JOINT EFFECTS OF DYNAMIC TIME SLOT SCHEDULING SCHEMES AND SOFT HANDOFF ON THE PERFORMANCE OF TOO OS-COMA SYSTEMS WITH 20 RAKE RECEIVERS

- In this paper, we derive analytical expressions to assess the performance of Time Division Duplexing (TDD) Direct Sequence-Code Division Multiple Access (DS-CDMA) systems with coherent bi-dimensional (2D) Rake receivers. Considering either hexagonal macrocellular and microcellular cross-shaped networks, we propose and evaluate different approaches to model the effects of the intercellular multiple access interference (MAl) on the performance of DS-CDMA systems with 2D Rake receivers. These results are then used on the performance comparison between coherent and optimum 2D Rake receivers. It is shown that soft handoff allows gains of 2 dB in the Signal-to-Interference-plus-Noise-Ratio (SINR) at the 2D Rake receiver output. Simulation results, ratified by theoretical upper bounds, show that the dynamic time slot allocation schemes allow considerable increase of the SINR at the receiver output with a concomitant improvement on the throughput.


INTRODUCTION
Considering a multitude of parameters, it has been concluded that the time variant and irregular spatial temporal channel characteristics have a strong influence on the performance of TDD DS-CDMA systems with 2D RAKE receivers [I]. In this paper, it is shown that dynamic time slot allocation algorithms substantially improve the uplink performance of TDD DS-CDMA systems with wavefield transceivers. In order to accomplish the above mentioned objective, this paper has been organized as follows. A description of the 2D Rake receiver is presented in Section 2. Analytical expressions to estimate the performance of the coherent 2D Rake receiver are developed in Section 3. A brief description of a network simulator is done in Section 4. A comparison between analytical and simulation results is carried out in Section 5. The effects of soft handon-and dynamic time slot scheduling on the system performance are investigated in Section 6 and 7, respectively. Finally, some final remarks are done in Section 8.

2D RAKE RECEIVER
The 2D Rake receiver, constituted of an array of M antennas and P taps per antenna. reduces interference by means of spatial and temporal processing in order to produce an improved decision variable to the detection circuit. A description of 2D Rake receiver can be found in [2, pp. 81]. At this section, it is presented the steps to numerically estimate the SINR at the 2D Rake receiver output. Assuming a chip and phase synchronous system, the SINR for the k-rh user in a interference limited coherent binary phase shift keying (BPSK) DS-CDMA system can be evaluated by [3, pp. 40]: (1)

wI! RII,k \V k
where Go is the processing gain; W k is a column vector that contains 'the MP coefficients of the 2D Rake receiver for the k-th target user; R s . k is the desired signal covariance matrix, R u • k is the MAl plus noise covariance matrix observed by the k-th user: and (.)H represents the Hermitian operator. Assuming a frequency selective fading channel with inbound diversity L and negligible intersymbolic interference (L«G p ) . then the k-th user's M by L channel matrix can be stated as: where h u is the M column vector that models the arrival at the antenna array of 1-th multi path of the k-th user. P u Revista da Sociedade Brasileira de Telecornunicacoes Volume 18, Nurnero 1, Junho de 2003 models the average power per antenna received due to the k-th terminal. It is equal to one when the MS is controlled by the target BS. and Pk. as explained at Section 4. is a function of among other parameters, the user spatial location, path loss and log-normal shadowing when this MS contributes with extemal MAl to the target cell.
For an antenna array (AA) with M correlated antennas (i.e. the number of spatial diversity branches M[) is equal to 1). the steering vector is given by: hk,/ = Cf.k,/[c I1 3 /;. o/ cl13kJJ ·"cj~k.\1-1/ f. (3) where Cf.u is a complex random variable (RV) that models the channel gain for the l-th path of k-th user.
If it is assumed an array with M correlated antennas. then the relative phase at the m-th element for a linear equally spaced (LES) is given by [3, pp. 16]: A where d is the spacing between the isotropic array elements. I, is the wavelength of frequency carrier, and SLI is the Direction-of-Arrival (DOA) at the azimuth for the I-th path of the k-th user. For a circular equally spaced (CES) array with M correlated antennas, the relative phase at the m-th element with respect to the center of the circular array of radius R is given by [3, pp. 17J: A .

