BROADBAND INDOOR WIRELESS SYSTEM WITH IN-CELL FREQUENCY REUSE BASED ON SECTORED ANTENNAS *

Resumo: Neste artigo investiga-se urn novo sistema de multiplo acesso para comunica~Oes sem fio de banda larga em interiores utilizando antenas setorizadas. 0 que 0 difere de outros sistemas previamente propostos, que tambem utilizam antenas setorizadas, e a sua capacidade de reusar frequencias em setores distintos da microcelula : terminais portateis 10­ calizados em setores distintos da microcelula podem compar­ tilhar 0 mesmo espectro de frequencia se a nivel de interfe­ rcncia mutua for aceitavel. Porem, isto requer uma cuidadosa programa~ao das transmissoes a fim de evitar interferencias destrutivas. A program~ao Gtima, a que maximiza 0 nt1mero de pacotes transmitidos por quadro, se encontra na classe de problemas NP-completos para a caso de tres ou mais trans­ missoes simultiineas. Como este tipo de problema nao pode ser resolvido em tempo real, propOe-se urn algoritmo sub­ 6timo chamado "First Fit Algorithm". 0 problema IS estudado experimentalmente para 0 caso em que a microcelula e divi­ dida em dez setores (setoriza~ao de nivel dez). Urn modelo estatistico de propaga~ao por carninhos multiplos e utilizado para estender os resultados para outros niveis de setoriza~ao. o sistema proposto pode proporcionar urn grande incremento na capacidade da microcelula. Por exemplo, enquanto os sis­ temas previamente propostos podem transmitir somente urn pacote de informa~ao par vez, este novo sistema e capaz de transmitir, em media, perto de tres pacotes simultaneamente. Este resultado e valido para urn nive! de interfercncia mutua maximo de 10 dB com setoriza~iio de nivel dez em urn am­ biente interno com paredes divisorias feitas com blocos de concreto. Abstract: This paper investigates a new multiple ac­ cess system for broadband indoor wireless communications based on sectored antennas. Unlike previous sectored an­ tenna indoor systems, this system incorporates the capability of reusing spectrum in different antenna sectors of the base station. It is shown that portable terminals located in different sectors of the indoor microcell may transmit/receive simul­ taneous data packets on the same frequency if their mutual interference is below a threshold level (or capture threshold) that guarantees an acceptable packet error rate. However, this requires careful scheduling of packet transmissions in order to avoid transmitting packets that would jam each other dur­ ing the same time slot. When trying to transmit more than two packets per time slot, the optimum scheduling problem, the one that maximizes the number of packets transmitted per

Abstract: This paper investigates a new multiple ac cess system for broadband indoor wireless communications based on sectored antennas.Unlike previous sectored an tenna indoor systems, this system incorporates the capability of reusing spectrum in different antenna sectors of the base station.It is shown that portable terminals located in different sectors of the indoor microcell may transmit/receive simul taneous data packets on the same frequency if their mutual interference is below a threshold level (or capture threshold) that guarantees an acceptable packet error rate.However, this requires careful scheduling of packet transmissions in order to avoid transmitting packets that would jam each other dur ing the same time slot.When trying to transmit more than two packets per time slot, the optimum scheduling problem, the one that maximizes the number of packets transmitted per

INTRODUCTION
Sectored Antennas have been used for some time in mobile cellular systems as a means of reducing interference and con sequently increasing system capacity.More recently, sectored antennas have also been applied to Wireless Local Area Net works (WLAN) [I] [2].In [1] the use of directional antennas is considered to be an excellent technique for dealing with multipath propagation problems.In [2] sectored antennas are proposed in order to combat the severe co-channel interfer ence arising from a small frequency reuse factor.Although [1] and [2] propose different rules for the use of sectored an tennas, the final goal in both cases is to achieve an increase in system capacity.
The multiple access schemes described in [1] and [2] allow transmission/reception in only one of the antenna sectors at a time, usually in the one that provides the best communication channel between the base station and a given portable.Fig ure I-a shows sectored antennas similar to those in [l] and [2].The RF switch matrix used to select the desired antenna from the set can be fabricated compactly and inexpensively using either a Gallium Arsenide Monolithic Microwave Inte grated Circuit (GaAs MMIC) or microwave diode switching elements [4].
In [3], a new multiple-access scheme is proposed to achieve in-cell frequency reuse by allowing simultaneous transmissions over different antenna sectors.This new multiple-access scheme requires a multi-port sectored an tenna system as the one illustrated in Figure l-b, which rep resents the same set of antennas as in Figure I-a but with a switch matrix capable of simultaneously selecting two anten nas and connecting each to a desired port that is connected to a transceiver.The sectored antenna system of Figure l-b has the potential to double the capacity of the system by al lowing simultaneous transmissions/receptions to occur in two antenna sectors sharing the same frequency spectrum.How ever, as we explain in Section 2, this kind of spectrum sharing requires compatible portables.
The schemes proposed in [1] and [2] employ sectored an tennas in both the base station and portable modules.The scheme proposed in [3] assumes that this approach causes the system to become excessively complex, and, due to the size of the sectored antenna system, not suitable for a portable ter minal.Therefore the conservative approach of concentrating the complexity of the system in the base station is adopted in order to be able to use simpler antennas in the portables: sec tored antennas are used in the base station and simple omni directional antennas are used in the portables.
The results presented in [3] are based on measurement data obtained with a sectorization level of 10 (using 10 sectors in the base station).In this paper we use statistical modeling of indoor multipath propagation in order to investigate the per formance of the multiple access proposed in [3] when operat ing with different levels of sectorization.

