) as
#
"
1
1
?1
Ps(G; })
G can be
:
(7)
If partial frequency reuse is adopted, the bandwidth available in a cell is 1=K of the system bandwidth, and therefore the actual throughput is given by
S (G) = S (KG) :
(8 )
The throughput S represents the system efficiency, and provides the performance of the system in terms of number of admitted users per cell (i.e., the system capacity). The evaluation of (8) for different values of K allows to investigate the trade-off between channel efficiency and cochannel interference. To obtain numerical results, we need to specify the interference distribution, which depends on the direction of communications, on the frequency-reuse pattern, and on the power-control policy. This will be done in the rest of this section, where we consider several specific cases. A. Mobile-to-base (uplink) channel In the mobile-to-base (uplink) direction, due to the circular symmetry, the dependence on } is actually reduced to the distance, r. As for interfering transmissions, Assumption I and the independence of the interference from the angular position of the interferer assure that transmissions in cell i can be seen as originated uniformly within the circular ring described by cell i, when it is rotated around base station 0. If we denote by Ri1 and Ri2 the inner and outer radii of this ring, following the analysis carried out in [10], we obtain, when N potentially interfering cells are considered, N e? Y d p 2 i=1 ?1
Z
Ps(G; r0) =
1
2
2 2
1?G
Ji (; r0) ; R2i2 ? R2i1
(9)
where
Ji (; r0) =
? Z Ri e dx p 2 Ri ?1
Z
1
x2 2 2
2
1
2rdr
? 1 + b?1 100:1(?x) r
0
r
;
(10) In (9), the product represents the joint conditional probability of success. Each term takes into account an interferer, and the product form is assured by Assumptions II and III. The outer integral is the average over the shadowing of the intended user. On the other hand, the integrals in (10) correspond to averaging the shadowing and the location of the i-th interferer. Eqs. (9) and (10) allow to study different frequency-reuse schemes. Based on the above equations, the probability of successful transmission and the average throughput can be analytically evaluated
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for any K . For K = 1, however, a further simplification is possible, based on the following assumption, that generalizes Assumption I: Assumption Ib. Interfering transmissions are originated according to uniform spatial distribution, of density G transmissions per cell, in the region outside cell 0. With this assumption, all terms of the product in (9) become equal, Ri1 is replaced by 1 and Ri2 and N tend to infinity. In more detail, since a circular ring with R1 = 1 and large R2 contains approximately R22 ? R21 cells of area , we have
N ' R22 ? 1;
as R2
!1
(11)
and
Ps (G; r0)
e? 1 ? G J (; r0) p d lim R !1 ?1 R22 ? 1 2 Z 1 ? e p e?GJ (;r ) ; d 2 ?1 Z
=
1
2 2 2
R22 ?1
2
=
J (; r0) =
Z
0
?
1
?1
e dx p
x2 2 2
Z
2
1
1
2rdr ? ; 1 + b?1 100:1(?x) rr0
(13)
B. Base-to-mobile (downlink) channel In the base-to-mobile direction, the situation is different, since the transmitters are fixed and the receiver is randomly located. As a result, Assumption I is naturally satisfied. For the parameters related to the base to mobile traffic, we will use the same notation as for the mobile to base case. The analysis reported in [5] leads to the following expression for the success probability:
Ps(G; }) =
N ? e? Y 1 ? GJi (; }) ; d p 2 i=1 ?1
1
2 2 2
(14)
i=1
#
20
i 2i 100:1(i? i ) ri? r0i 0
>b :
(16)
The compensation of the attenuation due to shadowing, implemented in the above power-control scheme, has the drawback of doubling the parameter 2 of the shadowing of the interferers. In fact, each term in the denominator of (16) contains the factor 100:1(i?0i ) , in which i and 0i are two i.i.d. Gaussian r.v.’s. This may have a negative effect on the overall performance, especially in the presence of large shadowing fluctuations. To evaluate the effect of compensating the shadowing, we consider a modified power-control scheme, the near-far power-control scheme, which compensates for the distance attenuation only. In this case, the probability of success is given by "
#
2 0 :1 Ps = P PN 0210 0:1i ? > b : ri r0i i=1 i i 10 0
(17)
We remark that we want to understand how the control of different propagation effects affects the performance; therefore, we do not discuss the feasibility of this second scheme, which would require tracking the mobile position. The analytical computation of (16)-(17) is too complex (although possible), so we turned to Monte-Carlo evaluation. IV. NUMERICAL RESULTS AND DISCUSSION
with
Ji (; }) =
PN
(12)
as reported in [1]. A comparison between the two evaluation methods (each interferer distributed in its own cell, and all interferers distributed within the whole region) shows that the difference in results is negligible.
