Methods for making a cellular system, transmitting to a mobile user in a cellular system, and evaluating the performance of a cellular system

1. Field of the Invention

The present invention relates to wireless telecommunications. More particularly, the present invention relates to a new cellular architecture for cellular systems such as Code Division Multiple Access (CDMA) Smart Antenna Array Systems.

2. Description of the Related Art

In wireless communications systems, including second generation (2G) and third generation (3G) systems, a viable option for improving system capacity is to employ a smart antenna array in both the forward link (from the base station to the mobile) and the reverse link (from the mobile to the base station). As used herein, the term smart antenna refers to an antenna that can detect the angle at which a signal is received, and that can transmit a focused beam in a desired direction or directions as well as selectively receive a transmitted signal from a desired direction or directions. In the reverse link, the base station can achieve improved capacity by suppressing the interfering signals from different direction of arrival angles (DOAs) by using spatial diversity. In the forward link, the base station can use the DOA capabilities of the reverse link system to focus a directional beam to a user at any given angle and suppress the signal to other users.

One side effect of smart antenna arrays is the non-uniform gain pattern that results in a multi-user interference environment. When a cluster of cells is arranged in the conventional Wide Beam Tri-sector Cell (“WBTC”) architecture, the result is a large soft handoff region which can degrade the system leading to reduced capacity.

What is needed is a new architecture for cellular systems employing smart antennas in which the soft handoff area is reduced relative to the conventional WBTC architecture.

The new cellular architecture is called the Interleaved Wide Beam Tri-sector Cell (IWBTC) architecture in which base stations have an orientation and are arranged in a regular pattern based on a three sector cell with each sector in the shape of a hexagon. In this architecture, neighboring base stations are aligned in a first direction and staggered, preferably by approximately 10.89 degrees, in a second direction perpendicular to the first direction. In addition, neighboring base stations in the first direction have the same orientation, while neighboring base stations in the second direction are rotated by approximately sixty degrees with respect to each other. The architecture of the invention may be used in any cellular system, but is particularly well suited to CDMA systems which do not use frequency division (that is, in CDMA systems in which neighboring base stations transmit over the same range of frequencies), and which employ smart antennas. The architecture takes advantage of the smart antenna array characteristics (when CDMA base stations employ the smart antenna array in the forward and reverse channels), resulting in a significantly decreased soft handoff area and thus a significant improvement as compared to the conventional WBTC architecture.

In another aspect of the invention, a system and method for evaluating cellular architecture performance are provided. In the method, equations for defining the smart antenna array are provided, then the interference is calculated, and finally an equation for asymptotic capacity is provided to compare the performance of the IWBTC and WBTC architectures.

In still another aspect of the invention, the smart antenna is used to direct a transmission to a mobile user in three different directions: a first direction on which the signal strength received from the mobile unit is highest (the “primary multipath”), as well as the directions on either side of the first direction on which the next-highest signal strength is received (the “secondary multipaths”). In preferred embodiments, one half of the transmitted power is directed toward the primary multipath, while one quarter of the transmitted power is directed toward each of the two secondary multipaths.

These and other features, objects, and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout and wherein:

FIG. 1 is a schematic drawing showing a cluster of cells in the WBTC architecture according to a conventional architecture.

FIG. 2 is a schematic diagram showing a cluster of cells in the IWBTC architecture according to the present invention.

FIG. 3 is a polar plot showing average gains of a smart antenna due to interference suppression.

FIG. 4 is a schematic diagram, similar to FIG. 1, showing the antenna coverage of several contiguous cells of the WBTC architecture.

FIG. 5 is a schematic diagram, similar to FIG. 2, showing the antenna coverage of several contiguous cells of the IWBTC architecture.

FIG. 6 is a graph showing the capacity improvement of the IWBTC architecture over the WBTC architecture for a 3 element smart antenna array.

FIG. 7 is a graph showing the capacity improvement of the IWBTC architecture over the WBTC architecture for a 5 element smart antenna array.

FIG. 8 is a graph showing the capacity improvement of the IWBTC architecture over the WBTC architecture for a 10 element smart antenna array.

FIG. 9 is a schematic diagram of a non-rotated wideband hexagonal cell architecture.