COMPATIBILITY CONDITION
The concept of compatibility is explained with the help of Figure 2 which shows a base station using a 2-port sec tored antenna system to communicate simultaneously with two portables, PI and P 2 .The signal strength values quoted in this figure were chosen for illustrative purposes.The re flectors represent reflecting structures, for example, walls or metallic doors.In order to verify the compatibility between portables PI and P 2 , the minimum Signal-to-Interference Ra tio (SIR) acceptable for communication between the base sta tion and a portable has to be specified.This parameter is the capture threshold, which we name II.Its value is depen dent on the coding and on the modulation scheme employed.For example, spread spectrum modulation schemes can oper ate with a level of interference above the level of the signal, which results in a negative value of II (in decibel).However, the proposed multiple access scheme is intended to operate with narrow band (non spread spectrum) modulation schemes which can achieve high spectrum efficiency, around 1 bpslHz, as required in the FCC proposal for V-NIl wireless networks [5].Therefore we will be considering values of II in the range of5 to 20 dB.It is assumed that an up-link transmission and a down-link transmission can not occur simultaneously: either both trans missions are in the up-link direction (from portable to base station) or both are in the down-link direction (from base sta tion to portable).This assumption is made because the level of interference that a down-link transmission would cause in an up-link reception would be unacceptable: in the base sta tion, the power level of a transmitted signal is much higher than the power level of a received signal.
In the down-link case, the base station uses antenna sector 5 to transmit to portable PI, and antenna sector 8 to transmit to portable P 2 .Portable PI receives a signal from antenna sector 5 at an average power level of 0 dBm and interference from antenna sector 8 through a reflected path at an average power level of -20 dBm.Simultaneously portable P 2 receives a signal from antenna sector 8 at an average power level of -10 dBm and interference from antenna sector 5 through a reflected path at an average power level of -100 dBm.There fore, the SIR for the signal received by portable PI is 20 dB, and the SIR for the signal received by portable P 2 is 90 dB.Then we say that portables PI and P 2 are compatible in the down-link case if II :::; 20 dB.In the up-link case, the base station receives, through an tenna sector 5, the signal transmitted by P j at an average power level of 0 dBm and interference of -100 dBm from the reflected signal transmitted by P 2 , yielding an SIR of 100 dB for the P j transmitted signal.Simultaneously, the base station receives, through antenna sector 8, the signal transmitted by Aleandro S. Macedo and Elvino S. Sousa Broadband Indoor Wireless System with In-Cell Frequency Reuse Based on Sectored Antennas P2 at an average power level of -I 0 dBm and interference of -20 dBm from the reflected signal transmitted by PI, yield ing an SIR of 10 dB for the P 2 transmitted signal.Therefore we say that portables PI and P 2 are compatible in the up-link case if II ::; 10 dB.
In this example, which does not consider the power con trol mechanism that we describe below, compatibility in the down-link case does not necessarily correspond to compati bility in the up-link case.In fact, we observed through mea surement results that the average number of compatibilities among portables in an indoor microcell is, in general, larger for the down-link case than for the up-link case.This down link/up-link average compatibility asymmetry arises because, in the up-link case, portables located closer to the base sta tion cause stronger interference with the signals of portables located on the periphery of the indoor microcell.In a sense this problem is similar to the near-far effect that decreases the up-link capacity of CDMA systems.Therefore it is expected that power control can be used to improve the average number of compatibilities in the up-link case.
Consider now the use of power control in Figure 2. The power control mechanism assumes that the portables adjust their transmitting power so that the base station receives, through the best sector for communication with a given portable, the same average power level from any portable.In this case, portable P 2 increases its transmitted power so that the base station can receive its signal with the same power level of the signal received from portable P 1. Then P2 has to add 10 dB to its transmitted signal power.By doing so, it also adds 10 dB to the interference caused in the P j signal.This is shown in figure 2-c.If the up-link SIR values are recal culated with the power control values of figure 2-c, the SIR values obtained are 90 dB for the PI signal and 20 dB for the P:z signal.Therefore, the minimum of the two SIR values, 20 dB, is 10 dB better than the minimum SIR value obtained without power control.
In order to express the compatibility conditions mathemat ically we define the following parameters: • Gp,s (Portable-Sector Power Gain): represents the av erage power received through the channel between portable P p and antenna sector s.It has the same value for both up-link and down-link channels (provided that the same power level is transmitted in both cases).This is true because we assume that up-link and down-link transmissions occur in the same frequency band (but not at the same time); therefore up-link and down-link chan nels are reciprocal.
• B(i): represents the best antenna sector for communi cating with Pi.
The Gp,s parameters are illustrated in figure 3.
Using these definitions, we can express the conditions for the existence of compatibility in the down-link case between two portables Pi and Pj as:

