684
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
A Comparison of Reverse Link Access Schemes for Next-Generation Cellular Systems Suman Das, Member, IEEE, and Harish Viswanathan, Senior Member, IEEE
Abstract—We consider different transmission options on the reverse link of cellular systems for packet data. The different transmission options are classified based on the nature of in-cell and out-of-cell interference power statistics. The categories are: (a) no in-cell interference, averaged out-of cell interference; (b) no in-cell interference, bursty out-of-cell interference; and (c) averaged in-cell interference, averaged out-of-cell interference. Depending on whether the reverse link transmission is time multiplexed one user at a time transmission, or simultaneous transmission by multiple users with or without in-cell orthogonality, the interference structure falls into one of the above three categories. We analyze the throughput performance of the system in each of these cases when incremental redundancy is employed to combat uncertainty in the interference power. We compare the different options under an in-cell rise-over-thermal (IROT) constraint and provide some insights for reverse link design for next-generation cellular systems. Our results show that transmission option (a) with an optimal choice of the number of simultaneous transmissions within the cell has the best performance over several different scenarios. Timemultiplexed transmissions, despite the bursty out-of-cell interference power structure, has throughput comparable to that of a multiple-user orthogonal transmission system for small cells where mobiles have sufficient transmit power to meet the target IROT. Index Terms—Code-division multiple access (CDMA), hybrid automatic repeat request (HARQ), orthogonal frequency-division multiple access (OFDMA), time-division multiple access (TDMA).
I. INTRODUCTION
N
EXT-GENERATION cellular systems are expected to support a high volume of packet data traffic on both the forward and the reverse links. While significant enhancements have been proposed and already implemented in third-generation cellular systems for the forward link [1]–[3], the reverse link is only currently being optimized for packet data. Although data traffic is asymmetric, with the forward link carrying more traffic than the reverse link, significant enhancements will be required even on the reverse link to meet the future traffic demand. When considering reverse link design, one can consider several transmission options and modulation techniques that impact the nature of the in-cell and out-of-cell interference power statistics. For example, one can consider simultaneous transmission by several users in each cell using asynchronous or synchronous code-division multiple access (CDMA) or time-multiplexed transmissions with a single user (or a small number of users) transmitting in each cell at any given time. Each of these options leads to a different interference structure. Reverse link scheduling has been considered in [4] and some Manuscript received January 21, 2005; revised August 24, 2005. The authors are with Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974 USA (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/JSAC.2005.862419
of the references cited therein in the context of a single cell system. Most of the previous work in the area of packet data on the reverse link is on devising algorithms for efficient use of system resources for a particular technology. Furthermore, often simplistic assumptions of single-cell and/or fixed out-of-cell interference power are made. To the best of our knowledge, this is the first attempt to characterize the interference power statistics for different transmission approaches and quantify the effect of the interference on system performance. Enhancements such as channel-aware scheduling with timemultiplexed transmissions and incremental redundancy (IR) have been introduced for packet data on the forward link since packet data is delay tolerant. Similar schemes can be applied on the reverse link to enhance the performance. However, the forward and reverse links are fundamentally different in that the interference at the mobile on the forward link is generated by surrounding base stations that are fixed in location, while the interference at the base station on the reverse link comes from other mobiles in the same cell and surrounding cells and thus depends on which mobiles are transmitting at a given time. For example, in the case of time-multiplexed transmission in which only a single user transmits in each cell, unlike on the forward link, the interference on the reverse link is highly bursty because the location of the user that is transmitting in the surrounding cells is changing from slot to slot, depending on who is scheduled for transmission in the surrounding cells. Thus, the gain that one obtains due to in-cell interference avoidance and scheduling in the time-multiplexed transmission could be offset by the unpredictability of the interference power and the signal-to-interference-and-noise ratio (SINR) at the receiver. Since packet data is delay tolerant, using link layer retransmission schemes such as incremental redundancy, it is possible to implement a variable rate transmission efficiently, in spite of the uncertainty in SINR at the receiver. So, it is possible that time-multiplexed transmissions outperform the power-controlled multiple simultaneous user transmission in spite of the unpredictability of the interference power. On the other hand, simultaneous transmission by a number of users in each cell makes the interference power vary more slowly from slot to slot since the interference is generated by a large number of users transmitting at lower powers. This makes the SINR more predictable. However, in this case, there is in-cell interference or bandwidth splitting among the users transmitting simultaneously that could make this approach inefficient. We are thus motivated to develop a framework and then compare different transmission options on the reverse link. We classify the different transmission options according to the interference power statistics. The three categories we con-
0733-8716/$20.00 © 2006 IEEE
DAS AND VISWANATHAN: COMPARISON OF REVERSE LINK ACCESS SCHEMES FOR NEXT-GENERATION CELLULAR SYSTEMS
