Downlink Coverage and Capacity of a Distributed Repeater System in ...
IEICE TRANS. COMMUN., VOL.E91–B, NO.4 APRIL 2008
1211
LETTER
Downlink Coverage and Capacity of a Distributed Repeater System in a WCDMA Multicell Environment JaeSeon JANG†a) and NohHoon MYUNG† , Nonmembers
SUMMARY In this letter, the influence of the downlink average ratio of the other cell interference to other-user interference in the serving cell (DARI) on the distributed repeater system (DRS) performance is analyzed. It is found that the improvement of DARI depends on a propagation path loss environment. Applying the computed DARI to a 3-RS DRS cell, as high as 13.9% capacity enhancement was obtained when the path loss exponent is 4.5. In addition, by using the power allocation equation, it is expected that a hexagonal DRS cell without coverage holes or excessive coverage overlap can be realized. key words: WCDMA, distributed repeater system (DRS), distributed antenna system (DAS), base station, repeater
1.
Introduction
Repeaters are widely used in Wideband Code Division Multiple Access (WCDMA) networks, because they are cost effective and can provide high quality mobile communications services to subscribers in shadow areas such as underground locations, subways, highways, and mountains. Unlike digital cellular systems (DCS) and personal communication services (PCS), which are uplink capacity limitation systems, WCDMA networks have smaller downlink capacity than the uplink capacity [1], [2]. The main reason is better receiver techniques such as receiver antenna diversity and multi-user detection can be adopted in a base station (BS). Notably, it is more important to enhance the downlink capacity than to increase the uplink capacity in a WCDMA system. It is anticipated that in future cellular networks, distributed antenna system (DAS) cells using a repeater will provide an effective means of expanding coverage and enhancing capacity [3], [4]. However, to date, a specific analysis of DARI of DRS cells with respect to maximizing the cell capacity in mobile cellular networks has not yet to be reported. Furthermore, output power allocation schemes of BS and each repeater station (RS) to maintain the constant hexagonal cell shape have not been presented in the literature. In this letter, we focus on the influence of DARI on the DRS performance in WCDMA networks. In addition, we derive a dynamic power allocation equation according to a desired cell radius in order to eliminate coverage holes and excessive coverage overlap in the DRS cell. Finally, the cell capacity of the system model is given through numerical Manuscript received April 25, 2007. Manuscript revised October 15, 2007. † The authors are with Korea Advanced Institute of Science and Technology (KAIST), Korea. a) E-mail: [email protected] DOI: 10.1093/ietcom/e91–b.4.1211
results in multi-cell environments. 2.
System Model
The proposed DRS model is shown in Fig. 1. The DRS cell consists of a perfect hexagonal BS cell and 3 · (2Φrr + 1) lozenge-shaped RS cells, where Φrr is the ratio of the radius of a BS cell to that of a RS cell. The BS cell is divided into three sectors for maximizing the DRS cell coverage though it can be an omni or other sector types. However, every RS cell should be a sector type in order to eliminate the coverage holes or the excessive coverage overlap in the DRS network. In the proposed DRS, the central BS provides each RS with a dedicated traffic channel and the connection between the central BS and all RSs is either wired or wireless. 3.
Analysis of Coverage and Capacity of the Proposed DRS Network
3.1 Coverage Analysis In order to eliminate coverage holes or excessive coverage overlap in the proposed DRS cell, we allocate the output power of a BS and each RS dynamically according to a desired cell radius. Let the radius of the BS cell and the RS cell be R and r, respectively. The coverage ratio of a BS cell to a
Fig. 1
Proposed distributed repeater system architecture.