COMPATIBILITY CONDITION FOR THE N-PORT CASE
In the previous section, we considered compatibility for the 2-port case, which implies using a system of sectored anten nas with two ports as shown in figure l-b.Now we consider a system of sectored antennas with N ports as shown in fig ure4 .Figure 4: The N-port sectored antenna system.
An N-port antenna system would allow a maximum of N simultaneous transmissions in N different antenna sectors.As such it would have a switching matrix capable of selecting N of the antenna sectors and connecting each of them to one of N ports (each port is connected to a transceiver).In this case the conditions for compatibility among N portables P 1 , P 2 , .(3) and, in the up-link case, the compatibility conditions are given in (4).Note that these N portables represent a subset of all the portables in the microcell.
If the N conditions of (3) are satisfied, then there may be N simultaneous packet transmissions during a time slot to these N portables (down-link case).This means that, during this time slot, the down-link system capacity is multiplied by N, i.e., N packets are transmitted through N sectors instead of the single packet that could be transmitted in this time slot if a single port sectored antenna system were used in the base station.Similarly, if the N conditions of (4) are satisfied, then there may be N simultaneous packet transmissions during a time slot from these N portables (up-link case), which corre sponds to the up-link system capacity being multiplied by N. In general, however, an increase in the number of ports does not correspond to a proportional increase in system capacity, as can be observed from measurement and simulation results presented later in this paper.The reason is that the number of subsets of N portables that correspond to compatible porta bles decrease as N increases.For example, the probability of two portables being compatible is larger than the probability of three portables being compatible.Therefore, as the num ber of ports N increase, it is more likely that some of them will not be used during a given time slot due to a lack of com patible portables.The capacity gain eventually saturates at a given number of ports.

CHANNEL MEASUREMENTS
We devised an experiment which allowed us to measure the portable-sector power gain (G p • s , see Figure 3) values for a base station and portables located in some typical indoor envi ronments.With these values, we were able to verify the com patibility among portables using the conditions established in (3) or ( 4).The experimental setup is described with details in [3].It can measure with a sectorization level of ten, i.e., it assumes that the base station operates with ten antenna sec tors, each covering 36° of the horizontal plane.We measured different indoor locations using this experimental setup.One of them, which we chose to investigate in this paper, is the southwest section of the fourth floor of the Galbraith Build ing located in the University of Toronto Campus.This loca tion is depicted in Figure 5, and we named it location 1.It represents a closed indoor environment where the walls are made of a hard material, in this case concrete blocks.For this location, 50 uniformly distributed positions were measured to simulate 50 portables.

MEASUREMENT RESULTS
In this section, we present the measurement results in terms of average compatibilities which we define as follows.
The average compatibility between two portables is given by 1 where N p is the number of portables in the microcell, and I (i, j) is defined for portable i and j as I, if portables i and j satisfy { 0, otherwise.
Here, AC2 represents the fraction of all two portable com binations that correspond to compatible pairs.Therefore it represents the probability of two randomly picked portables being compatible.Broadband Indoor Wireless System with In-Cell Frequency Reuse Based on Sectored Antennas The average compatibility among three portables is given by 1 N" NI' NI' AC3 = N;:" L L L I(i,j, k), (7) (3 ) ;=1 j=i+1 k=J+ 1 where I (i, j, k) is defined for portable i, j and k as I, if portables i, j and k satisfy compatibility condition.
Here, AC3 represents the fraction of all three portable combinations that correspond to compatible triples.There fore it represents the probability of three randomly picked portables being compatible.
Similarly, ACn represents the fraction of all n portable combinations that correspond to compatible subsets of n portables.
Figure 6 shows the results obtained in the up-link case for the location I.The average compatibilities AC2, AC3 and AC4 are plotted as functions of the capture threshold.The solid curves are the results obtained considering the power control mechanism described in Section 2. Figure 7 shows the average compatibilities obtained in the down-link case for location l.In the down-link case, assuming that the same power level is transmitted to all the portables, we obtained average compatibilities close to those obtained in the up-link case with power control.In order to understand the meaning of these measurement results, let us assume a multiple access scheme in which a base station operating with a sectored antenna system like that shown in figure 4 allocates packets in time slots in or der to transmit them to portables in the microcell.Let us also assume that there is no compatibility verification in this process, i.e, packets are picked randomly.Therefore, when two or more packets are transmitted in the same time slot, they may be received with errors if the receiving portables are not compatible, and in this case we say that a collision oc curs.The probability that a time slot is collision-free depends 0.1e ,'i::", '''a '" '\" of\'\\ on the number of packets transmitted in this time slot.This probability is the average compatibility among the portables.
Consider for example a capture threshold of 10 dB in Fig ure 7.In this case the probability of a collision-free time slot is approximately 0.4 if two packets are transmitted together, and approximately 0.04 if three portables are transmitted to gether.We may conclude that such a multiple access scheme would provide poor throughput due to the small likelihood of collision-free transmissions.A new multiple access scheme that verifies compatibility among the portables in order to avoid simultaneously transmitting packets that can jam each other is proposed in [3].Such a scheme can significantly im prove the throughput when compared with the one-port case described in [1] and [2].This new multiple access scheme is described in the following section.