FIG. 10 is a schematic diagram showing an offset angle between two smart antennas.

The present invention will be discussed with reference to preferred embodiments of cellular architectures and systems and methods for evaluating the same. Specific details, such as the number of elements in a smart antenna, etc., are set forth in order to provide a thorough understanding of the present invention. The preferred embodiments discussed herein should not be understood to limit the invention.

Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, FIG. I illustrates a conventional WBTC cellular architecture 100 including 7 hexagonal cells numbered 0 - 6 . Each hexagonal cell 0 - 6 includes three diamond-shaped sectors 10 . The triangle 112 in the middle of each hexagonal cell 0 - 6 represents a smart antenna array such as the antenna arrays described in co-pending U.S. application Ser. No. 09/610,470, filed Jul. 5, 2000, entitled “Smart Antenna with Adaptive Convergence Parameter,”) and co-pending application Ser. No. 09/661,155, filed Sep. 13, 2000, entitled “Smart Antenna with No Phase Calibration for CDMA Reverse Link”. The contents of both of these applications are hereby incorporated by reference herein. In preferred embodiments, each antenna array 112 is three sided, with each side including two or more antenna elements. In highly preferred embodiments, the elements are arranged linearly. It will be recognized by those of skill in the art that it is possible to arrange the elements in a rectangular, circular or patch arrangement. Each side of the antenna array 112 corresponds to a sector 110 in a cell 0 - 6 . Cell boundaries are indicated by solid lines in FIG. 1, while sector boundaries are indicated by dashed lines.

The average gain pattern of an exemplary smart antenna array 112 is illustrated in FIG. 3 . In the polar plot of FIG. 3, the lines A, B, C correspond to 10 element arrays, 5 element arrays, and 3 element arrays, respectively. As can be seen in FIG. 3, especially for the 10 element case, the smart antenna array 112 provides an average gain pattern that covers 120 degrees, which is the same coverage provided by antennas referred to in the art as wide beam antennas. Accordingly, smart antennas 112 have heretofore typically been employed using wide beam architectures such as the WBTC architecture 100 shown in FIG. 1 .

FIG. 4 illustrates the average gain pattern A of FIG. 3 superimposed over the WBTC architecture 100 of FIG. 1 . In order to ensure sufficient coverage in sector 110 a of cell 1 , it is necessary to ensure that the average gain A extends completely to the corners Z of sector 110 . However, this results in large overlap areas (also referred to herein as soft handoff areas), between adjacent gain patterns A. As shown in greater detail below, these large soft handoff areas degrade system performance.

FIG. 2 shows the IWBTC architecture 200 of the present invention where cells are organized in an interleaved structure called the Interleaved Wide Beam Tri-sector Cell (IWBTC) architecture according to the present invention. In FIG. 2, each cell comprises 3 hexagonal sectors 210 corresponding to a base station including a smart antenna array 212 , 213 . Each hexagonal sector 210 is a regular hexagon with all sides and all angles between sides being equal. Each of the arrays 212 are arranged in a substantially straight column, as are each of the arrays 213 . However, each of the arrays in any one column are rotated about the center of the cell by approximately 60 degrees with respect to neighboring arrays in the two adjoining columns. The rotation provides slightly better performance as compared to an architecture in which the arrays are not rotated, such as the architecture 900 of FIG. 9 . Furthermore, although the arrays 212 , 213 are arranged in straight columns, the rows formed by the arrays are not straight. Due to the shape of the hexagonal sectors (which are regular hexagons), neighboring arrays are offset. Preferably, due to the assignment of the antenna arrays to the sectors, neighboring antenna arrays in a row are offset by an angle a of approximately 10.89 degrees with respect to the horizontal direction h, as illustrated in FIG. 10 . This angle may be calculated using ordinary principles of geometry. Those of skill in the art will recognize that this angle may be different by as much as several degrees. Differences may result from requirements improved by practical concerns such as the inability to locate an antenna exactly where desired.