sider are: (a) no in-cell interference, averaged out-of-cell interference; (b) no in-cell interference, bursty out-of-cell interference; and (c) averaged in-cell interference, averaged out-of-cell interference. Depending on whether the reverse link transmission is time multiplexed one user at a time transmission, or simultaneous transmission by multiple users with or without in-cell orthogonality, the interference structure falls into one of the above three categories. Examples of category (a) include synchronous CDMA transmission or orthogonal frequency-division multiplexing (OFDM) transmission with fast hopping. In these cases, users within the cell are orthogonal to each other and thus there is no in-cell interference. Each user suffers interference from all the users transmitting in the surrounding cells, and thus the out-of-cell interference is averaged in the sense that it does not fluctuate significantly over a short time duration. An example of category (b) is a CDMA or an OFDM system in which transmission among users within a cell is time multiplexed. Since in-cell users transmit at different times, there is no in-cell interference. Further, since the out-of-cell interference comes from a single user in each cell, the interference power is unpredictable or bursty. An example of category (c) is the asynchronous CDMA system with multiple simultaneous users transmitting within the cell. Clearly, in this case, each user experiences interference from many in-cell users as well as a large number of out-of-cell users. Thus, both the in-cell and out-of-cell interference are averaged. Note that the extent to which the averaging of the out-of-cell interference occurs depends on the number of simultaneously transmitting users. We develop a framework to analyze the throughput that is achieved in each of these transmission options. Since the interference power is bursty, we include incremental redundancy within the framework when comparing the different schemes. We consider both small cells in an urban environment (shadow fading standard deviation is small) as well as the large cell rural environment case (shadow-fading standard deviation is large). We compare the different options under an in-cell rise-over-thermal (IROT) constraint and provide some insights for the design of a physical layer on the reverse link for next-generation cellular systems. Our results show that transmission option (a) with optimal choice of the number of simultaneous transmissions within the cell has the best performance over several different scenarios. In Section II, we describe the system model and the generation of the interference power distribution. In Section III, we discuss the calculation of the system throughput using incremental redundancy. In Section IV, we present throughput results for different scenarios and draw several conclusions that provide insights for system design. We provide a summary and directions for future work in Section V. II. SYSTEM MODEL AND INTERFERENCE POWER CALCULATION The received signal at any base station from the point of view of decoding the signal from a given user is composed of three components: the signal from the desired user, signals from all the other users in the system constituting the interference, and thermal noise. Thermal noise includes other interference generated by other transmitters not in the system in addition to the
685
receiver noise. The ratio of the signal strength of the desired user to the thermal noise is the well-known signal-to-noise ratio (SNR). The ratio of the total interference power to the noise power is the interference over thermal (IOT) ratio. IOT can depend on the specific user considered (in the case of multiple-user transmission within the cell) and also varies across base stations for a given user. IOT plays an important part in determining the throughput of the system since the transmission rate depends on the SINR and not just the SNR. We study the IOT distribution for the different transmission options. Another related ratio that we consider is the rise over thermal (ROT). This is the ratio of the total received signal power (both the desired as well as the interfering power generated by all the users in the system) to the background thermal noise. For a multiuser multicell system it is important to control the ROT distribution. The stability of the control loops such as closed-loop power control require that the system operates within a certain ROT limit. Coverage is determined by the operating ROT in a power-controlled system. Furthermore, it is important to limit ROT to restrict adjacent channel interference generated in the adjacent frequency bands. For example, current voice CDMA systems operate such that the ROT of the system should not exceed 7 dB 99% of the time. We consider both IOT and ROT to study the interference power distributions and throughput performance of the different transmission options because it is possible for two systems to have different IOT distributions but the same 95– 99 percentile target ROT distribution. In order to determine the interference power statistics, we have to specify how the transmit powers of the users are set and how they vary over time. To this end, we define the notion of IROT, which is essentially the ROT of a cell as though it were an isolated cell in the system, i.e., there is no out-of-cell interference. The users within the cell are power controlled to meet an IROT target subject to maximum transmit power limitations. In the power control scheme considered in this paper, when multiple users are transmitting simultaneously in a cell, each user contributes an equal fraction to the total IROT. Specifusers transmit in a given cell, user transmits ically, when , where is the repower ceiver noise power, is the target IROT, and is the average channel gain of the th user and includes the path loss corresponds to multipath fading and shadow fading , while channel gain. Note that this requires the knowledge of the unit with which each user is received at power SNR the base station. In practice, this has to be estimated at the base station to drive the power control algorithm. Note that we have chosen a power control scheme that guarantees equal rate for all users subject to the maximum power limit. Some users may transmit at a lower rate compared to other users because they are further away from the base station and in a bad fade compared to other users and hence limited by the maximum power rather than the IROT. When the required power to meet the target IROT exceeds the maximum mobile power for a particular user, the contribution to the IROT from other users is not increased to meet the target. Since the maximum power limit may be reached in some transmission options and not others, we will show not only the aggregate cell throughput but also individual user throughput as a function of the SNR of the users.