FRAME SCHEDULING
This section discusses how to take advantage of the existing compatibilities among portables in an indoor microcell in or der to increase system capacity.This can be done by properly scheduling simultaneous transmissions of packets that belong to compatible portables.Figure 8 depicts the scenario where scheduling is performed.It shows that the base station has a buffer where packets collected from a high speed wireline backbone network are temporarily stored while waiting to be transmitted to their destination portables during down-link time slots.It also shows that each portable has a buffer that temporarily stores packets generated in the end-user terminal equipment and are waiting to be transmitted to the base sta tion during granted up-link time slots.The scheduling prob lem consists in finding among the awaiting packets those that can share a time slot in the next frame, namely, those that belong to compatible portables.Let us suppose that Figure 9-a represents the values of the Cp,s parameters, as defined in Section 2, related to the porta bles and the base station of figure 8.The values quoted in this figure were chosen for illustrative purposes.With these values, the two by two compatibility relations among the portables can be obtained, as shown in figure 9-b for a cap ture threshold of 10 dB, where "I" means compatibility and "0" means incompatibility.Let us also suppose that a 2-port frame has been scheduled using these compatibility relations.figure 10 represents this frame with its down-link and up-link portions.Here, the word "port" is used to denote a port in the sectored antenna system which can be switched to anyone of the antenna sectors.Therefore, in this figure, the base station operates with a two-port sectored antenna system as shown in figure I-b.The frame is composed of a number of equal time slots, each capable of carrying one packet per port.Thus, with the two-port antenna system, a maximum of two pack ets can be transmitted per time slot.For example, each packet could transport one ATM (Asynchronous Transfer Mode) cell [7] plus some wireless overhead.The packet owners and the sectors being used for the transmission of each packet are also shown in figure 10.The first time slot of the down-link sub frame carries two packets, one for PI and the other for P 3.For each packet, the base station uses the antenna sectors that pro vide the best signal level, namely, sectors 2 and 6.The time slot and frequency spectrum sharing between a PI packet and a P: 3 packet is possible because of the compatibility between their owners.
We propose that up-link and down-link modes use the same frequency spectrum (Time Division Duplex).This guarantees reciprocity between up-link and down-link channels, allow ing the Cp,s parameters to be used for both down-link and up-link compatibility verification with the conditions defined in (1) and (2), respectively.Up-link/down-link traffic does not need to be symmetrical.In fact it is expected that the up-link traffic will be a small fraction of the down-link traffic.This is the case, for example, for the current traffic in the Internet where the down-loading of files generates highly asymmetri cal traffic.Accordingly, the down-link subframe in figure 10 was made intentionally larger than the up-link subframe for illustrative purposes.
It is assumed that scheduling is performed in the base sta tion (central control architecture).For this purpose the base

Base Station
Sec1 Sec2 Sed Sec4 SeeS Sec6 Sec7 SeclJ PI -50 -5 -32 -lOt - 10 -20 -50 -40   ... ~ P., -40 -10 -2fJ -4 -60 -56 -15 -41 oC:l P, -23 -50 -lfJ -20 -6    receives updated information about the compatibility rela tions among the portables and about the number of packets waiting transmission in each buffer.For Variable Bit Rate (VBR) services, the number of packets that arrive in the porta bles' buffers and in the base station's buffer during one frame duration varies from frame to frame.This means that each new frame requires its own scheduling.Therefore the time available for scheduling each frame is one frame duration: during the transmission of the i-th frame, the base station is working out the scheduling of the (i + 1)-th frame, which has to be ready for transmission before the end of the i-th frame transmission.