/
If the multipath fading is uncorrelated in all antenna elements (i.e. M[)=M). then the spatial temporal signature for both topologies (i.e. LES and CES arrays) is given by: where Uk.hm is a complexRV that models the channel gain for k-th user at the I-th path at the m-th antenna element. It can be emphasized that in (3) )=1 . .
vhere K is the number of MSs physically located in each of one of NBS hexagonal BSs. and the Additive White Gaussian Noise (A WGN) power in a bandwidth W is 2u/W. where N o=2u/ is the noise one-side power spectral density. hiP is the identity matrix of order MP. The multipath channel response is a matrix of dimension MP by P+L-l: 1I 0 HI where 0 is a Mx 1 all-zero vector [2. pp. 87]. In derivation of (9). it was assumed. in agreement with the quasi synchronous assumption. a finite impulsive response (FIR) multipath channel with L taps and whose delay between each multipath was set to one chip period. The cross-correlation between the k-th user's symbol sequence and the whole received signal is given by: Pk= Hkep=Hk'P,.
where ep is a column \ ector of dimension (P~L-1) with ones at the P-th position and zeros elsewhere. and H,'P' indicates the Psth column of H k. The signal covariance matrix for the k-th target user. with dimension MP by MP. is given by: Therefore. the MAl plus noise covariance matrix observed by the k-th user is given by: Using the Wiener-Kolmogorov theory [4. pp. 194J. the \\\ that minimizes the MSE at 2D Rake receiver output is given by: Using Woodbury's identity (or matrix inversion lemma [3, R 1 pp. 39J) to (R is given by Eq. 8), then the maximum SINR solution for the k-th user can be stated as: where ~ is a scale constant which does not affect the SINR. as it equally applies to all signals. Using (14) in (1). the SINR can be rewritten as:

MF-K{l+/)
F where the A WGN has been neglected due to interference limited assumption and the factor I/P= IlL in the denominator comes from (7). It has also been used that the trace of matrix product AB equals the trace of matrix product BA. If the magnitude of multipath fading is supposed to be a Nakagami-m RV, it can be verified that the SNIR probability density function (PDF) at the output of the MRC 2D Rake receiver is of Gamma kind with shape parameter 0 equals to MPm Observing that: (i] (22) models the SINR at each one of the MP fingers of the MRC receiver (it is assumed that P=L); (ii) the spatial-temporal diversity gain is implicated in the shape parameter 0=MPm; (iii) for a receiver with just one antenna and one finger. then the SINR at the receiver output is also Gamma distributed. but with the shape parameter 0 in (21) equals to m (the Nakagami-m fading figure). Finally, it can remarked that the Gamma R V degenerates in an impulse function when 0-+:<:.
The jargon pole point or pole capacity is used to designate the capacity obtained with perfect power control assumption and neglectable A WGN assumptions, but which serves as a useful reference point for network planners. Evidently, the 2D RAKE receiver reduces to an antenna array (AA) receiver if the number of filter taps per antenna, P, is set to one. Therefore, the spatial signature for an LES AA receiver over an A WGN channel is given by: Therefore. a coherent combining receiver has a normalized response given by: wf =.Jllll e~imilliJk .. ·eilJ/-lrrr.\lIlak Hllh(Sd), (24) where Il hk II is the Euclidian norm of the steering vector h k .
Modeling the MAl as a flat power spectrum. then the normalized MAL interference at AA output can be stated as:

MICROCELLULAR AND MACROCELLULAR NETWORKS
The main characteristics of the system level simulator with full interactivity between all cells are [7, pp. 185; 344]: • The network consists of homogenous hexagonal macrocells with 19 BSs or cross-shaped microcells with 25 BSs. It is assumed X=200m and W=50 m (see Fig. 1 where rt" and ~k.» denote the distance and the lognormal shadowing. respectively. between the k-th MS and the n-th BS: T is the path loss exponent when rk'; is greater than the distance from the BS antenna to where the curve changes its gradient (i.e. Xj.), It is observed that the path loss is set to 2 for rk"<X,,, The lognormal shadowing is a Gaussian RV in decibels (dB) with zero mean and standard deviation of n,h dB. Its range is between the open range -4u s h < Sk.ll < 2u h · For out-of-signal (OOS) path. there is an s additional loss Loos=20 dB when the MS turns a comer. It is assumed XI>=O In and Loos=O dB in the macrocellular hexagonal network.
• The slow power control (PC) dynamics is abstracted in the sense that the average power transmitted by the MSs is the minimum average power to arrive with a unitary average power at each antenna of the minimum loss BS participating in the soft handoff, . .

\ L u Lk.2 LANES
Therefore. the average power received at the target cell due the k th MS is given by: Lk.1 It is emphasized again that P,= I when the k-th MS is controlled by the target cell, i.e. the slow power loop compensates perfectly the attenuation due to the assumed log-linear long-term propagation model (see 2). • The DOA of each discrete multipath are T uniformly I tl, -5' .8; 5' J distributed. The mean DOA Sk is uniform.y distributed in each sector (i.e, between _60 0 and +60 0 in sector 0 and so f011h) in macrocellular networks. For rnicrocells the DOA is assumed to be a Gaussian RV with standard deviation of ]Oil and whose the first moment in South, East. N011h and West directions are set to au. 90°, 180 0270", respectively.
• In hexagonal topology it is used a LES array at each sector whose elements an; separated by half-wavelength of frequency carrier (i.e. d=i~ 2 in -l) to avoid grating lobes.
• It is used circular arrays in the cross-shaped microcells to avoid the phase ambiguity that occurs in the LES arrays [3, pp. 16].

SIMULATION VERSUS ANALYTICAL RESULTS
In this section. the Signal-to-Noise Ratio (SNR) has been set to ]00 dB. i.e. interference limited system has been considered. In figures 1 to 3. it is assumed an equal strength (ES) Rayleigh frequency selective fading channel with 3 taps, i.e. L=3. As a direct consequence of the law of large numbers. Fig. 2 shows that the similitude between analytical and simulation results increases with the channel load. Besides pointing out the larger effects of spatial diversity on the system performance, Fig. 3 also ratifies the excellent agreement between simulation and analytical results. Theoretically, it is expected that the intercellular MAl reduce the capability of the optimum 2D RAKE receiver in canceling the interference. Consistently, Fig. 4 shows that the performance gain of the optimum 2D Rake receiver in relation to the MRC 2D Rake receiver diminishes considerably when the intercellular MAl is taken into account. The other cell interference factor f was set to 0.6 to estimate the analytical response when it is assumed a macrocellular cellular system 19 BSs .  For uniformly distributed DOA. Tab. la shows: (i) a good agreement between numerical (equations 25 and 26) and simulation results; (ii) a sensible reduction of system performance in hot spot scenarios (i.e. reduction of DOA spread). Analyzing Tab. 1b it can be infered the following: (i) the performance gain due to optimum SINR solution (Eq. 14) reduces considerably when the AA becomes severely overloaded: (ii) both receivers lead to a gain of 3 dB in the average SINR when the processing gain is doubled .
The results shown in this section are minor samples of the extensive efforts that have been carried out in order to validate [9J a packet network simulator that has been developed in Cusing object oriented paradigm approach.