c 2008 The Institute of Electronics, Information and Communication Engineers Copyright
IEICE TRANS. COMMUN., VOL.E91–B, NO.4 APRIL 2008
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RS cell equals Φrr = R/r. Each sector of a one DRS cell has a perfect hexagonal BS cell and (2 · Φrr + 1) lozenge-shaped RS cells. The total output power of a sector of the proposed DRS cell should be the same as that of a conventional such as Pt, DAS = Pcb = Pb + (2 · Φrr + 1) · Pr = 43(dBm) (1) where Pcb is the total transmission power of the classic cell, Pb is the output power of a BS cell, and Pr is the output power of each repeater in RS cell. We assume a path loss model given by L(d) = C · log(dr )(dB)
(2)
where d is the distance from the transmitter, γ is the path loss exponent, and C is a constant. For the given pathloss model, the output power of a BS cell is given by Pb = (Φrr )γ Pr to maintain the same received power level at both the BS cell and the RS cell boundaries. Then, from (1), the transmission power of a sector of BS and each RS are obtained, respectively, by (Φrr )γ · Pcb (2 · Φrr + 1) + (Φrr )γ 1 · Pcb Pr = (2 · Φrr + 1) + (Φrr )γ
Pb =
(3) (4)
3.2 Capacity Analysis In a WCDMA system, the total output power of a BS to support mobile stations is determined by [5] Pb =
1 Nth Fm Lbm (di ) (1 − ηL )
N
vi
i=1
(Eb /No )i W/Ri
(5)
where Nth is the thermal noise level, Fm is the noise figure of a mobile station, Lbm (di ) is the path loss between a BS and a mobile station, vi is the voice activity factor of the ith mobile station, (Eb /No )i is the required bit energy to noise ratio of the ith mobile station, W is the spreading bandwidth, Ri is the data rate of the ith mobile station, and ηL is the system loading factor, that is ηL =
N (Eb /No )i vi [(1 − αi ) + Ii ] W/Ri i=1
(6)
where Ii is the ratio of other cell interference to other user interference of the ith mobile station in the given cell and αi is the orthogonality factor of the ith mobile station, which is determined by the following equation [6] ⎡ ⎤−1 ⎢⎢⎢ ⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥ F 2 |am | ⎢ ⎥⎥⎥⎥ α = 1 − ⎢⎢⎢⎢⎢ (7) ⎥⎥⎥ L ⎢⎢⎢m=1 ⎥ ⎥ ⎢⎢⎢ |a f |2 ⎥⎥⎥⎦ ⎣ f =1, f m
where F is the number of rake fingers in a mobile station
and L is the number of multi-paths in the serving cell. DARI is defined as the downlink average ratio of the other cell interference to other-user interference in the serving cell so DARI in the classic cell structure is given by [7] ⎤ ⎡ Nb ⎥ ⎢⎢⎢⎢ (n0 , b) ⎥ Pcb Lbm ⎥⎥⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥⎥ 1 ⎢⎢⎢⎢ b=1 ⎥⎥⎥ E ⎢⎢⎢ Iclassic =
(n , 0) ⎥⎥⎥ Nc all n ⎢⎢⎢ Pcb L 0 bm 0 ⎥⎥⎦⎥ ⎢⎢⎣⎢ ⎡ (n0 , 0) ⎤ N b −1 ⎢⎢ Lbm ⎥⎥⎥ ⎥⎥⎦ E ⎢⎢⎢⎣ (n (8) = 0 , b) L b=1 all n0 bm where Nc is the number of maximum users in the classic 0 , 0) is the path loss cell, Nb is the number of total BSs, L(n bm between the n0 th user in the serving BS and the serving BS, 0 , b) is the path loss between the n0 th user in the servand L(n bm ing BS and the bth BS. DARI in a DRS cell is more complex than that in the classic cell. We need to consider two cases. The first case is when the concerned mobile station is in a BS cell. In this case, the received power from RS cells also contributes to the other cell interference along with the received power from other BS cells, while other user interference in a serving cell consists of the interference from users in the same BS cell. Then, DARI is given by ⎧ ⎡ (n0 , 0) ⎤ ⎡ (n0 , 0) ⎤⎫ ⎪ ⎪ Ntb −1 Ntr −1 ⎪ ⎪ 1 ⎪ ⎨ ⎢⎢⎢⎢ Lbm ⎥⎥⎥⎥ Pr ⎢⎢⎢⎢ Lbm ⎥⎥⎥⎥⎪ ⎬ E E Ib = + ⎥ ⎥ ⎢ ⎢ ⎪ ⎪ ⎦ ⎦ ⎣ ⎣ ⎪ ⎪ (n , r) (n , b) 0 0 ⎪ ⎪ Nbu ⎩ P ⎭ b Lbm Lbm r=0 all n0 b=1 all n0 (9) where Nbu is the number of maximum users in a BS cell, Ntb is the number of total BSs in the considered multi DRS cells, Ntr is the number of total RSs in the considered multi 0 , r) is the path loss between the th user in DRS cells, and L(n bm the serving BS and the rth RS. Note that the factor Pr /Pb in the second term in (9) accounts for different transmit power from a BS and a RS. The second case is when the mobile station is in a RS cell. In this