THE FIRST FIT ALGORITHM
The necessity of solving the scheduling problem in less than one frame duration was stated in the previous section.How ever, it turns out that for the N -port case (N ~ 3), the op timum scheduling problem, which maximize the number of packets transmitted per frame, is in the NP-Complete class of problems (problems that can not be solved in polynomial time, or Non Polynomial problems) [6].The practical result Aleandro S. Macedo and Elvino S. Sousa Broadband Indoor Wireless System with In-Cell Frequency Reuse Based on Sectored Antennas is that, for a large number of packets, solving it in real time becomes impractical.
The NP-Completeness of this problem is not proved here, but it is indicated that it can be proved by mapping the N Dimensional Matching problem [6] to the N-channel (N ::::: 3) frame scheduling problem.By knowing that the N Dimensional (N 2 3) Matching problem is in the class of NP-Complete problems, it is established that the N -channel frame scheduling problem (N 2 3) is also in this class.The 2-port optimum frame scheduling problem is a special case that requires further investigation to determine if it belongs to the NP-complete class or if it belongs to the P class (problems that can be solved in polynomial time [6]).However we pre fer to concentrate on finding a sub-optimum frame schedul ing solution that fits the generic N -port case, and that can be solved in real time.This sub-optimum solution is the First Fit Algorithm (FFA) that we describe below.
The FFA can be better explained with the help of figure 11.This algorithm places the packets into the time slots one at a time in the order that they arrive in the buffer.It does so according to the following simple rules: 1. First, the algorithm occupies the time slots of the first port.If, after performing this step, there are packets left in the buffer, then it performs the following steps.
2. For allocating packets in ports 2 and up, the algorithm al ways places the next packet of the buffer into the lowest indexed time slot containing only packets that are com patible with the packet being allocated.The conditions of compatibility are given by (3) for the down-link case and by (4) for the up-link case, where N is such that N -1 is the number of packets already allocated in the time slot.When searching for the lowest-indexed time slot, the port index has priority over the time slot index.Therefore the algorithm looks first for a time slot in port 2, and if it can not find a valid time slot, then it looks for one in port 3, and so on.This helps to distribute packet transmissions evenly in the time axis.
3. If a packet does not fit in any of the time slots of this frame, then the algorithm leaves it to be transported in the next frame and tries to allocate the next packet of the buffer by going back to step 2.
4. The algorithm repeats steps 2 and 3 until all the packets of the buffer are considered or until the frame is full.
In the scheduling of down-link packets, the packets are stored in the base station's buffer while awaiting transmis sion, so the FFA operates in a local buffer.However, in the scheduling of up-link packets, the buffer is distributed in the sense that it is composed of all the portables' buffers.In this case the base station has to receive updated information about the number of packets awaiting transmission in each portable buffer, so that the distributed buffers can be operated in con junction as if they were a single buffer.
The FFA serves the packets according to their order of ar rival in the buffer.However, this algorithm could be modified in order to serve packets according to some policy that privi leges real time services.See [8] for example.It has been assumed that the base station keeps updated in fonnation about the compatibility condition among the porta bles and about the number of packets awaiting transmission in each buffer.In [3], a frame structure with overheads that allow the base station to acquire and update this infonnation is proposed.

FFA SIMULATION
Simulations were run in order to evaluate the FFA perfor mance in location 1.Only up-link traffic was simulated, and performance was evaluated with and without power control.The traffic model used in these simulations was a well be haved VBR service in which a new packet for portable i (i = 1, 2, ... M) arrives in its buffer during a time slot ac cording to the Bernoulli process.It was assumed that the base station had immediate knowledge of a packet arrival.
The simulation results can be seen in Figure 12.These results were obtained assuming a capture threshold of 10 dB and a frame size of 20 time slots.However, it was shown in [3] that the maximum throughput is not dependent on the size of the frame though it affects the latency of the packets, so a small frame size is desirable.The curves are for mean buffer occupancy and throughput as functions of the system load, which is the traffic generated by all the M portables, where each portable contributes }[ of the total load.Throughput is defined as the average number of packets transported per time slot.From the graphs we can observe that the throughput is equal to the load up to a point where it saturates.At this point the system reaches its maximum throughput, and thus the mean buffer occupancy rises rapidly.
In location 1, the maximum throughput with three ports was around 2.1 without power control and around 2.5 with power control.The results obtained with four ports (not plot ted) were not significantly better than those obtained with three ports.The reason can be seen in figure 6, where the value of the average compatibility among four portables (AC4) is practically zero at a capture threshold of 10 dB.However, we should note that the 3-port case with power control was able to provide a maximum throughput of 2.5, even though the average compatibility among three porta bles (AC3) is only 0.04 at a capture threshold of 10 dB (see FIG. 6).
Figure 12 shows the FFA maximum throughputs (the  points where the curves saturated) for a capture threshold of 10 dB.In [3], the measurement results were analyzed in terms of the FFA maximum throughput as a function of the capture threshold.For example, Figure 13 shows the up-link maxi mum throughput that can be achieved in location 1 with dif ferent capture threshold values.However, due to a feature of the measuring experiment, the results in Figure 13 are valid only for a sectorization level often.In the following section, we describe a statistical model for indoor multipath propaga tion which can be used to investigate how the sectorization level affects the average compatibility among the portables and, consequently, how it affects the maximum throughput in the microcells.Intuitively, we can expect that the use of a higher sectorization level, which translates into using anten nas with better directivity, can improve the average compati bility among the terminals, since antennas with better direc tivity can filter out more of the interfering multipaths.
The problem was investigated through Monte Carlo simu lations of an indoor multipath propagation statistical model.This was preferred over two other options: simulation by means of ray tracing [12][13] and actual measurements us ing antennas of different beamwidths.
The main difficulty related to ray tracing is that this tech nique requires a detailed description of the indoor layout and a knowledge of reflection and transmission coefficients of walls, doors.windows, etc.We also had the option of measur ing indoor locations using antennas of different beamwidths.However.we considered this approach too complicated be cause each sectorization level would require its own directive antenna.and so the measurements would have to be repeated for each sectorization level investigated.Moreover, these two options have the drawback of being ad hoc, unlike an indoor multipath propagation statistical model that can be applied to 78 any location provided that some parameters in the model are adjusted appropriately.9 •

MODEL DE SCRIPTION
In this section, we describe a statistical model for indoor propagation.The model is proposed by Spencer et al. [9] as an extension of the Saleh-Valenzuela model [11], and it accounts for amplitude, time and angle of ray arrival.The statistical model for indoor multipath propagation proposed by Saleh and Valenzuela does not take into consideration the angles of arrival of the multipaths, which are necessary in our investigation.However, it has served as the starting point for a statistical model developed by Spencer et al. that incorporates the angle of arrival into multipath propagation.The resulting model is a combination of two statistically independent pro cesses, one governing ray amplitudes and arrival times, and the other governing ray angles of arrival.