The architecture 200 described above in connection with FIG. 2 results in a greatly reduced soft handoff region, as illustrated in FIG. 5 . In a manner similar to FIG. 4, FIG. 5 illustrates the average gain pattern A of FIG. 3 superimposed over the IWBTC architecture 200 of FIG. 2 . It is obvious from a comparison of FIGS. 4 and 5 that the soft handoff areas in FIG. 5 are greatly reduced relative to FIG. 4 . Table 1 shows the fractional portion of the soft handoff area compared to the sector area size. For example, when a 10 element smart antenna array is used, the WBTC architecture has a soft handoff area equal to 70% of its sector area where as the IWBTC architecture has an area equal to about 18%. As a result in the decrease in soft handoff area size, the IWBTC architecture results in a significant improvement in performance as compared to the conventional WBTC architecture.

It should be noted that the IWBTC architecture described herein bears some resemblance to the Interleaved Narrow Band Tri-Cell (INBTC) architecture described in “A New Cellular Architecture Based on an Interleaved Cluster Concept,”) IEEE Transactions on Vehicular Technology, Vol. 48, No. 6, November 1999, by Li-Chun Wang (“Wang”). However, there are several important differences between the two systems. First, Wang's architecture employs a 60 degree directional narrow beam antenna, while the present invention employs a smart antenna array, wherein each of the 3 sides of the antenna array is comprised of several omni-directional antenna elements. The smart antenna has an average gain pattern that is generally considered to be wide beam. Second, the only reason provided by Wang for rotating antenna arrays by sixty degrees deals with frequency reuse considerations, which are applicable to cellular systems other than CDMA. There is no recognition by Wang of the tie between soft handoff area size and system performance and no discussion in Wang of improving system performance by reducing soft handoff area size. Nor is there any discussion in Wang of the improvement in reducing soft handoff size area realized as a result of rotating antenna arrays. In contrast to Wang, the present invention is particularly useful for CDMA systems, in which neighboring base stations transmit over the same range of frequencies (i.e., there are no frequency reuse concerns). Still further, there is no suggestion in Wang for employing a smart antenna to transmit to a mobile unit on three multipaths as described further below.

In accordance with the invention, the following describes the mechanism used to evaluate the performance of the various architectures for comparison. First the smart antenna array is defined, then the interference is derived, and finally an equation for the asymptotic capacity is derived to compare the performance of the two architectures.

Since the base station determines when the mobile is handed off based on the received FER (Frame Error Rate), the method for finding the handoff boundary is to find the location where the loss to the given cell exceeds the loss to the adjacent cell. The following equation provides this: Range  ( r , θ ) = r 1 4 G avg  ( θ 1 ) - r 2 4 G avg  ( θ 2 )

where r 1 is the distance to the given base station, r 2 is the distance to the adjacent base station, G avg (θ) is the average suppressing gain of the antenna array, θ 1 is the angle from the perpendicular of the antenna array of the given base station to the user, and θ 2 is the angle from the perpendicular of the adjacent antenna array to the user.

Preferred embodiments of the present invention use a smart antenna array that can be described as follows: The antenna array response vector for M ant antenna elements can be written as: a     ( θ ) = [ 1      - j     2     π      sin     θ λ     …      - j  ( M ant - 1 )  2     π      sin     θ λ ] T ( 1 )

where M ant is the number of antenna elements, T is the transpose, and θ is the incident angle called DOA from a user. The antenna elements are assumed to be spaced at d=λ/2 (one-half wave length) apart. Let θ 1 be the DOA from the desired user. The optimum weight vector resulting from the adaptive algorithm from “Computationally Efficient Smart Antennas for CDMA Wireless Communications,” submitted to the IEEE Transactions on Vehicular Technology, March 2000 by Song and Kwon (“Song and Kwon”), the contents of which are hereby incorporated herein by reference, can be approximately written as: W _  ( θ 1 ) = [ 1      - j     π     sin     θ     …      - j     π  ( M ant - 1 )  sin     θ 1 ] T . ( 2 )