case, contrary to the first case, the serving cell becomes a given RS cell so that the received power from BS cells also contributes to the other cell interference along with the received power from other RS cells, while other user interference in a serving cell consists of the interference from users in the same RS cell. Then, DARI is expressed as ⎧ ⎡ (n , 0) ⎤ ⎡ (n , 0) ⎤⎫ ⎪ ⎪ Ntr −1 Ntb −1 ⎪ ⎪ 1 ⎪ ⎨ ⎢⎢⎢ Lrm0 ⎥⎥⎥ Pb ⎢⎢⎢ Lrm0 ⎥⎥⎥⎪ ⎬ ⎢ ⎢ ⎥ ⎥ E E Ir = + ⎪ ⎪ ⎣ ⎣ ⎦ ⎦ ⎪ ⎪ (n , r) (n , b) 0 0 ⎪ ⎪ Nru ⎩ P ⎭ r b=0 all n Lrm Lrm r=1 all n0 0 (10) where Nru is the number of maximum users in a RS cell, 0 , 0) is the path loss between the n0 user in the serving RS L(n rm 0 , r) is the path loss between the n0 th and the serving RS, L(n rm 0 , b) is the path user in the serving RS and the rth RS, and L(n rm loss between the n0 th user in the serving RS and the bth BS. Similarly to (9), the factor Pb /Pr reflects different transmit power from a BS and a RS.
LETTER
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4.
Numerical Results
In this letter, we consider the downlink system of a distributed repeater system that consists of seven hexagonal cells. Each cell has a three sector BS located at the center and 3 · (2Φrr + 1) RSs located at the BS border or the DRS cell border. The mobile stations are distributed uniformly. In addition, for a fair comparison, the total output power of the classic cell the proposed DRS cells set equally as in Sect. 3.1, and no physical channel limitation is assumed. Then, Ib and Ir are given in multi-cell downlink environments using parameters given in Table 1. Figure 2 shows the coverage increase ratios between the classic cell and the DRS cells. The coverage increase is smaller with Φrr , but larger with the path loss exponent. With the same total output power (20 watts at 43 dBm), the coverage increase of a 3-RS DRS cell (i.e., Φrr = 1) is as much as 51.6% greater than the classic cell when the path loss exponent is 5. Figure 3 shows DARI of the classic cell and the DRS cells. For DRS, DARIs of RS cells and a BS cell are different as given in (9) and (10) so they are averaged considering the area of RS cells and a BS cell. Figure 3 indicates that DARI of a DRS cell becomes lower than that of a conventional cell if the path loss exponent is greater than a certain value −DARIs of Φrr = 1, Φrr = 2, and Φrr = 3 DRS cells are lower than that of the classic cell when the path loss exponent is higher than about 3.3, 5.0, and 3.7, respectively. It should be note here that a Φrr = 3 DRS cell outperforms a Φrr = 2 DRS cell in terms of DARI, while DRS with Φrr = 1 is the most beneficiary in terms of DARI. Figure 4 shows the capacity enhancement of DRS over a conventional cellular system in terms of per cell capacity, which corresponds to average capacity achieved by a transmitter (or an antenna). Since a DRS cell has a larger number
of transmitters (or cells such as RS cells and a BS cell) than a conventional cell, per cell capacity (or capacity per transmitter) can be a reasonable performance metric for a fair comparison. Considering different coverage areas of a BS cell and RS cells in DRS, per cell capacity in DRS is obtained by a weighted sum of capacities of RS cells and a BS cell, where the weights are proportional to the area of each cell and 0 < weight < 1. As DARI in Fig. 3, the capacity improvement of a DRS cell over a conventional cell grows as the path loss exponent increases. As shown from Fig. 2 to Fig. 4, the path loss exponent determines the optimum numbers and radius of RS cells in DRS systems since interference from other cells is mainly determined by a cell structure and a propagation path loss. A steeper drop of propagating power by a higher path loss exponent allows closer distance from interfering cells in cell planning. So we can find the optimum cell structure of DRS systems according to a given propagation environment. From the numerical results, Φrr = 1 DRS cell is the opti-
Fig. 2 Coverage comparisons between the classic cell and the proposed DRS cells. Table 1
System parameters.