Modeling Ray Amplitude and Ray Arrival Time
This part of the model is actually the Saleh-Valenzuela model itself.It assumes that, in the time axis, rays arrive in clusters.The cluster arrival time (Tz, see Figure 14), which is defined as the arrival time of the first ray ofthe cluster, is modeled by a Poisson arrival process with rate A. A Poisson arrival pro cess is also used, but with rate A, to model ray arrival times (Tkl' see figure 14) within a cluster.The distributions of clus ter and ray arrival times are given respectively by (9) and -\ -).(T,,-T'/,_ldJ P(Tid I T(k-1)1 ) -/\e , (10) where I represents the l-th cluster and kl represents the k-th ray within the l-th cluster.
------- Let us assume that the kl-th ray has amplitude 13k! and phase ¢kl' Therefore the channel impulse response is given by In this model, 13kl is a Rayleigh distributed random variable whose mean square value is illustrated in figure 14, and is expressed mathematically by a double-exponential decay f3fl = 13 2 (0, O)e-T,/f e-r"h, where ,82(0,0) is the average power of the first arrival, and r and 'Y are cluster and ray power-decay time constants, re spectively.The following expression for 13 2 (0, 0) is derived by Saleh and Valenzuela [11]: (13) where r is the separation distance of the transmitter and re ceiver, G(lm) is the channel gain at a distance of 1 meter (r = 1), and a is the channel loss parameter which depends on the characteristics of the indoor environment.A typical value of a for office buildings is 3 [11], but values as high as 6 have been reported for office buildings with metalized partitions [14].
In [9] and [II], To, the arrival time of the first cluster, is defined in different ways.We will assume the definition given in [9], which is c where c is the speed of light.

Modeling the Ray Angle of Arrival
In their measurements, Spencer et al. could not observe any correlation between the angle and the time of ray arrival.Based on this fact, they propose a statistical model for ray an gle of arrival that is independent on the ray arrival time.The following expression represents the proposed angular impulse response of the multipath channel: where f3kl has the same meaning as in Equation 11; 81 is the mean angle of the l-th cluster, that is, the mean angle of the rays arriving within the loth cluster; and Wkl is the angle deviation from 81 making the kl-th ray arrive at an angle of 8 / +Wkl.
It is proposed in [9] that 8 1 be uniformly distributed throughout the interval [0,21r) and that the ray angle devia tion, W kl, be modeled as a zero mean Laplacian distribution with standard deviation a:

Estimated Parameters
The resulting statistical model, which accounts for amplitude, time, and angle of arrival, is defined by five parameters: A, ,x, r, 'Y, and a. Table I shows Spencer et al.'s estimations for these parameters, which were based on measurements taken in two different buildings and reported in [10].The frequency used in these measurements was 7 GHz, which is relatively close to the 5.8 GHz frequency that we used in our measure ments [3].
In order to understand why the parameter values are building-dependent, we need a physical interpretation of the model.Spencer et al. observed that the strongest cluster was almost always associated with a direct line of sight path, even when this line was blocked by walls.Weaker clusters were apparently caused by back wall reflections and doorway openings.Therefore the formation of clusters is related to building superstructures.The rays within a cluster are related to smaller objects, such as furniture, that are in the vicinity of the transmitter and the receiver.