This form of the weighting will be true when the adaptive antenna system finds the angle that maximizes the received power of the mobile. In a smart antenna array system, the average suppressing gain over the uniformly distributed interference for the desired user on the reverse channel, can be found from Song and Kwon as: G avg  ( θ ) = 1 π  ∫ π 2 π 2  1 M ant 2   W _ H  ( θ )  a _  ( θ n )  2      θ n ( 3 )

where the weight vector, W H , resulting from the blind adaptive algorithm is for the desired signal DOA of θ, H represents the Hermitian of the vector which is simply the complex conjugate of the transpose of the vector, θ n is the DOA of the undesired user, a (θ d n ) is the array response vector for the undesired signal of DOA θ n , and M ant is the number of antenna elements. This gain can then be plotted for all expected directions of the desired user arrivals. FIG. 3 shows the average gain of the smart antenna verses the direction of desired user signal arrival for 3, 5, and 10 antenna elements in a polar chart. FIG. 3 shows 10 Log 10 (1/Gain(θ), where levels are in dB. It can be seen that as the DOA reaches the outer edges of the sector (±60°), the average gain decreases. The problem is particularly pronounced in the three-antenna element case. The five-antenna element case is somewhat better and the ten-antenna element configuration has the best coverage verses DOA.

For the forward channel, the beam pattern can be assumed to be the same as the reverse channel in the ideal case. The forward channel interference will be derived from the smart antenna array beam power. From “Song and Kwon”, the following equation describes the beam power: Power     ( θ , θ n ) =  W _ H  ( θ )  a _  ( θ n )  2 M ant 2 ( 4 )

where θ is the angle of the transmit beam and θ n is the DOA of user n. The beam power is normalized to 1 for the forward channel transmission from the base station. It has been shown that the number of users that can be nulled is equal to M ant −1, where M ant is the number of antennas. This invention assumes there are more users or signals than antenna elements where not all users can be nulled. Under these assumptions there will be insufficient suppression of undesired multipaths which add to the overall interference. It is assumed that the users in the system do not have smart antennas and that all the base stations in the system have smart antennas that are used in both the forward and reverse links.

The forward channel capacity is based on the signal-to-interference power ratio (SIR) received at the mobile. The source of interference is multipath from the same cell base station and from other cells. This interference derivation assumes orthogonal channels transmitted from the base such that under no multipath, there is no co-channel interference. It is assumed that the major contribution to interference is multipath signals. It is also assumed that the forward channel weighting vectors can be determined without errors based on the receiver weighting vectors. The base transmits on multiple DOA to each user. Each channel transmitted from the base station is assumed to be orthogonal and the source of the same cell interference is multipath.

In a smart antenna environment where the forward channel signal is beam formed toward the desired user, the interference to that user will be the amount of signal transmitted toward him that was intended for other users. Therefore, the key to finding the amount of interference is in determining the amount of signal transmitted toward the desired user due to all other users. The same cell and other cell interference will then be derived from these results. The single cell transmit power will be shown first for the 1-path case assuming the base station only transmits in one direction for each user. Then the 3-path case will be shown where the base station transmits to all users on 3 multipaths. The total power transmitted with 1-path for each user to a user at angle θ due to n users in the same cell can be defined as: P 1  Cell , 1  path  ( θ ) = ∑ i = 1 n   W _ H  ( θ )  a _  ( θ i )  2 M ant 2 ( 5 )

where θ is the angle at which we are calculating the power to the desired user and θ i is the angle at which the base is transmitting to user i. Although the majority of the power transmitted toward a user is focused, the “tail” contributes interference toward other users. The single cell forward link power received at the mobile in the absence of interference is normalized to 1 for these equations. For a base station transmitting on three paths for each user, a power profile of 50%, 25%, and 25% is assumed in the present invention without loss of generality. Then, the power becomes: P 1  Cell , 3  path  ( θ ) = 1 2  ( ∑ i = 1 n   W _ H  ( θ )  a _  ( θ i )  2 M ant 2 ) + 1 4  ( ∑ i = 1 n   W _ H  ( θ )  a _  ( θ i + θ subpath1 )  2 M ant 2 ) + 1 4  ( ∑ i = 1 n   W _ H  ( θ )  a _  ( θ i + θ subpath2 )  2 M ant 2 ) . ( 6 )

With this approach the primary DOA would carry 50% of the path power and the 2 other paths would carry 25% each compared to the 1-path case in equation (5). For the simulation results presented here, it is assumed that the two sub-paths are located ±10° away from the primary path.