Fig. 3 cells.
DARI comparisons between the classic cell and the proposed DRS
IEICE TRANS. COMMUN., VOL.E91–B, NO.4 APRIL 2008
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results have effectively quantified the effects of DARI on capacity and shown that the performance improvement of DRS over a conventional cellular system depends on the path loss exponent. As another contribution of this letter, the derived power allocation equation can be used to eliminate coverage holes and excessive coverage overlap in the DRS cell. References
Fig. 4 Capacity comparisons between the classic cell and the proposed DRS cells.
mum cell structure in terms of both coverage and capacity for a typical urban environment where the path loss exponent is in the range between 3.5 and 4.5. 5.
Conclusion
In this letter, we have derived DARI and the power allocation equations for WDCMA DRS networks. Our numerical
[1] T. Westman and H. Holma, “CDMA system for UMTS high bit rate services,” Proc. VTC 1997, pp.825–829, 1997. [2] K. Pehkonen, H. Holma, L. Keskitalo, E. Nikula, and T. Westman, “A performance analysis of TDMA and CDMA based air interface solutions for UMTS high bit rate services,” Proc. PIMRC 1997, pp.22–26, 1997. [3] H. Viswanthan and S. Mukherjee, “Performance of cellular networks with relays and centralized scheduling,” IEEE Trans. Wireless Communications, vol.4, no.5, pp.2318–2328, Sept. 2005. [4] W. Choi and J.G. Andrews, “Downlink performance and capacity of distributed antenna systems in a multicell environment,” IEEE Trans. Wireless Communications, vol.6, no.1, pp.69–73, Jan. 2007. [5] K. Sipila, Z.C. Honkasalo, J.L. Steffens, and A. Wacker, “Estimation of capacity and required transmission power of WCDMA downlink based on a downlink pole equation,” Proc. VTC 2000, pp.1002– 1005, 2000. [6] S. Burger, H. Buddendick, and G. Wolfle, “Location dependent CDMA orthogonality in system level simulations,” Proc. VTC 2005, pp.419–423, 2005. [7] K.Sh. Zigangirov, Theory of Code Division Multiple Access Communication, pp.345–347, John Wiley & Sons, 2004.
1211
LETTER
Downlink Coverage and Capacity of a Distributed Repeater System in a WCDMA Multicell Environment JaeSeon JANG†a) and NohHoon MYUNG† , Nonmembers
SUMMARY In this letter, the influence of the downlink average ratio of the other cell interference to other-user interference in the serving cell (DARI) on the distributed repeater system (DRS) performance is analyzed. It is found that the improvement of DARI depends on a propagation path loss environment. Applying the computed DARI to a 3-RS DRS cell, as high as 13.9% capacity enhancement was obtained when the path loss exponent is 4.5. In addition, by using the power allocation equation, it is expected that a hexagonal DRS cell without coverage holes or excessive coverage overlap can be realized. key words: WCDMA, distributed repeater system (DRS), distributed antenna system (DAS), base station, repeater
1.