AVERAGE COMPATIBILITY SIMULATIONS
This section shows how the statistical model described in the previous section can be used to simulate average compatibil ity among portables.We first define the dimensions of the in door location.Here, we assume an area of 25 x 30 m 2 , which is the area of our indoor location 1 (see Figure 5).In order to compose a simulation scenario, we place the base station at the center of this area, and we place M portables (we will be considering M = 50) at random positions uniformly dis tributed within the area.This is illustrated in Figure 15.
Next, the steps in the following list are repeated in order to generate a total of four clusters and 15 rays per cluster for each portable.These numbers were chosen based on the ob servation that using more than four clusters and more than 15 rays per clusters did not alter the simulation results signifi cantly.
• Portable-Base distance T is used in (14) to compute the arrival time of the first cluster To.
• The probability distributions of ( 9) and ( 10) are used to draw the cluster arrival times CFt) and the ray arrival times (T /.:/ ), respectively.
• Portable-Base distance T is used in (13) to compute the average power of the first arrival (,6~0)' • Cluster arrival time, ray arrival times and the average power of the first arrival are used in (12) to compute the mean square value of the ray amplitudes (f3f/).
• A Rayleigh distribution with mean square values of f3f/ is used to draw the kl-th ray amplitude (,6/.:/).
• A random phase ¢>h'/ is drawn for each ray using uni form distribution in the interval [0, 21r).Therefore the channel impulse response for the kl-th path is given by ,6h,/e-h 'o(t -T/ -T/.:/).
• The angle of the line of sight path 8 (see figure 15) is used as angle of arrival for the first cluster 8 0 .This is based on the observation made by Spencer et al. that the strongest cluster was almost always associated with a direct line of sight path, even when this line was blocked by walls.
• A random angle of arrival 8/ is drawn for each of the three remaining clusters using a uniform distribution in the interval [0, 21r).Note that this does not incorporate possible angular correlations among clusters of neigh boring portables.figure 16 illustrates why cluster arrival angles of neighboring portables are likely to be corre lated.We investigated the effect of these correlations, and concluded that they cause only a slight decrease in the average compatibilities, so they can be disregarded.
• The probability distribution of ( 16) is used to draw the angle of arrival deviation w/.:/ for each path.Therefore the ray angle of arrival of the kl-th ray is 8/ + W/.:/.

Computing Average Power
Once we have obtained the angle of arrival and channel im pulse response for each path, we can proceed to compute the average power received by the base station in each of its an tenna sectors when a given portable transmits.In order to compute the average power received in each sector, we need the channel impulse response between the i-th sector and a given portable.Assuming four clusters and 15 rays per clus ter, this can be expressed by where gi (8) is the i-th antenna sector gain at angle 8. Now we are ready to compute the average power received in each sector when a given portable transmits.We are inter ested in the average power received in a bandwidth of 20 MHz centered at 5.8 GHz which represents the setup of the measur ing experiment described in [3].This can be expressed as 1 11);,.10"Gi --20 1 lOG , I Hi(J -5.8 x 10 9 )1 ' 2 dj, (18) x -lOx 10" where Hi (I) is the channel frequency response between the portable and the i-th sector which is the Fourier transform of hi(t): Hi(J) = i:hi (t)e-.i2rrjtdt.We can use (18) to compute the average power received in the i-th antenna sector when portable p transmits.Let us rename it Gp,i; it can also be seen as the average power re ceived by portable p when the base station transmits through its i-th antenna sector.This is true because up-link and down link transmissions occur in the same frequency band, there fore there is up-link/down-link channel reciprocity.Consider antenna sector B (p) which provides the best average power to portable p. Therefore the best average power for portable p is Gl',B(p).In order to verify compatibility among portables, we use these values in the conditions defined in (3) and ( 4) for the down-link case and for the up-link case, respectively.

RESULTS
The steps described in the previous section were followed to simulate average compatibilities among portables uniformly distributed in a 25 x 30 m 2 indoor location.The results were averaged over ten different scenarios, so that, for a given set of parameters, the simulations were run ten times, and a dif ferent draw of portables positions was used for each run.The results were then presented as the average of these ten out puts.We chose to simulate only down-link average compat ibilities since, as we saw in Section 5, up-link average com patibilities are close matches to down-link average compati bilities when power control is used.
The first simulation used the parameter values in Table 1 for building 1 which are: r = 33.6 ns, l' = 28.6 ns, 1/A = 16.8 ns, 1/A = 5.1 ns, and (J = 25.5°.The channel loss parameter used was a = 3.However, changing the value of a did not affect the simulation results, as expected for the down-link case. We have to decide on the number of sectors to simulate.Let us start with a sectorization level of 10 and assume that each sector employs a hom antenna like the one which was used for the measurements reported in Section 5.This antenna has approximately 36° of 3 dB beamwidth and its radiation pattern is shown in Figure 17.figure 18 shows the simulation results compared with the Capture Threshold (dB) average compatibilities measured in location 1.We can see that the measured and the simulated results did not match very well.However, the matching can be improved by adjusting the simulation parameters as follows.In Table 1, the main differences between the estimates of the two buildings are the values of rand 1'.The lower values of r and l' in building I arise because there is greater atten uation with internal walls of cinder blocks than in building 2 whose internal walls are gypsum board [10].Therefore, we can expect location 1 (see FIG. 5), whose internal walls are concrete blocks, to attenuate more than building 1.For ex ample, we simulated average compatibilities with r = 10 ns and l' = 10 ns, and compared them with the average com patibilities of location 1.The results are shown in figure 19.We can see that matching was improved at low values of the capture threshold, but the mismatch worsened at higher cap ture threshold values.This made us think that, while taking measurements in location 1, the horn antenna radiation pat tern may have been distorted due to the proximity of the mea suring equipment and metal structures on the ceiling (light fixtures).The most likely form of distortion is enhancement of the back and side lobes, which may have been caused by rays that were reflected into the main lobe by the equipment and/or by the light fixtures.In order to investigate this possi bility, we ran a simulation using the antenna radiation pattern of the horn antenna distorted by back/side lobes in each sec tor.We added three -15 dB back/side lobes to the original antenna pattern.The resulting empirical antenna pattern is shown in Figure 20.
Figure 21 shows the average compatibilities simulated with this distorted antenna pattern compared with the aver age compatibilities measured in location 1.As the curves matched very well, we concluded that antenna back/side lobes are responsible for the loss in average compatibility at the high capture threshold values observed in Figure 19.Therefore, antennas with small sidelback lobes in their radia tion patterns should be used to prevent this from happening.Also, metal structures, such as light fixtures should be kept as  far as possible from the antennas to avoid distorting their ra diation patterns.However this is important only if the system is to be operated at high values of the capture threshold.