Z
"
Ps = P
2
2 2
attenuated reduces interference. Second, the compensation reduces the retransmissions of the disadvantaged users, located at the cell edge. Since the throughput must be equal for all users, disadvantaged users constitute the bottleneck of the system, so that improving their performance improves the overall performance. Power control is also crucial in systems like CDMA [12], and may provide a considerable gain in performance in systems like TDMA. The classic power-control scheme assumes that only the longterm attenuation (i.e., attenuation due to the path loss law, r? , and to the shadowing) is compensated. In such a scheme, the transmitted power for user i, PTi , is inversely proportional to r0?i 100:10i , where the subscript 0i refers to the attenuations on the path from user i to its own BS, as opposed to the subscript i, which denotes the same quantities with reference to the intended BS. The probability of success (2) can be written as
1 e? ; dx p 2 1 + b?1 100:1(?x) r ?1 r
Z
1
x2 2 2
(15)
0
i
where the interference from the nearest N cochanel cells is considered, and ri , i = 0; 1; : : :; N , represents the distance between the intended receiver position }, randomly located, and the i-th BS. Different reuse schemes can be easily studied by appropriately choosing the N BSs and the set of ri’s. Note also that, unlike in the uplink case, the distance alone is not sufficient, since there is no circular symmetry. However, the throughput can still be computed from (7). C. Power Control Power control consists in assigning different transmitted power levels to different users, e.g., to compensate for the different attenuations they experience. Such a technique is expected to enhance performance through two mechanisms. First, avoiding transmission of unneeded large power by (or to) users who are not severely
The approximate analysis presented in the previous section provides a quantitative evaluation of the average throughput in CDPA, and allows to compare the spectral efficiencies of systems with different reuse schemes. In particular, we consider K = 1; 3 and 7. Note that our analysis is limited to throughput, and does not deal with other important parameters, such as, for example, transmission delay. Note also that particular relevance assumes the analysis for K = 7, since this frequency reuse scheme is the one actually implemented in existing systems, e.g., GSM [4]. This system, with a capture ratio of 10 dB, is expected to guarantee an outage probability not greater than 1%. Even if GSM and 7-CDPA are conceptually different (the former uses circuit-switching, which does not include retransmissions), the 7-CDPA retransmission probability can be assumed as an estimate of the average outage probability in GSM, because the propagation effects are the same in the two systems. In Figure 2a we compare the performance of different reuse schemes (K = 1; 3; 7), measured by S (G), for the shadowing parameter = 0 dB and the capture ratio b = 6 dB (note that = 0 dB means that the lognormal attenuation in dB is Gaussian
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0.40
0.30
S*
0.40
(a)
uplink downlink b = 6 dB σ = 0 dB
0.30
S*
0.20
0.20
K=1
K=1 K=3
0.10
K=3
0.10
K=7
K=7 0.00 0.0
(b)
uplink downlink b = 10 dB σ = 0 dB
0.2
0.4
0.6
0.8
0.00 0.0
1.0
0.2
0.4
0.6
G 0.40
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S*
0.8
1.0
G 0.40
(c)
uplink downlink b = 6 dB σ = 6 dB
0.30
S*
0.20
(d)
uplink downlink b = 10 dB σ = 6 dB
0.20
K=1 K=1
K=3
0.10
K=3
0.10
K=7
K=7 0.00 0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.0
G
=
=
0.4
0.6
0.8
1.0
G
Fig. 2. Average normalized throughput per cell, S , vs. the offered load per cell, G: downlink and uplink, K dB (b); 6 dB, b 6 dB (c); 6 dB, b 10 dB (d).
=
0.2
=
with zero standard deviation, i.e., it is a constant). Similar curves for the cases = 0 dB, b = 10 dB, = 6 dB, b = 6 dB, and = 6 dB, b = 10 dB, are reported in Figures 2b, 2c and 2d, respectively. It can be seen that the throughput curves for K = 1 have a maximum for G < 1, whereas the others are always increasing up to G = 1. The maxima presented by the curves for K = 1 show that this system suffers from congestion, due to cochannel interference. However, congestion can be easily controlled since the traffic G is completely managed by the base station, which polls terminals. The probability of success for K = 7 is always close to 1, and the throughput increases almost linearly with G. Actually, in G = 1 and for no shadowing, the average retransmission probability in the uplink channel is 0:015 and 0:039 for b = 6 dB and b = 10 dB, respectively (0:046 and 0:111 at the cell border). Note that this indicates that, with our propagation model, GSM specifications are not met. Some interference is still observed for K = 3 and, when G is large, the throughput increases less than linearly. As expected, the throughput decreases as the capture ratio increases. However, the degradation caused by the increase of b is almost negligible in systems with high channel fragmentation (K = 7). Also, the difference in the performance of uplink and downlink channels, which is significant for K = 1, small and large b, almost disappears for large K .