Introduction
Repeaters are widely used in Wideband Code Division Multiple Access (WCDMA) networks, because they are cost effective and can provide high quality mobile communications services to subscribers in shadow areas such as underground locations, subways, highways, and mountains. Unlike digital cellular systems (DCS) and personal communication services (PCS), which are uplink capacity limitation systems, WCDMA networks have smaller downlink capacity than the uplink capacity [1], [2]. The main reason is better receiver techniques such as receiver antenna diversity and multi-user detection can be adopted in a base station (BS). Notably, it is more important to enhance the downlink capacity than to increase the uplink capacity in a WCDMA system. It is anticipated that in future cellular networks, distributed antenna system (DAS) cells using a repeater will provide an effective means of expanding coverage and enhancing capacity [3], [4]. However, to date, a specific analysis of DARI of DRS cells with respect to maximizing the cell capacity in mobile cellular networks has not yet to be reported. Furthermore, output power allocation schemes of BS and each repeater station (RS) to maintain the constant hexagonal cell shape have not been presented in the literature. In this letter, we focus on the influence of DARI on the DRS performance in WCDMA networks. In addition, we derive a dynamic power allocation equation according to a desired cell radius in order to eliminate coverage holes and excessive coverage overlap in the DRS cell. Finally, the cell capacity of the system model is given through numerical Manuscript received April 25, 2007. Manuscript revised October 15, 2007. † The authors are with Korea Advanced Institute of Science and Technology (KAIST), Korea. a) E-mail: [email protected] DOI: 10.1093/ietcom/e91–b.4.1211
results in multi-cell environments. 2.
System Model
The proposed DRS model is shown in Fig. 1. The DRS cell consists of a perfect hexagonal BS cell and 3 · (2Φrr + 1) lozenge-shaped RS cells, where Φrr is the ratio of the radius of a BS cell to that of a RS cell. The BS cell is divided into three sectors for maximizing the DRS cell coverage though it can be an omni or other sector types. However, every RS cell should be a sector type in order to eliminate the coverage holes or the excessive coverage overlap in the DRS network. In the proposed DRS, the central BS provides each RS with a dedicated traffic channel and the connection between the central BS and all RSs is either wired or wireless. 3.
Analysis of Coverage and Capacity of the Proposed DRS Network
3.1 Coverage Analysis In order to eliminate coverage holes or excessive coverage overlap in the proposed DRS cell, we allocate the output power of a BS and each RS dynamically according to a desired cell radius. Let the radius of the BS cell and the RS cell be R and r, respectively. The coverage ratio of a BS cell to a
Fig. 1
Proposed distributed repeater system architecture.
c 2008 The Institute of Electronics, Information and Communication Engineers Copyright
IEICE TRANS. COMMUN., VOL.E91–B, NO.4 APRIL 2008
1212
RS cell equals Φrr = R/r. Each sector of a one DRS cell has a perfect hexagonal BS cell and (2 · Φrr + 1) lozenge-shaped RS cells. The total output power of a sector of the proposed DRS cell should be the same as that of a conventional such as Pt, DAS = Pcb = Pb + (2 · Φrr + 1) · Pr = 43(dBm) (1) where Pcb is the total transmission power of the classic cell, Pb is the output power of a BS cell, and Pr is the output power of each repeater in RS cell. We assume a path loss model given by L(d) = C · log(dr )(dB)
(2)
where d is the distance from the transmitter, γ is the path loss exponent, and C is a constant. For the given pathloss model, the output power of a BS cell is given by Pb = (Φrr )γ Pr to maintain the same received power level at both the BS cell and the RS cell boundaries. Then, from (1), the transmission power of a sector of BS and each RS are obtained, respectively, by (Φrr )γ · Pcb (2 · Φrr + 1) + (Φrr )γ 1 · Pcb Pr = (2 · Φrr + 1) + (Φrr )γ