686
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
The same power control strategy is employed for all three transmission options. A comparison across different transmission options is made for the same target IROT rather than a target ROT. ROT, being dependent on signals generated by users in multiple cells, is not directly controllable. However, we will see that with our approach to the power control, the 95 and 99 percentile ROT for the different transmission options are close even though the ROT distributions are different, making the comparison legitimate. Note also that for the power control scheme specified, the total average transmit powers utilized in the different options could be different. This is indeed realistic since battery power is not a fundamental limit (users may recharge batteries frequently if they achieve more throughput by transmitting more often and at higher powers) and one should not limit the use of average transmit power when comparing the different transmission options. A comparison based on a fixed target IROT/ROT is more meaningful. Analysis of out-of-cell interference power distributions has been done in [5] and [6] for cellular systems. Expressions involving multiple integrals are given for the interference power cumulative distribution functions (CDF). However, these integrals have to be evaluated numerically. Besides, the number of integrals increases with the number of interfering users, making the evaluation difficult. Thus, we resort to direct Monte Carlo simulations to obtain interference power CDFs. Our system model is comprised of 19 hexagonal cells arranged in a hexagonal lattice with two ring of cells surrounding the center cell. When sectorization is studied, each cell has three sectors. The users are distributed uniformly across the 19 cells. We assume that the interference contribution at the central cell base station from users outside these 19 cells is insignificant. Signals transmitted by the users are subject to distance-based propagation loss, log-normal shadow fading, and fast fading due to multipath propagation. The base station that receives the strongest average signal strength (averaged over the fast fading) from a particular user is considered to be the serving base station for that user. Transmitter antennas are assumed to be omnidirectional and receiver antennas are omnidirectional or three-sector. Having established the framework, we now discuss the interference statistics obtained for transmission options (b) and (c), defined in the previous section. For transmission option (c) the statistics depend on the number of simultaneously transmitting users within the cell. We present results for various numbers of users. We also present results for two different scenarios, the small-cell scenario in which the cell radius is 1 km with log-normal shadow-fading standard deviation of 4.2 dB and a large-cell configuration in which the cell radius is 2.5 km with log-normal shadow-fading standard deviation of 8 dB. Two scenarios are considered because the results and conclusions depend on these parameters. Note that option (b) can be viewed as a special case of option (a) or (c) when only one user is transmitting. Fig. 1 shows the IOT distributions for the large-cell configuration for transmission option (b) (single-user transmission per cell leading to no in-cell interference and bursty out-of-cell interference) and option (c) (multiple simultaneous user transmis-
Fig. 1.
IOT distribution for transmission options (b) and (c).
sion with spreading within the cell leading to averaged in-cell and out-of-cell interference) for the case of 20 simultaneously transmitting users. IOT distribution is obtained through Monte Carlo simulations involving 2000 random placement of users and 10 000 slots per placement. Mixed mobile speeds of 3, 60, or 120 km/h, chosen at random for each mobile, are used to instantiate the fast fading channels. The target in-cell ROT was set at 6 dB. The following propagation parameters were used to obtain the results: thermal noise density 174 dBm/Hz, 1.25-MHz bandwidth, 5-dB receiver noise figure, 21-dBm maximum mobile transmit power, 17-dB base station receive antenna gain, 2-dB cable loss, 1-dB mobile antenna gain, 10-dB penetration loss, path loss exponent of 3.57 and path loss intercept of 29.2, and 0.5 shadow-fading correlation across base stations. Also shown in the figure is the log-normal distribution with the empirically obtained mean and standard deviation to try to fit the distribution obtained through simulation. Since the fit is reasonably accurate, we use the log-normal approximation with appropriate mean and variance in subsequent throughput calculations. This modeling simplifies the throughput computations described in the later sections. From the figure, we see that the IOT distribution for the transmission option (c) has a larger mean and a smaller variance compared to time multiplexed transmission option (b), which has a small mean but a large variance. The trend in the mean and the variance of the IOT distribution with an increasing number of users transmitting simultaneously is tabulated in Tables I and II along with throughput values for the medium-cell and the small-cell configurations, respectively. The difference in the IOT characteristics can be explained by closely inspecting the components of IOT in different modes of transmission. In a multiuser transmission mode, the total IOT consists of two components, the nearly constant in-cell interference (variability only because users are limited by the maximum power constraint) users and the variable out-of-cell interference power. For transmitting simultaneously within the cell, with perfect power control as described previously, the in-cell IOT cannot exceed . If the number of transmitting users does not change from slot to slot, this component of the total IOT remains
DAS AND VISWANATHAN: COMPARISON OF REVERSE LINK ACCESS SCHEMES FOR NEXT-GENERATION CELLULAR SYSTEMS
687
TABLE I INTERFERENCE POWER AND THROUGHPUT IN BPS/HZ OF OMNIDIRECTIONAL CELLS WITH RADIUS 1.0 km AND 4.2-dB SHADOW-FADING STANDARD DEVIATION
TABLE II INTERFERENCE POWER AND THROUGHPUT OF THREE-SECTOR CELLS WITH RADIUS 1.0 km AND 4.2-dB SHADOW-FADING STANDARD DEVIATION
Fig. 2.