SOFT HANDOFF
The external interference in the target cell can be modeled as a sum of two components [5, pp. 189]:  In this section it has been considered an ES Rayleigh frequency selective fading channel with 3 taps. Fig. 7 shows the effects of number of preferential cells, N e , on the throughput. The throughput is calculated as: k=O where pr-:(k) is the probability of k packets being acknowledged (ACK) at the BS when the channel is loaded with K packets. The packet is ACK if the SINR at the receiver output is greater than a threshold SINR,j. If in Fig.  7a the path loss exponent and the standard deviation are set to 3 and 12 dB, respectively. then it is expected a considerable performance degradation when No is not set to 19. Physically. the above characteristics occur due to the excess of the intercell interference generated in the region So' However, if the path loss exponent and the standard deviation are set to 4 and 8 dB, respectively. then the path loss attenuates the intercell interference generates in the region So and thus the performance loss is not so relevant.
Mutatis mutandis. the system performance in microcellular environments (see fig. 7b) ratify the following important conclusion: it is necessary, even with the advanced 2D Rake receivers. a well-optimized pilot search mechanism in such way that the MSs transmit the minimum possible average power.
Hereafter. it is assumed that the "best" BS (i.e. the BS that presents the minimum medium-term attenuation) logically controls a given MS. In the following, it is fundamental to do some comparison between numerical and simulation results in order to obtain credibility to the shown simulation results.    Fig. 8, it is possible to observe a considerable reduction of the other-cell MAl in microcellular Manhattan environments. Fig. 8 also shows. for a hypothetical system without shadowing, a good agreement between the simulation results and the elucidative numerical results derived in [7. pp. 344-362]. Analyzing carefully these numerical results. it is verified that R. Steele, C-C Lee and P. Gould, in order to simplify a very complex scenario, did not take into account that MSs physically located in the target cell can also generate intercellular MAl in this target cell. This is absolutely true when the shadowing is absent. However. it can be noticed, in according with the two first columns of Tab. 2, discrepancies between numerical and simulation results when the lognormal shadowing is considered. Therefore. in order to validate the simulations results, it is also shown simulation results (third column of Tab. 2) where the users in the target central cell do not generate intercellular MAl (i.e. in according with the assumption used in the analytical model of [7]). These outcomes indicate the correctness of the simulation results. .....  The intercellular MAl can be also be modeled as a spatial temporal white process characterized by its average value.
where f is the first moment of the intercellular MAl at the target cell. Another possible approach is to model the covariance matrix of the received signal in a multicellular system as: ; .: It has been carried out in Fig. 9 a comparison between different approaches to model the external MAL In Fig.  9a, it is assumed a macrocellular system with 1=4 and CJ,h=8 dB, so that the normalized mean and standard deviation of external MAl are given by 0.6 and 0,45, respectively. In Fig. 9b, it is considered a microcellular system, with X b=200. f'=4, CJ,b=8 dB (normalized mean and standard deviation of external MAl are given by 0.22 and 0.31, respectively). 10% and 1% mean that 90% and 99% of MSs will have an SlNR above the respective curve. The simulation of full network is important to evaluate some essential aspects concerning the planning and performance assessment of cellular systems (i.e. soft and softer handoff, macrodiversity, distributed power control, and so forth). The software to simulate a full network is relatively complex. However, Fig. 9 shows that (32) to (34) allow obtaining first order results with a considerable reduction on the computational burden, since it is only necessary to simulate the target cell. Therefore, it is possible to use this approach as an important tool for software validation. When in soft handoff, the IvlS is connected to N sof t BSs, and the selection diversity is implemented on a frame basis, that is. the better frame received bv either BSs is accepted by the network. show that when the channel is lightly loaded, then the soft handoff allows improvement between 1.0 and 1.5 dB in the SINR statistics observed at the 2D Rake receiver output. It can be also noticed a neglectable additional gain when more of two BSs are involved in the soft handoff. It is emphasized again that 10% means that 90% of MSs will have an SINR above the respective curve. Supposing it is feasible to implement soft handoff with MRC technique. Fig. 11 shows that the soft handoff (actually a softer handoff) in macrocellular networks allows gains around of 2 dB in SINR observed at the 2D Rake receiver output. However, Fig. 12 indicates that in a microcellular system it is expected a reduction of the gains due to macrodiversity. Naturally, this characteristic comes upon of the greater isolation between the microcells in Manhattan networks.
In cdmoOne systems. for instance, the power control of MSs in soft hand ofI is distributed. i.e. the MS only increases its transmitted power if all BSs involved in soft handoff order to. Otherwise, the transmitted power is decreased. It can be noticed that the distributed power control reduces the intercellular MAL In this paper it has been assumed that the MSs are power controlled by the BS with lesser attenuation in the downlink. so we can expect that the soft handoff with distributed power control allows gains still more relevant in relation to those ones showed in this section (e.g. in the link budget of cdtnaOne systems it has been assumed a soft handoff gain of 3 dB).