Pb =
(3) (4)
3.2 Capacity Analysis In a WCDMA system, the total output power of a BS to support mobile stations is determined by [5] Pb =
1 Nth Fm Lbm (di ) (1 − ηL )
N
vi
i=1
(Eb /No )i W/Ri
(5)
where Nth is the thermal noise level, Fm is the noise figure of a mobile station, Lbm (di ) is the path loss between a BS and a mobile station, vi is the voice activity factor of the ith mobile station, (Eb /No )i is the required bit energy to noise ratio of the ith mobile station, W is the spreading bandwidth, Ri is the data rate of the ith mobile station, and ηL is the system loading factor, that is ηL =
N (Eb /No )i vi [(1 − αi ) + Ii ] W/Ri i=1
(6)
where Ii is the ratio of other cell interference to other user interference of the ith mobile station in the given cell and αi is the orthogonality factor of the ith mobile station, which is determined by the following equation [6] ⎡ ⎤−1 ⎢⎢⎢ ⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥ F 2 |am | ⎢ ⎥⎥⎥⎥ α = 1 − ⎢⎢⎢⎢⎢ (7) ⎥⎥⎥ L ⎢⎢⎢m=1 ⎥ ⎥ ⎢⎢⎢ |a f |2 ⎥⎥⎥⎦ ⎣ f =1, f m
where F is the number of rake fingers in a mobile station
and L is the number of multi-paths in the serving cell. DARI is defined as the downlink average ratio of the other cell interference to other-user interference in the serving cell so DARI in the classic cell structure is given by [7] ⎤ ⎡ Nb ⎥ ⎢⎢⎢⎢ (n0 , b) ⎥ Pcb Lbm ⎥⎥⎥⎥⎥ ⎢⎢⎢ ⎥⎥⎥⎥ 1 ⎢⎢⎢⎢ b=1 ⎥⎥⎥ E ⎢⎢⎢ Iclassic =
(n , 0) ⎥⎥⎥ Nc all n ⎢⎢⎢ Pcb L 0 bm 0 ⎥⎥⎦⎥ ⎢⎢⎣⎢ ⎡ (n0 , 0) ⎤ N b −1 ⎢⎢ Lbm ⎥⎥⎥ ⎥⎥⎦ E ⎢⎢⎢⎣ (n (8) = 0 , b) L b=1 all n0 bm where Nc is the number of maximum users in the classic 0 , 0) is the path loss cell, Nb is the number of total BSs, L(n bm between the n0 th user in the serving BS and the serving BS, 0 , b) is the path loss between the n0 th user in the servand L(n bm ing BS and the bth BS. DARI in a DRS cell is more complex than that in the classic cell. We need to consider two cases. The first case is when the concerned mobile station is in a BS cell. In this case, the received power from RS cells also contributes to the other cell interference along with the received power from other BS cells, while other user interference in a serving cell consists of the interference from users in the same BS cell. Then, DARI is given by ⎧ ⎡ (n0 , 0) ⎤ ⎡ (n0 , 0) ⎤⎫ ⎪ ⎪ Ntb −1 Ntr −1 ⎪ ⎪ 1 ⎪ ⎨ ⎢⎢⎢⎢ Lbm ⎥⎥⎥⎥ Pr ⎢⎢⎢⎢ Lbm ⎥⎥⎥⎥⎪ ⎬ E E Ib = + ⎥ ⎥ ⎢ ⎢ ⎪ ⎪ ⎦ ⎦ ⎣ ⎣ ⎪ ⎪ (n , r) (n , b) 0 0 ⎪ ⎪ Nbu ⎩ P ⎭ b Lbm Lbm r=0 all n0 b=1 all n0 (9) where Nbu is the number of maximum users in a BS cell, Ntb is the number of total BSs in the considered multi DRS cells, Ntr is the number of total RSs in the considered multi 0 , r) is the path loss between the th user in DRS cells, and L(n bm the serving BS and the rth RS. Note that the factor Pr /Pb in the second term in (9) accounts for different transmit power from a BS and a RS. The second case is when the mobile station is in a RS cell. In this case, contrary to the first case, the serving cell becomes a given RS cell so that the received power from BS cells also contributes to the other cell interference along with the received power from other RS cells, while other user interference in a serving cell consists of the interference from users in the same RS cell. Then, DARI is expressed as ⎧ ⎡ (n , 0) ⎤ ⎡ (n , 0) ⎤⎫ ⎪ ⎪ Ntr −1 Ntb −1 ⎪ ⎪ 1 ⎪ ⎨ ⎢⎢⎢ Lrm0 ⎥⎥⎥ Pb ⎢⎢⎢ Lrm0 ⎥⎥⎥⎪ ⎬ ⎢ ⎢ ⎥ ⎥ E E Ir = + ⎪ ⎪ ⎣ ⎣ ⎦ ⎦ ⎪ ⎪ (n , r) (n , b) 0 0 ⎪ ⎪ Nru ⎩ P ⎭ r b=0 all n Lrm Lrm r=1 all n0 0 (10) where Nru is the number of maximum users in a RS cell, 0 , 0) is the path loss between the n0 user in the serving RS L(n rm 0 , r) is the path loss between the n0 th and the serving RS, L(n rm 0 , b) is the path user in the serving RS and the rth RS, and L(n rm loss between the n0 th user in the serving RS and the bth BS. Similarly to (9), the factor Pb /Pr reflects different transmit power from a BS and a RS.