unchanged. The out-of-cell interference, on the other hand, can change from slot to slot due to variation in channel conditions to base stations other than the serving base station. Note that power control only eliminates the effect of channel variations to the serving base station. The fast-fading component across base stations is usually independent, hence the out-of-cell interference at any given base station changes from slot to slot. However, the out-of-cell interference power exhibits an averaging affect due to multiple users’ signals being combined in the base station. Furthermore, the in-cell interference power is the dominant component of the interference since in-cell interferers are closer to the base station. Thus, in a multiple-user scenario, we have a large dominant fixed IOT component and slowly varying smaller out-of-cell interference component. This leads to an IOT distribution with a large mean and small variance. In the case of a single user at a time transmission, the IOT is composed only of the out-of-cell interference as there are no in-cell interferers in the system. Thus, a large portion of the interference seen in the multiple simultaneous users scenario is not there in this case, leading to a small mean for the IOT distribution. The out-of-cell interference in this case changes dramatically from slot to slot, depending upon which users transmit in the neighboring cells. Thus, the out-of-cell interference can vary wildly in a single-user transmission. In the absence of any in-cell IOT, the IOT only consists of the wildly varying out-of-cell IOT , and this leads to a distribution with small mean and large variance. Transmission option (a), in which multiple users transmit simultaneously within the cell but are orthogonal to each other, has a mean of IOT similar to that of option (b) since there is no in-cell interference, while variance is similar to that of option (c) since out-of-cell interference is averaged over several users. The mean is larger in this case than that of option (b) because fewer users are limited by the maximum transmit power constraint, hence there is more out-of-cell interference power. Fig. 2 shows the ROT distribution for the different transmission options. The ROT characteristics are also different for
ROT distribution for different transmission schemes.
similar reasons as in the case of IOT. However, observe that the 95 and 99 percentile points of the ROT distributions are comparable. The differences in the nature of the interference distribution could lead to different throughput performance. Clearly, a smaller mean interference power is better. However, if the smaller mean is achieved at the expense of a large variance and unpredictability in the interference power as in the case of single user at a time transmission case it is a priori unclear that its throughput performance would be better. In Section III, we define the notions of throughput used in this paper and present results comparing the throughput achieved by the different schemes. III. THROUGHPUT CALCULATION We first compute the ergodic throughput, which is the average throughput achieved by a user over a large number of slots, assuming that the transmission rate in each slot is the achievable rate corresponding to the SINR at the receiver for that user’s signal during that slot. This throughput measure is meaningful under the assumption that the SINR is constant during the slot. For short slots at moderate speeds and small cells (so that the interfering transmission originating in surrounding cells arrives at the base station with slot boundaries that approximately coincide with that of the signal slot), it is reasonable to assume that both the signal power and interference power remain constant during the slot. Also, there must be a sufficient number of symbols during the slot so that practical coding schemes will achieve rates close to the capacity. Finally, the Shannon rate for a given SINR is achievable only when the transmitter knows a priori the transmission rate. Since the interference power is not predictable prior to the start of the transmission, this is not possible in practice. Hence, we propose the use of hybrid automatic repeat request (HARQ) transmission scheme. In particular, we consider the incremental redundancy (IR) transmission in which the receiver jointly decodes signals received in the original and subsequent retransmissions until the packet is received correctly. We also compute throughput achieved by this HARQ scheme. The ergodic throughput serves as an upper bound to the HARQ throughput.