= 1, 3 and 7; = 0 dB, b = 6 dB (a); = 0 dB, b = 10
The effect of shadowing is on one hand to impair the channel because of the additional attenuation, and on the other to enhance capture of more disadvantaged users, due to random power levels. This results in a lower maximum throughput but a more stable behaviour, as it is observed from the results for K = 1 in Figures 2c and 2d. For systems with small cochannel interference ( K = 3 and 7), the effect on capture is negligible, and a larger always degrades the performance. From the results analyzed so far, we may conclude that, for b = 10 dB, the reduction, to some extent, of the frequency-reuse degree is beneficial in CDPA. In any case, the system with K = 7 presents the poorest performance. In this system the retransmission probability always exceeds 1%. This makes the comparison with circuit systems that use this frequency-reuse pattern (like GSM) even more favorable to CDPA systems. The effect of power control is investigated in Figures 3 and 4. Figure 3 reports the same results as Figure 2a (i.e., no shadowing and b = 6 dB), along with the corresponding curves obtained using power control. It can be clearly seen that power control improves the performance of the uplink channel for K = 1. Furthermore, in all cases it equals the performance of uplink and downlink channels, thus enhancing the performance of systems with K < 7. As an additional benefit, the curves with power control do not present congestion. When shadowing is present, power control, as usually imple-
GLOBECOM’95, SINGAPORE, NOV. 1995 0.40
0.30
S*
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uplink, p.c. downlink, p.c. uplink, no p.c. downlink, no p.c.
b = 6 dB σ = 0 dB
0.20
K=1 K=3 0.10
K=7 0.00 0.0
0.2
0.4
0.6
0.8
1.0
G Fig. 3. Average normalized throughput per cell, S , vs. the offered load per cell, G: downlink and uplink, 0 dB, b 6 dB, K 1, 3 and 7; with and without power control.
=
0.40
=
=
uplink, no p.c. downlink, no p.c. classic power control distance power control
0.30
REFERENCES
b = 6 dB σ = 6 dB
S*
[1] F. Borgonovo, L. Fratta, M. Zorzi, “Capture-Division Packetized Access (CDPA) for cellular systems”, in Proc. ICCC WCN’94, The Hague, Netherlands, 21-23 Sept. 1994.
0.20
K=1
[2] F. Borgonovo, L. Fratta, M. Zorzi, “Performance analysis of CaptureDivision Packetized Access (CDPA) for cellular systems”, in Proc. Fifth WINLAB Workshop on Third Generation Wireless Networks,East Brunswick, N.J., April 1995, pp.121-138.
K=3
0.10
K=7 0.00 0.0
0.2
0.4
0.6
0.8
1.0
G Fig. 4. Average normalized throughput per cell, S , vs. the offered load per cell, G: 6 dB, b 6 dB, K 1, 3 and 7; “classic” and distance power control schemes compared with downlink and uplink performance without power control.
=
=
trade-off exists between the bandwidth wasted by retransmissions and the bandwidth wasted by subdividing spectrum usage in K parts. The optimal choice depends mainly on the capture threshold b of receivers. With b = 6 dB, the pure CDPA (K = 1) provides the highest throughput, while, with b = 10 dB, as in GSM, the optimal choice is 3-CDPA, which yields a throughput that is almost doubled with respect to K = 7 (GSM). The performance when power-control techniques are used have also been investigated. It has been found that power control further enhances the performance of pure CDPA, if shadowing is absent. If shadowing is present and compensated by the power control, the performance decreases in all cases. The effects of power control are always negligible for K = 7. A simulation model, that can provide more detailed results about the feasibility and the advantages of K-CDPA is under development. Some preliminary results have proven the validity of the analysis reported in this paper [3]. Further studies are in progress to investigate the overall spectral efficiency considering also the bandwidth penalty incurred to reduce the capture-threshold. The above analysis is being extended to include the more realistic case in which the shadowing values in successive slots are correlated. Strategies to combat long-term shadowing are being considered as well.
=
mented, may be harmful, as proven by the curves given in Figure 4. Here, the curves corresponding to the two power-control strategies described in Section III.C are compared, for = 6 dB and b = 6 dB. As a reference, the curves with no power control are shown as well. For the case of power control, only the curve for the uplink channel is reported, since there is almost no difference between uplink and downlink. For K = 1, the “classic” power control which compensates for shadowing performs worse not only than the near-far power-control strategy, but also than the case with no control. This shows that the increased interference may overweigh the improvement in the intended signal. The nearfar power-control policy, on the other hand, provides much better performance. However, if partial frequency reuse is employed (K = 3; 7) the power control is almost ineffective, and its implementation would be discouraged as far as throughput performance is concerned. V. CONCLUSIONS In this paper we have analyzed an extension of the CDPA technique which operates with partial frequency reuse. In such a system, a
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