LETTER
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4.
Numerical Results
In this letter, we consider the downlink system of a distributed repeater system that consists of seven hexagonal cells. Each cell has a three sector BS located at the center and 3 · (2Φrr + 1) RSs located at the BS border or the DRS cell border. The mobile stations are distributed uniformly. In addition, for a fair comparison, the total output power of the classic cell the proposed DRS cells set equally as in Sect. 3.1, and no physical channel limitation is assumed. Then, Ib and Ir are given in multi-cell downlink environments using parameters given in Table 1. Figure 2 shows the coverage increase ratios between the classic cell and the DRS cells. The coverage increase is smaller with Φrr , but larger with the path loss exponent. With the same total output power (20 watts at 43 dBm), the coverage increase of a 3-RS DRS cell (i.e., Φrr = 1) is as much as 51.6% greater than the classic cell when the path loss exponent is 5. Figure 3 shows DARI of the classic cell and the DRS cells. For DRS, DARIs of RS cells and a BS cell are different as given in (9) and (10) so they are averaged considering the area of RS cells and a BS cell. Figure 3 indicates that DARI of a DRS cell becomes lower than that of a conventional cell if the path loss exponent is greater than a certain value −DARIs of Φrr = 1, Φrr = 2, and Φrr = 3 DRS cells are lower than that of the classic cell when the path loss exponent is higher than about 3.3, 5.0, and 3.7, respectively. It should be note here that a Φrr = 3 DRS cell outperforms a Φrr = 2 DRS cell in terms of DARI, while DRS with Φrr = 1 is the most beneficiary in terms of DARI. Figure 4 shows the capacity enhancement of DRS over a conventional cellular system in terms of per cell capacity, which corresponds to average capacity achieved by a transmitter (or an antenna). Since a DRS cell has a larger number
of transmitters (or cells such as RS cells and a BS cell) than a conventional cell, per cell capacity (or capacity per transmitter) can be a reasonable performance metric for a fair comparison. Considering different coverage areas of a BS cell and RS cells in DRS, per cell capacity in DRS is obtained by a weighted sum of capacities of RS cells and a BS cell, where the weights are proportional to the area of each cell and 0 < weight < 1. As DARI in Fig. 3, the capacity improvement of a DRS cell over a conventional cell grows as the path loss exponent increases. As shown from Fig. 2 to Fig. 4, the path loss exponent determines the optimum numbers and radius of RS cells in DRS systems since interference from other cells is mainly determined by a cell structure and a propagation path loss. A steeper drop of propagating power by a higher path loss exponent allows closer distance from interfering cells in cell planning. So we can find the optimum cell structure of DRS systems according to a given propagation environment. From the numerical results, Φrr = 1 DRS cell is the opti-
Fig. 2 Coverage comparisons between the classic cell and the proposed DRS cells. Table 1
System parameters.
Fig. 3 cells.
DARI comparisons between the classic cell and the proposed DRS
IEICE TRANS. COMMUN., VOL.E91–B, NO.4 APRIL 2008
1214
results have effectively quantified the effects of DARI on capacity and shown that the performance improvement of DRS over a conventional cellular system depends on the path loss exponent. As another contribution of this letter, the derived power allocation equation can be used to eliminate coverage holes and excessive coverage overlap in the DRS cell. References
Fig. 4 Capacity comparisons between the classic cell and the proposed DRS cells.
mum cell structure in terms of both coverage and capacity for a typical urban environment where the path loss exponent is in the range between 3.5 and 4.5. 5.
Conclusion
In this letter, we have derived DARI and the power allocation equations for WDCMA DRS networks. Our numerical
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