688
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
For a given IROT target and users transmitting simultafor user is given by neously in slot , the SINR (1) is the maxfor transmission options (b) and (c), where is the IOT during imum received SNR of user in slot and slot . The maximum received SNR is limited by the maximum transmit power and is given by (2) where is the maximum transmit power and is the slowly varying part of the user’s channel gain that includes the is the fast fading gain. path loss, shadow fading, and For the case of transmission option (a), since orthogonality is achieved by bandwidth splitting (OFDM) or spreading (synchronous CDMA) by a factor for transmission by simultaneous users, the SINR is given by
Since the ergodic throughput is only an upper bound to the achievable throughput, we next investigate the HARQ throughput. HARQ transmission is implemented as follows. Transmissions are either new transmissions or retransmissions. For a new transmission, a information packet size is picked based on the current channel gain and the interference power statistics. No knowledge of the actual interference power is assumed. For the chosen packet size, an incremental redundancy code is constructed so that if the accumulated mutual information exceeds the packet size, then the packet can be decoded correctly. If the first transmission is unsuccessful, additional redundancy bits are transmitted in the retransmissions until the packet can be successfully decoded or the maximum number of transmissions is reached [8]. The HARQ throughput can be calculated based on the renewal-reward theorem [7], [8] for a given maximum number of be the accumulated mutual informaretransmissions . Let tion after transmissions. Then, the HARQ throughput is given by
(3) in the numerator is because the signal where the factor of occupies only of the signaling dimensions, hence interferof the band determines ence power and noise power in only the SINR. The ergodic cell throughput is then given by (4) and (5) where is the Shannon capacity of an additive white Gaussian noise (AWGN) channel at SNR . Note that the above expression for the cell throughput is under the assumptions of equal resource allocation and a full buffer traffic model where users always have data to send. Equal resource allocation implies equal time allocation (as in a round-robin scheduler) and equal received power across all users subject to transmit power limitations. As explained in the previous section, not all users achieve the same throughput because of the maximum transmit power constraint. Thus, in addition to computing the sector throughput, we also determine the ergodic throughput as a function of the average SNR, which is achieved by users in different locations users in the system, within the cell. When there are a total of of the time, given each user gets to transmit a fraction simultaneous users. Hence, the ergodic user throughput for a given user when there are a total of users in the system is given by (6) and (7)
(8) where is the discrete set of transmission rates that are available in the system. Note that the transmission rate is picked optimally for a given channel condition, i.e., path loss and fastfading values since these are slowly varying compared to the interference power and hence relatively predictable. Thus, the transmission code rate can be adjusted depending on the path gains. The accumulated mutual information is the sum of the mutual information achieved in each transmission, i.e.,
In Section IV, we calculate numerically the throughput for the three different transmission options for various numbers of simultaneous users and draw several conclusions. IV. THROUGHPUT COMPARISONS We first discuss the effect of the mean and the variance of the interference power on the throughput. Each throughput point was obtained by fixing the mean and the variance of the total interference power to a fixed value and computing the SINR distribution, assuming perfect power control to combat the fast fading, as explained in Section III, for a single user whose location is randomly chosen within a cell radius of 1 km and with shadow fading of 4.2 dB. The average ergodic and HARQ throughput were then calculated according to the expressions in in (8) in bits per the previous section. The discrete rate set second per Hertz is {1/16, 1/8, 1/10, 1/4, 1/2, 1, 3/2, 2, 4}. The same propagation parameters as described in Section II to generate the IOT distributions were used to obtain the results in this section.
DAS AND VISWANATHAN: COMPARISON OF REVERSE LINK ACCESS SCHEMES FOR NEXT-GENERATION CELLULAR SYSTEMS
689
TABLE III INTERFERENCE POWER AND THROUGHPUT OF OMNIDIRECTIONAL CELLS WITH RADIUS 2.5 km AND 8-dB SHADOW-FADING STANDARD DEVIATION
TABLE IV INTERFERENCE POWER AND THROUGHPUT OF THREE-SECTOR CELLS WITH RADIUS 2.5 km AND 8-dB SHADOW-FADING STANDARD DEVIATION
Fig. 3.
HARQ throughput dependence on variance of interference power.
Fig. 4. Throughput dependence on mean interference power.
Fig. 3 shows the average throughput normalized by the ergodic throughput for the incremental redundancy HARQ scheme with a maximum of one, two, and four transmissions for different values of interference power (in decibels relative to noise power) variance with the mean fixed at two. Observe that with increasing variance, a higher number of transmissions is required to approach the ergodic throughput as expected. Thus, a system with bursty interference power statistics such as transmission option (b) will require HARQ for efficient operation. With four transmissions, a significant fraction of the ergodic throughput is achieved. Also note that because of the finite set of allowed transmission rates, even with a small variance, the throughput increases with the number of transmissions since intermediate rates that are achieved through retransmission may match the SINR better than any rate in the initial transmission rate set . This is known to be one of the benefits of HARQ [9]. Fig. 4 shows the average throughput for different values of mean interference power (in decibels relative to noise power) with the interference power variance fixed at seven. Not surprisingly, the throughput decreases with increasing mean interference power since the SINR is lower with higher interference
power. However, note that a larger mean interference power typically occurs when multiple users are simultaneously transmitting. Thus, although the per user throughput is reduced, system throughput can increase. Clearly, the mean and the variance are determined by the type of transmission option, the number of users, the cell radius, and other propagation parameters. The average cell/sector throughput performance for the three different transmission options are presented in Tables I–IV for four different scenarios, namely, omnidirectional small cell (1-km cell radius, 4.2-dB shadow-fading standard deviation), three-sector small cell, omnidirectional large cell (2.5-km cell radius, 8-dB shadow-fading standard deviation), and three-sector large cell, respectively. We make several interesting observations based on these results. In each of these tables, the first column provides the number of simultaneously transmitting users. The one user case corresponds to option (b). The remaining rows correspond to transmission option (a) and (c) for different number of users; rows with next to the number of users are for option (a) and rows without the are for option (c). The second column provides the mean and the variance of the IOT (in decibels) distribution. The third column gives the 95% and 99% points of the ROT distribution. The purpose of this column is to show that the different schemes operate with roughly the same ROT tail distribution. The fourth column shows the ergodic throughput computed as explained in the previous section. The last column contains the HARQ throughputs for a maximum number of transmissions per code block equal to one, two, or four. A. Effect of Interference Power Variance From Tables I and II, we see that the ergodic throughput decreases with an increasing number of users, but the single transmission throughput increases with the number of users. On the other hand, the four transmission HARQ throughput decreases with an increasing number of users as in the ergodic case. This shows that in the absence of HARQ (single transmission), it is best to have multiple simultaneous transmissions that reduce the interference power variance. On the other hand, when HARQ
690
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
is available, the variance in the interference power plays a less significant role.