Using the solutions presented in equations (5) and (6), the same cell and other cell interference factors can be found. It is accepted that, for the single antenna case, the same cell interference may be set to the signal strength of the primary desired multipath. This interference can be quantified into an interference factor (K same ) independent of the number of users in the system. The same cell interference factor represents the relative interference power compared to the same cell signal level, S(θ), received at the mobile: I sc S  ( θ ) = K same , ( 7 )

where I sc is the same cell interference power for either the 1-path case or the 3-path case. The denominator, S(θ), can be defined as S     ( θ ) = P     ( θ ) r γ ( 8 )

where r is the distance from the cell to the mobile and γ is the power law used. For all simulations in this invention, the power law used is 4 without loss of generality. If the same cell interference is assumed to be equal to the primary desired multipath, S(74), then K same =1. For the smart antenna case, this assumption will be made for the same cell interference factor.

To determine the other cell forward channel interference, it is assumed the same levels are transmitted from all other cells. The main factor in this case is the angle of arrival of the signal and the distance from the cell to the desired mobile. The following equation can be used to find this value for the single antenna case: I oc = ∑ i  1 r i γ  ( r , d i , θ i ) ( 9 )

where r i is the distance to the i-th base station. This assumes the antenna gains are equal which is a valid assumption for the single antenna case. The name used for the other cell interference factor is K other . For the smart antenna array system, equation (9) becomes: I oc , SA = ∑ i  P 1     Cell  ( θ oc ) r i γ  ( r , d i , θ i ) ( 10 )

where θ oc is the angle from the other cell to the desired user relative to its antenna array, and P 1Cell represents either the 1 path or the 3 path single cell interference of equation (5) or (6), respectively. The reason for the expression of the other cell interference in this form is that the primary difference between the same cell and the other cell interference is the distance from the base station to the user. Therefore the amount of interference from all other cells is reduced by the power law, γ, of the distance from that cell to the user. To find the ratio of the other cell interference to the same cell desired power, K other is calculated as I oc , SA S  ( θ sc ) = ∑ i  P     ( θ oc )  r γ P     ( θ sc )  r i γ  ( r , d i , θ i ) = K other ( 11 )

where S(θ sc ) is the total forward link power received at the mobile from the reference cell without interference, and r is normalized to 1. The worst case would be the location furthest from the given cell while still remaining in the cell, just before handoff.

To provide simulation results for the other cell interference, K other is calculated for the two different sector architectures described in FIGS. 1 and 2. In Tables 2 and 3, the value of S(θ) is averaged over θ and represents the total forward link power received at the mobile from the reference base station in the absence of interference. This value can be calculated as S=19.202 for a user at the cell edge for a ten-element smart antenna array. The total forward channel interference factor may be defined as:

K f =K same +K other .  (12)

Smaller values of K f translate into lower interference. Table 2 shows the calculated other cell interference for the WBTC architecture resulting in K other =1.246. With K same =1 the resulting K f for the WBTC case is 2.246 for the 3-path case. Table 3 shows the calculated other cell interference for the IWBTC architecture resulting in K other =1.762. With K same =1 the resulting K f for the IWBTC case is 2.762 for the 3-path case.

Table 2. This table shows the three-path interference data for the IWBTC architecture of the 6 nearest cells. The cell numbers in column 1 correspond to the cell numbers of the IWBTC architecture in FIG. 1 . The distance and angle columns represent the distance and angle from the cell's base station to the desired user (at the reference cell edge, 30° relative to the antenna array). The fourth column identifies the interference at the given angle to a user at distance R from it's base station and the last column calculates the interference to the desired user in the reference cell from the cell specified in column 1. The total other cell interference for this case is 23.919. With S=19.202, K other=I/S= 1.246.

Table 3. This table shows the three-path interference data for the IWBTC architecture of the reference cell (same cell) and the 6 nearest cells. The cell numbers in column 1 correspond to the cell numbers of the IWBTC architecture in FIG. 2 . The distance and angle columns represent the distance and angle from the cell's base station to the desired user (at the reference cell edge, 30° relative to the antenna array). The fourth column identifies the interference at the given angle to a user at distance R from it's base station and the last column calculates the interference to the desired user in the reference cell from the cell specified in column 1. The total other cell interference for this case is 33.8431. With S=19.202, K other =I/S=1.762.