A Model for Generating Antenna Patterns
So far, our simulations have been based on the antenna pat tern of the horn antenna used for the indoor measurements re ported in [3].For the following simulations, we will generate antenna patterns using a model where the antenna beamwidth is a variable.With this model, the i-th antenna sector normal ized field strength radiation pattern can be generated as for antenna main lobe otherwise, (21 where ao is a uniform side lobe which we assume to be 30 dB below the main beam gain, and <P is the 3 dB beamwidth of the antenna.The formula used in (21) to obtain the main lobe of the antenna resulted from an approximation to the formula for unidirectional radiation from uniform aperture distribu- Figure 21: Average compatibilities simulated with distorted antenna pattern (dashed lines) compared with average com patibilities measured in location 1 (solid lines).
tion (see [15]-p.517).For example, Figure 22 shows the pattern for antenna sec tor 1 (i = 1) with <P = 36° superimposed on the pattern of the horn antenna which we have used in the measurements.With this antenna pattern model we can simulate average compatibilities with a generic sectored antenna system with Ns sectors using N s antennas with <P = 360 0 / tv.,.For exam ple, Figure 23 shows sectored antenna systems with 3, 5, 10 and 20 antennas.

FFA Maximum Throughput as a Function of Sectorization Level
Figure 24 shows the FFA maximum throughput obtained with sectorization levels of 4, 10, 20 and 50 sectors, and with r = These results show that there is considerable potential for increasing the maximum throughput by increasing the num ber of sectors in the microcell.The limit to this capacity gain seems to be related to the complexity of the sectored antenna system, since it is not obvious to us that, for example, a 50 sector antenna system built to operate at a frequency of 5.8 GHz can be made compact enough to be installed indoors.

CONCLUSIONS
This paper investigated a new indoor communication system in which a base station uses sectored antennas, and portable terminals use ornni-directional antennas.The system is able to handle simultaneous packet transmissions in a microcell.
The compatibility concept was proposed, and experimen tal results of average compatibility were obtained assuming sectorazation level of ten in a closed indoor environment rep resented by a section of a building floor.
A multiple access scheme that is able to take advantage of the compatibilities among portables in order to transmit more than one data packet per time slot was proposed.The FFA algorithm was proposed for scheduling simultaneous packet transmissions in the microcell.
A statistical model of indoor multipath propagation was used to investigate the performance of the proposed system with different sectorization levels.The simulation parameters of this model were adjusted to fit the experimental results ob tained with sectorization level ten.The simulations showed that there is considerable potential for increasing the maxi mum throughput by increasing the number of sectors in the microcell.

Figure 2 :
Figure 2: (a) A base station communicating simultaneously with two portables; (b)Table of average power levels (dBm) received without power control; (c) Table of average power levels (dBm) received with power control.

Figure 3 :
Figure 3: Illustration of the Gp,s parameter.

Figure 6 :
Figure 6: Up-link average compatibilities in location l.

Figure 7 :
Figure 7: Down-link average compatibilities in location l.

Figure 8 :
Figure 8: A microcell with its base station and portables.

Figure 9 :Figure 10 :
Figure 9: (a) Cp,s parameters; and (b) Matrix of compatibility of pairs of portables in the microcell in figure 8.

Figure 11 :
Figure 11: The First Fit Algorithm.

Figure 12 :
Figure12: FFA perfonnance for up-link traffic in location I with power control (solid lines) and without power control (dashed lines) assuming a capture threshold of 10 dB.

Aleandro S.Figure 14 :
Figure 14: A representation of the clustering phenomenon in multipath propagation.

Figure 17 :
Figure 17: (a) Polar coordinate plots of power radiation pat tern on logarithmic scale; and (b) normalized field strength pattern on linear scale of the horn antenna used in the exper iment.Note: the plotted values were normalized by making the maximum value equal to 60 dB in the logarithmic plot, and by making the maximum value equal to 1.0 in the linear plot.

Figure 18 :
Figure18: Average compatibilities simulated with parame ters of building 1 (dashed lines) compared with average com patibilities measured in location 1 (solid lines).
Figure 20; (a) Polar coordinate plots of distorted power ra diation pattern on logarithmic scale; and (b) distorted field strength pattern on linear scale of the horn antenna used in the experiment.

Figure 22 :
Figure 22: Radiation patterns on logarithmic scale (a) and on linear scale (b) of 36° beamwidth antenna (solid) and horn antenna (dashed).
•. , P N in the down-link case are given in (3).

Table 1 :
Parameters estimated by Spencer et al.