TABLE V INTERFERENCE POWER AND THROUGHPUT OF THREE-SECTOR, 1-km CELLS WITH 1/3 FREQUENCY REUSE AND 4.2-dB SHADOW-FADING STANDARD DEVIATION
B. Effect of In-Cell Interference Transmission options (a) and (c) both allow multiple simultaneous users that result in relatively small variance in interference power. However, while in transmission option (a) the transmissions within a cell are orthogonal, in transmission option (c) the transmissions interfere with each other. Thus, (a) has a smaller mean interference power than (c), as can bee see in the tables. Also, since the dominant portion of the interference in (c) is in-cell, the variance for (c) is smaller than that of (a). Because of the smaller mean, transmission option, (a) outperforms (c) for any number of users. In particular, for the 20-user case, the benefit of the orthogonal reverse link is about 39% in Tables I, II, and IV, and 51% in Table III. However, note that the optimal number of users is not 20. C. Optimal Number of Users From Tables I and II, we note that for the small-cell case the HARQ throughput with four transmissions is highest for transmission option (b) and involves transmission by a single user in each slot. However, in the case of large cells, as seen from Tables III and IV, transmission option (a) with ten users performs best. This is explained by the fact that in the case of a small cell, a single user is able to transmit sufficient power to meet the allowed IROT target, while that is not the case in a large cell where additional orthogonal users’ transmissions are required to meet the target IROT. This also shows that operating at lower in-cell and total ROT is not efficient. D. Best Transmission Option From the results on average cell/sector throughput, the best transmission option is option (a) coupled with the optimal number of users. The optimal number of users depends on the cell size, as explained above. Recall that OFDM transmission with multiple users sharing the bandwidth is an example of transmission option (a). Note that our modeling and analysis does not capture transmitter effects such as amplifier backoff and receiver nonidealities, such as channel estimation errors that could be different for different schemes. For example, OFDM transmission may require a larger amplifier backoff compared to CDMA transmission because of higher peak to average ratios. Without including such effects, we observe that multiple-user OFDM is superior. The next best transmission option is option (b), which is the time-multiplexed transmission scheme with one user at a time transmission. Note that for this transmission scheme, to achieve high received signal to noise ratios, either subchannelization (with OFDM modulation) or spreading with CDMA codes can be used.
cell/sector configurations. Note that these gains are for average throughput with the round-robin scheduler. We discuss the issue of fairness subsequently. The gains can be larger with schedulers that dynamically pick the optimum number of users as opposed to the static method used here for throughput evaluation. On the other hand, other factors that affect performance in practice, as discussed in the previous subsection, that have not been taken into account can reduce the gains. F. Effect of Sectorization In comparing Table I to II and Table III to IV, we observe that with sectorization the mean interference power increases more for transmission options (a) and (b) compared to transmission option (c). This is because in option (c) the dominant interference is from other transmissions within the cell and this does not increase in going from omnidirectional to the three-sector case. On the other hand, since the out-of-cell interference increases in going from omnidirectional to three-sector, the other two options show a relatively larger increase in mean interference. Nevertheless, the change in throughput is comparable for all the options because the low operating SINR of option (c) compared to the other two options results in a large change in throughput for the same change in mean interference power. Thus, going from omnidirectional to three-sector does not increase the capacity by a factor of three but only by a factor of about 2.5. G. Effect of Cell Size Comparing Tables I and II with Tables III and IV, we observe that the throughput is reduced for all transmission options in the case of the larger cell size. This is because of the maximum transmit power limit imposed on the transmissions. With the same maximum transmit power limit, the users are unable to meet the target IROT of 6 dB for some user locations. Thus, the overall ROT is lower in the large cell case compared to the small cell case. Also, note that the mean interference power relative to noise is lower for the large cell case since the interferers are further away. Nevertheless, because of the transmit power limitations the large cell case has smaller system throughput.