The interference factors, K same and K other (or K f ) can be used in an interference equation developed for the single antenna case as follows. The total output power transmitted from the base station in the single antenna case is:

P total =P pilot +P sync +N p P paging +( K traf M t +M ho )α f P traf   (13)

where P pilot is the transmitter pilot channel power, P sync is the transmitter sync channel power, P paging is the transmitter paging channel power, P traf is the transmitter traffic channel power, N p is the number of active paging channels, M t is the number of active traffic channels, M ho is the number of other cell traffic channels used for soft handoff, α f is the voice activity factor, and K traf is the power control factor. P total in equation (13) represents the total power transmitted from the base station in terms of the channels. Since the smart antenna output power is dependent on the DOA of each user, equation (13) can be adapted to the smart antenna array as: P total  ( θ ) = P pilot + P sync + N p  P paging + ( K traf  ∑ n = 1 M t   W _ H  ( θ )  a _  ( θ n )  2 M ant 2 + ∑ n = 1 M ho   W _ H  ( θ )  a _  ( θ n )  2 M ant 2 )  α f  P traf ( 14 )

where θ is the angle at which we are calculating the power due to (M t +M ho ) users, θ n is the angle of the n-th user, and P total (θ) is the power transmitted by the smart antenna at the base station at angle θ. Equation (14) can be simplified by determining the average traffic channel power from an undesired user transmitted toward the desired user. The average interferer traffic channel power (ITCP) factor, ε, can be defined as: ɛ = ∑ n = 1 M users   W _ H  ( θ )  a _  ( θ n )  2 M ant 2 M users ( 15 )

where M users represents the number of users in a sector, θ represents the angle where the traffic channel power is accumulated from M users , and θ n represents the angle to user n. Equation (15) assumes that any angle, θ, between −60° and +60° will experience the same traffic channel power for a given number of antenna elements. For simulation results presented in this invention, the users are assumed to be uniformly distributed at the cell edge for a worst case scenario with a large number of users. The ITCP will then represent a factor independent of the number of users. Applying the ITCP to equation (14) results in:

{overscore (P)} total =P pilot +P sync +N p P paging +( K traf (1+ε( M t −1))+εM ho )α f P traf   (16)

where the angle is now removed since the average total power is independent of the DOA. The reason for the term K traf (1+ε(M t −1)) is because the desired user is accounted for with the “1”, all other undesired users not in the soft handoff region are accounted for in ε(M t −1), and all other undesired users in soft handoff are accounted for in εM ho . K traf does not apply for the εM ho term because these users are power controlled by some other base station.

To find the power arriving at the mobile from the base station, equation (16) may be used with the appropriate processing gains and losses applied. For example, ( E b N 0 , T ) traf = PG traf  P traf N m  L T  ( R ) + K f  P _ total = ρ traf ( 17 )

where E b /N 0,T is the bit energy to noise power density required at the mobile, PG traf is the processing gain of the traffic channel, P traf is the transmitted traffic channel power, N m is the mobile receiver's thermal noise power, L T (R) is the total free space loss to the mobile at distance R, and K f is the interference factor (the sum of K same and K other ). The processing gain can be calculated for a channel using: PG = W R b ( 18 )

where W is the bandwidth of the signal and R b is the bit rate. Assuming the bit rates are 1.2288 Mbps, 1200 bps, 4800 bps, and 9600 bps, the values of the processing gain are 1, 1024, 256, and 128 for the pilot, sync, paging, and traffic channels, respectively. Applying equation (17) to equation (16) results in a traffic channel power solution of: P traf = N m  L T  ( R )     ρ traf PG traf 1 - K f  ( ρ pil + ρ sync PG sync + N p  ρ pag PG pag + ( K traf + M ho  ɛ 1 + ( M t - 1 )     ɛ )  ( 1 + ɛ  ( M t - 1 ) )  α f  ρ traf PG traf ) . ( 19 )

With the numerators of the channel power solutions remaining constant, the key to the forward link capacity lies in the denominator since it contains the only terms relating to the number of users in the system. For all channel powers, the common denominator is: 1 - K f  ( ρ pil + ρ sync PG sync +    N p  ρ pag PG pag +    ( K traf + M ho  ɛ 1 + ( M t - 1 )     ɛ )  ( 1 + ɛ  ( M t - 1 ) )  α f  ρ traf PG traf ) .