MAXMIN SINR SCHEDULING SCHEME
The dynamic allocation scheme aims at loading each time slot with MSs that have their spatial signatures with 10\\ cross-correlation and. as a consequence. it increases the SINR at the input of the detection circuit [II]. In order to accomplish an investigation on the scheduling effects on the system performance. it is assumed that: ti) 5 MSs are physically located at each BS of a TDD DS-CDMA system with N,lofS time slots per uplink frame; (ii) each BS acquires and broadcasts information to the MSs using a MAC pooling protocol [12]; (iii! the channel transfer function for all MSs is known at each BS;

RECEIVERS OVER AN AWGN CHANNEL
As mentioned at Section 3, the 2D RAKE receiver reduces to an AA receiver if the number of filter taps per antenna. P, is set to one. For an AA receiver with perfect power control in a single-cell system, the SINR for the k-rh user can be expressed by (see 8 i.e. when the rows of hkhr are mutually orthogonal. It is observed that: Therefore. if due to scheduling the channel is loaded with terminals whose spatial signature is fulfilled (44), then the SINR is lower bounded by: ivf Based on Tab. 3, it can be drawn that: (it the scheduling scheme significantly increases the SINR at receiver output.
In these results the compatibility test is not implemented in order to make a fair comparison between analytical and the simulations results: (ii) the superior performance of circular array may be explained by the spatial distribution of the MSs, i.e. it is assumed that for the LIS )j2 array in a 3 sectored single cell system the DOA is uniformly distributed between -60° and -so". while for the circular 1,/2 array in the one-sector single cell system the DOA is assumed to be a U(00,360 D ) RV. It is also important to emphasize the following: (i) the discrepancies between the theoretical and simulations results observed in a system without scheduling is expected, since this lower bound has been derived taking into account a highly improbable event (i.e. all MSs with the same spatial signature. see 41); (ii) although it is extremely hard for the scheduling scheme to find MSs that fits the constrain (44), the minimum SINR values obtained by simulation are relatively near to the derived theoretical lower bound (see 43 Finally. this subsection is finished with the claim that the results shown. besides giving a mathematical insight on the interrelations between the spatial domain characteristics and scheduling schemes, also give confidence in relation to the correctness of the simulation results.