E. Gain Over Traditional Asynchronous CDMA
H. Frequency Reuse Versus Universal Reuse
Treating the asynchronous CDMA system [transmission option (c)] with 20 users, which is closest in our model to current generation cellular systems, as the baseline we observe that the gains of a synchronous CDMA or OFDM system with orthogonal transmissions within the cell [transmission option (a)] ranges between 44% and 52% in our results for the different
Table V shows the average HARQ throughput with a maximum of four transmissions for the case of three-sector small cell scenario, but with a frequency reuse of 1/3 [10]. In a 1/3 reuse system, each of the three sectors in a cell employs a different carrier frequency, thus reducing the amount of interference. The reduced interference leads to higher cell throughput.
DAS AND VISWANATHAN: COMPARISON OF REVERSE LINK ACCESS SCHEMES FOR NEXT-GENERATION CELLULAR SYSTEMS
691
Fig. 5. Cumulative distribution function of per user throughput with roundrobin scheduler for a system with 20 users per sector, 1-km cell radius and 4.2-dB shadow-fading standard deviation.
Fig. 6. Cumulative distribution function of per user throughput with roundrobin scheduler for a system with 20 users per sector, 2.5-km cell radius and 8-dB shadow-fading standard deviation.
However, three times as much bandwidth is used. A comparison of the throughput results in Tables II and V shows that the 1/3 reuse system has a significantly lower spectral efficiency (throughput per unit bandwidth) than a universal reuse system for all transmission options. Thus, a universal frequency reuse system is preferred.
TABLE VI COMPARISON OF AVERAGE LOG-THROUGHPUTS FOR DIFFERENT CELL CONFIGURATIONS: SMALL CELL OMNI IS 1-km RADIUS, 4.2-dB SHADOW-FADING STANDARD DEVIATION. SMALL CELL SECTORIZED IS THREE-SECTOR CELLS WITH 1-km RADIUS, 4.2-dB SHADOW-FADING STANDARD DEVIATION. LARGE CELL OMNI IS 2.5-km RADIUS, 8-dB SHADOW–FADING STANDARD DEVIATION. LARGE CELL SECTORIZED IS THREE-SECTOR, 2.5-km RADIUS, 8-dB SHADOW–FADING STANDARD DEVIATION
I. Fairness The average throughput values are based on the assumption that equal time is allocated to each user as in a round-robin scheduler. However, since the path loss to different user locations within the cell are not equal, equal time allocation does not always guarantee throughput fairness. The users at the cell edge will achieve lower throughputs compared to users close to the base station. Furthermore, the different transmission options show different levels of fairness depending on the number of users that transmit simultaneously. Hence, we study the cumulative distribution function (CDF) of the throughput across the locations within the cell. Fig. 5 shows the CDF of throughput for the three-sector small cell scenario. In this case, it is clear that equal time allocation with power control to meet the target in-cell ROT results in throughput fairness for all transmission options since 90% of the users achieve the same throughput. On the other hand, for the large cell scenario in Fig. 6, the different transmission options have different levels of throughput fairness. Transmission option (b), which involves a single-user transmission per slot provides low throughput to users at cell edge compared to users close to the base station. Transmission options (a) and (c) with 20 simultaneous users per slot achieve a higher degree of fairness with 90% of the users receiving the same throughput. Another metric that captures fairness is the average of the logarithm of the throughputs achieved over different locations within the cell. Similar to the ergodic throughput, the average log-throughput metric (in decibels) is given by (9)
and (10) The use of average of log-throughputs deemphasizes the contribution of high throughputs achieved by users close to the base station compared to average of throughputs. Table VI shows the average log-throughput results for the four different cell configurations. Observe that in the case of the large cell, with this metric, transmission option (b) no longer outperforms transmission option (c) with 10 or 20 users, despite the loss from in-cell interference for the latter in contrast to the average throughput metric. In particular, for the three-sector large cell scenario, option (b) is worse than transmission option (c) by about 9% in terms of the log-throughput metric. Transmission option (a) with ten users performs the best even under this metric. The gain relative to traditional asynchronous CDMA [transmission option (c)] in terms of this metric is about 1.51 dB or 40%. As another fairness metric, we show the average cell throughput under the assumption of equal average throughput to all users in Table VII. Equal average throughput is guaranteed for all users by time allocation that is inversely proportional
692
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 3, MARCH 2006
TABLE VII COMPARISON OF AVERAGE EQUAL THROUGHPUTS IN BYTES PER SECOND PER HERTZ FOR DIFFERENT CELL CONFIGURATIONS. SMALL CELL OMNI IS 1-km RADIUS, 4.2-dB SHADOW-FADING STANDARD DEVIATION. SMALL CELL SECTORIZED IS THREE-SECTOR CELLS WITH 1-km RADIUS, 4.2-dB SHADOW-FADING STANDARD DEVIATION. LARGE CELL OMNI IS 2.5-km RADIUS, 8-dB SHADOW–FADING STANDARD DEVIATION. LARGE CELL SECTORIZED IS THREE-SECTOR, 2.5-km RADIUS, 8-dB SHADOW–FADING STANDARD DEVIATION