This denominator must be greater than zero. Since M t >>1 and ε>0, one simplification that can be made to this is to assume: M ho  ɛ 1 + ( M t - 1 )  ɛ ≈ M ho M t ( 21 )

where M ho represents the number of users in soft handoff and M ho /M t represents the percentage of users in soft handoff. Assuming a uniform distribution of users, this also represents the percentage of a sector's area that is in soft handoff. Adding K traf to equation (21) results in: K traf + M ho  ɛ 1 + ( M t - 1 )  ɛ ≈ K traf + M ho M t = K traf ′ . ( 22 )

Using equation (22), equation (20) becomes: 1 - K f  ( ρ pil + ρ sync PG sync +    N p  ρ pag PG pag + K traf ′  ( 1 + ɛ  ( M t - 1 ) )  α f  ρ traf PG traf ) > 0. ( 23 )

From this denominator, there results a singularity when the power reaches a threshold. This translates into a limitation on the number of supportable users. One way to show this is to compute the asymptotic capacity by solving for M t . The above equation becomes equal when we consider the upper bound, which can be called M ∞ as follows: M ∞ = PG traf K traf ′  ɛ     α f  ρ traf  [ 10 - M dB / 10 K f - ρ pil PG pil - ρ sync PG sync - N p  ρ pag PG pag ]    - 1 ɛ + 1 ( 24 )

where the numeric values of the processing gain have been included, and M dB is the margin and it represents the additional amount of traffic channel power required to meet a specified link reliability. In equation (20) M dB was not shown because it was assumed to be zero. Margin is necessary to overcome shadowing at the cell edge. The capacity presented here allows one to determine the capacity for margins between 0 dB and 3 dB.

If the numeric values of the processing gain are included, equation (24) may be rewritten as follows: M ∞ = 128 K traf ′  ɛ     α f  ρ traf  [ 10 - M dB / 10 K f - ρ pil - ρ sync 1024 - N p  ρ pag 256 ] - 1 ɛ + 1 ( 25 )

Equation (24) can be called the forward link asymptotic capacity. It represents the maximum capacity achievable with any specified set of channel powers. Using equation (24) the forward link capacity may be plotted under different conditions. The following is a discussion of the results of the simulation plotted in FIGS. 6-8 showing the capacity verses margin for different interference factors and soft handoff sizes.

For all results presented, the numeric processing gains from equation 25 and the following values from equation (24) are used: K traf =0.5, α f =0.4, ρ traf =7 dB, ρ pil =−15 dB, ρ sync =6 dB, ρ pag =6 dB, and N p =1. The first parameter to determine is the other cell interference, K other , and the resulting K f . FIG. 6 shows the capacity results for a 3 element smart antenna array system. The IWBTC architecture results in a greater capacity than the IWBTC system primarily due to the improved soft handoff region. FIGS. 7 and 8 show similar results for the 5 and 10 element smart antenna array case, respectively. Again, the IWBTC architecture achieves superior results. The methods discussed above may be used to calculate the asymptotic capacity in connection with any computer system including a processor, a memory connected to the processor, and an input/output device or devices connected to the processor.

As discussed above, it has been shown that the total signal strength received by a mobile user will be increased if the transmission from the smart antenna, rather than being directed to the user solely along the primary multipath, is directed along the primary multipath and a secondary and tertiary multipath. The secondary multipath is the multipath other than the primary multipath on which the strongest signal is received from the mobile user, while the tertiary multipath is the multipath other than the primary and secondary multipaths on which the strongest signal is received from the mobile user. It will normally, but not necessarily, be the case that the tertiary and secondary multipaths are on opposite sides of the primary multipaths. Furthermore, the angle formed between the primary and secondary multipaths will normally, but not necessarily, be equal to the angle formed by the primary and tertiary multipaths. In preferred embodiments, the transmission occurs on all three multipaths simultaneously.

Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.