SYSTEM PERFORMANCE WITH AND WITHOUT SCHEDULING
Unless otherwise remarked. it IS evaluated the performance of optimum 2D Rake receivers over a Rayleigh frequency selective fading channel using the default settings defined at Section 4. The number of traffic slots per uplink frame and the SNR at the receiver output are set to 10 and 10 dB. respectively. Figures 13a and l3b show the effects of number of spatial diversity branches on the throughput when the SINR(J is set to 5 dB and 8 dB. respectively. These figures show that the MaxMin SINR scheduling scheme allows an expressive improvement on the throughput in single-cell systems. It has also been noticed that the spatial diversity substantially improve the throughput, mainly in systems without scheduling. Fig. 14 clearly shows that scheduling reduces considerably the variance of the SINR observed at the receiver output Ratifying the results shown in Fig. 13. it is observed that similar effects (i.e. SINR variance reduction) are obtained with spatial diversity. Tab. 4 shows the mean and standard deviation of the SINR at the receiver output without and with scheduling (second line). When the number of users is sufficient large to avoid short-term variation of the MAI, then the average value of the SINR is independent of the spatial diversity.   15 shows a comparison between numerical and simulation results for the SlNR CDF at the 20 Rake receiver output. It is assumed that a Gaussian RV in decibels. whose parameters are given in Tab. 4. can model the SINR. These resnlts indicate that if the first moment and standard deviation of the SINR are known. then a Gaussian R V in decibels can be used as a first order estimation of the SlNR at the receiver output.  Taking into account that in multicellular environments the external MAl in the scheduling period is uncorrelated to the external MAl in the traffic time slots. then comparing the Fig. 16 with the Figs. 13 and 14 permits to infer that the scheduling effects on the system performance, albeit still relevant, is minor in relation to gains obtained in single cell systems. Fig. 16a also shows that when the scheduling is implemented. the improvement of soft handoff with selection combining (SC) technique on the performance is not so relevant. However. the implementation of soft handoff with MRC technique allows considerable gains on the SI1\JR even when the scheduling scheme is operational.    17 shows results for the throughput in a microcellular system considering optimum 2D Rake receiver (solid geometric figures). MRC 2D Rake receiver (open geometric figures) with scheduling (solid straight lines) and without scheduling (dash straight lines) schemes. Analysing carefully these results permit to infer that: (i] for an environment without diversity spatial (i.e. MD=l), then the system with optimum 2D Rake receiver presents a considerable performance gain in relation to the MRC 2D Rake receiver. However. this gain performance diminishes considerable when a system with full spatial diversity is assumed; Iii) the minor power unbalancing due to the full spatial diversity (i.e. M D=8) reduces tile gains attainable with the scheduling scheme. However. the throughput multiplication due to the scheduling is still considerable even with M D=8.
Besides showing remarkable improvement due to the scheduling in microcellular cross-shaped networks, Fig. 18 shows that the parameter X, (see 27) does not int1uence significantly the SINR at the receiver output. Comparing Fig. 18 with Fig. 16a. it can be verified that the effects of soft handoff on the Manhattan networks are similar to those ones observed in macrocellular environments. Coherent with the results shown in Fig. 8, the outcomes of Fig. 17 indicate that the SINR does not change much when X, is Firstly, it is emphasized that when the compatibility test is operational (as in the earlier Figures of this Section), then the MSs are only scheduled if the SINR estimated at the scheduling phase is greater than a pre-established threshold SINR(l. For either a single-cell system without spatial diversity (Fig. 19a) and a single-cell system with full spatial diversity (Fig. 19b), it can be verified that the compatibility increases the throughput. As it has been assumed a full correlation between the channel transfer function observed in each scheduling and traffic period. then this readily explain why the throughput reaches an asymptotic platform when the compatibility test is operational. It can be verified that above a given threshold, the average number of terminals that do not pass at the compatibility test (and. therefore. they are not scheduled at each frame) increases ;:. the same rate of channel load, However. the same phenomenon does not occur when a multicellular system is investigated (see Figs. 19c and 19d) In this case, although the compatibility test allows a considerable performance gain, this performance improvement is reduced in relation to the single-cell system since the MAl observed at scheduling period does not present a perfect correlation with the MAl effectively observed at the traffic time slots because of the intercellular interference. Finally, the results shown in Fig. 19 indicate that there is an upper threshold where the throughput of the system without scheduling presents a better performance. It is noticed that this interesting characteristic occurs due to the high variance in the SINR statistics when the slot assignment is done in a random way. The MaxMin SINR scheme better equalises the SINR among the MSs in the same slot, but not for a value greater enough to overcome the SlNR o , when the system is overloaded. The throughput results show in Fig. 19 (from the operator point of view) and results on the SINR statistics at recei ver output show in Fig. 20 (from the user point of view) points out that the performance gain of MaxSINR receiver response in relation with the MRC receiverreduces with the spatial diversity, channel load and the intercellular MAl.   Figure 20: Effects of scheduling without compatibility test as a function of channel load, spatial diversity and type of receiver (Max SINR or MRC response) on the SINR of a system with hexagonal cells. G p=32. M=4; L=3, P=3.

FINAL REMARKS
Among of analytical results derived, remarks and conclusions that were done in the earlier sections, we emphasize that the dynamic time slot scheduling schemes can provide substantial improvements on the performance of TDD DS-CDMA systems with 2D Rake receivers. We also have shown that it is necessary to implement distributed power control in order to maximize the gains due to soft handoff. Finally, it is pointed out that. mutatis mutandis, the dynamic time slot scheduling scheme is well suited for contention free service with point coordination function in 802. 11