here. On the other hand, practical imparities on the transmit and receive sides such as amplifier backoff and channel estimation and differences in signaling and synchronization overheads, such as the need for cyclic prefix that are not considered in this paper, can reduce the improvement relative to current systems. We have not considered the possibility of multiple antennas or interference cancellation at the base station receiver that may favor employing one transmission scheme over another. These would be interesting topics for future studies. ACKNOWLEDGMENT The authors would like to thank P. Polakos and G. Rittenhouse for their continued support. REFERENCES
to their instantaneous rates. Observe that option (a) performs the best, according to this metric in the large cell case, while options (a) and (b) are comparable in the small cell case. V. SUMMARY AND FUTURE WORK In this paper, we studied the reverse link system throughputs for various transmission options. The transmission options were distinguished by the interference characteristics observed at the receiving base station. The three categories considered were: (a) no in-cell interference, averaged out-of cell interference; (b) no in-cell interference, bursty out-of-cell interference; and (c) averaged in-cell interference, averaged out-of-cell interference. We compared the system-wide throughput under identical maximum allowable IROT criteria using both theoretical ergodic throughput as well as throughput achieved using HARQbased transmission scheme. The results showed that transmission option (a), which is realized in practice through an OFDM system with multiple-user transmission, achieves the highest performance for the various cell/sector scenarios considered. The gain relative to an asynchronous CDMA system, within the scope of our model, ranges from 40% to 53%. In the case of small-cell deployment, option (b), which involves single-user transmission, performs comparably to transmission option (a) when HARQ with maximum number of transmissions of four or more is allowed. HARQ was found to be effective in dealing with bursty interference. However, in power-limited scenarios as in large-cell or wider bandwidth deployments, the performance of this option is inferior and is even worse than that of traditional asynchronous CDMA under the log-throughput metric that takes fairness into account. We also compared universal reuse with 1/3 frequency reuse and the results showed that universal reuse is superior for all transmission options. Our results also indicated that for the best performing transmission option (a), the number of users transmitting simultaneously has to be optimized to achieve the best performance. This suggests that by dynamically adjusting the number of simultaneous transmissions, for example by allowing multiple-user transmission for users near the cell edge and single-user transmission for users closer to the base station so that the maximum transmit power does not impose a limit on the IROT achieved, can further increase throughput. Thus, an optimal scheduler might show a larger improvement than the round-robin scheduler considered
[1] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, and A. Viterbi, “CDMA/HDR: A bandwidth-efficient high speed wireless data service for nomadic users,” IEEE Commun. Mag., vol. 38, no. 7, pp. 70–77, Jul. 2000. [2] “CDMA 2000 high rate packet data air-interface specification,” Telecommun. Industry Assoc., TIA/EIA/IS-856, 2002. [3] (2002) UTRA high speed downlink packet access: UTRAN overall description. [Online]. Available: http://www.3gpp.org/ [4] K. Kumaran and L. Qian, “Uplink scheduling in CDMA packet-data systems,” in Proc. INFOCOM, San Francisco, CA, Apr. 2003, pp. 292–300. [5] M. Zorzi, “On the analytical computation of the interference statistics with applications to the performance evaluation of mobile radio systems,” IEEE Trans. Commun., vol. 45, no. 1, pp. 103–110, Jan. 1997. [6] T. Chebaro, “Statistics of signal to interference plus noise ratio in sectorized FH-TDMA with a single cell frequency reuse pattern,” in Proc. Int. Conf. Commun., Seattle, WA, 1995, pp. 863–868. [7] M. Zorzi and R. R. Rao, “On the use of renewal theory in the analysis of ARQ protocols,” IEEE Trans. Commun., vol. 44, no. 9, pp. 1071–1081, Sep. 1996. [8] G. Caire and D. Tuninetti, “The throughput of hybrid-ARQ protocols for the Gaussian collision channel,” IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 1971–1988, Jul. 2001. [9] H. Zheng and H. Viswanathan, “Optimizing the ARQ performance in downlink packet data systems with scheduling,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 495–506, Mar. 2005. [10] G. Stuber, Principles of Mobile Communication. New York: Kluwer, 1996.
Suman Das (S’03–M’04) received the B.S. degree in computer science and engineering from the Indian Institute of Technology, Kharagpur, in 1994, and the M.S. and Ph.D. degrees from Rice University, Houston, TX, in 1997 and 2000, respectively. Since then, he has been a Member of Technical Staff in the Wireless Technology Research Department, Bell Laboratories, Lucent Technologies, Murray Hill, NJ. His research interests include algorithms and architectures for signal processing and communication and design and analysis of future wireless networks.
Harish Viswanathan (SM’03) received the B.Tech. degree in electrical engineering from the Indian Institute of Technology, Madras, in 1992, and the M.S. and Ph.D. degrees in electrical engineering from Cornell University, Ithaca, NY, in 1995 and 1997, respectively. He is presently with Bell Laboratories, Lucent Technologies, Murray Hill, NJ. His research interests include information theory, communication theory, wireless networks, and signal processing.
