John Papandriopoulos

Jamie Evans

Subhrakanti Dey

Optimal Power Control in CDMA Networks with Constraints on Outage Probability

Keywords: CDMA, Decorrelator, large system analysis, MMSE receiver, multiuser detection, outage probability, power control

This paper proposes a new scheme that couples power control with a minimum outage probability multiuser detector. The resultant iterative algorithm is conceptually simple and finds the minimum sum power of all users with a set of outage probability constraints. Bounds on the outage probability expression are found that extend a previous result that did not include receiver noise. These bounds are used to create a sub-optimal scheme coupling power control and a MMSE multiuser detector. This new problem becomes a variant of an existing problem where outage probability constraints are first mapped to average SIR threshold constraints. Using a recent result that transforms complex SIR expressions into a compact and decoupled form, a non-iterative and computationally inexpensive power control algorithm is developed for large systems of users. Simulation results are presented showing the closeness of the optimal and mapped schemes, speed of convergence and performance comparisons with other standard receivers.

I. INTRODUCTION

Power allocation is an effective way to improve the performance of wireless communication systems. It can mitigate near-far effects occurring when a nearby interferer disturbs the reception of a remote user, whose desired signal is attenuated to a greater extent. Careful power allocation can also increase utilization in interference-limited systems such as CDMA, or those multiple access systems employing frequency reuse amongst cells, as in FDMA. Finally, by allocating minimum power across all users, battery life of mobile devices will be extended: users only need to expend sufficient power for acceptable reception as determined by their quality of service (QoS) specifications such as FER, BER or outage probability.

The power allocation problem has been studied extensively as an eigenvalue problem for non-negative matrices [START_REF] Aein | Power balancing in system employing frequency reuse[END_REF]- [START_REF] Grandhi | Centralized power control in cellular radio systems[END_REF], as iterative Power Control Algorithms (PCA) that converge each users' power to the minimum power result [START_REF] Foschini | A simple distributed autonomous power control algorithm and its convergence[END_REF]- [START_REF] Hanly | An algorithm of combined cell-site selection and power control to maximize cellular spread spectrum capacity[END_REF], optimization based approaches [START_REF] Julian | Robust and QoS constrained optimization of power control in wireless cellular networks[END_REF]- [START_REF] Bui | Optimal power control in CDMA over markov fading channels[END_REF] and other variations [START_REF] Yates | Integrated power control and base station assignment[END_REF]- [START_REF] Ulukus | Stochastic power control for cellular radio systems[END_REF]. A useful framework for uplink cellular power control is given in [START_REF] Yates | A framework for uplink power control in cellular radio systems[END_REF].

Much of this previous work deals with invariant channel models. Any power control scheme that attempts to follow fast fades would need to be highly efficient to be implemented in practice, or incur a power penalty due to intense signal processing and may require frequent communication with its assigned base station.

Of particular interest is the work presented in [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF] and [START_REF] Bui | Optimal power control in CDMA over markov fading channels[END_REF]. In [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF], a scheme whereby the statistics of the received signal to interference ratio (SIR) are used to allocate power, rather than an instantaneous SIR. The allocation decisions can then be made on a much slower time-scale (following log-normal shadowing variations for instance). In [START_REF] Bui | Optimal power control in CDMA over markov fading channels[END_REF], an optimization problem is considered using average SIR which yields locally optimal solutions.

In a multiple access system, multiuser detection (MUD) can be used to further enhance the performance of wireless systems by exploiting the structure of the multiple access interference [START_REF] Verdú | Multiuser detection[END_REF]. The optimal MUD is near-far resistant however has exponential complexity with the number of active users. The decorrelating detector, with polynomial complexity, can eliminate multiuser interference entirely at the expense of enhancing receiver noise power [START_REF] Verdú | Minimum probability of error for asynchronous gaussian multiple-access channels[END_REF]. Furthermore, in a CDMA system, the noise enhancement increases as the utilization increases until the detector becomes unusable. Minimum mean squared error (MMSE) detection [START_REF] Madhow | Minimum mean squared error interference suppression for direct-sequence spread-spectrum code-division multipleaccess[END_REF]- [START_REF] Madhow | MMSE interference suppression for direct-sequence spread-spectrum CDMA[END_REF] is based on the minimization of the expected squared error between a transmitted symbol and the received signal. It is also near-far resistant and reduces to the decorrelating detector as the AWGN power is zeroed. The MMSE receiver is considered a compromise between the matched filter and decorrelator.

A major difficulty in the analysis of a power controlled environment is the coupling of all users through the interference they cause each other. One simplifying case is the decorrelating detector as noted above, however recent work has shown that in a large system, decoupling of the interfering effects is also possible for several other receiver structures including the MMSE receiver [START_REF] Tse | Linear multiuser receivers: Effective interference, effective bandwidth and user capacity[END_REF]. This work will lead to a fully decentralized PCA that requires little computation.

Traditionally, power allocation and multiuser detection were considered separately. Power allocation assumed a fixed receiver structure and multiuser detection assumed fixed user transmitter powers. By jointly optimizing both power and linear receivers, an increase in user capacity in addition to a reduction of power consumption is possible [START_REF] Tse | Linear multiuser receivers: Effective interference, effective bandwidth and user capacity[END_REF]. Recent work [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF]- [START_REF] Yener | Interference management for CDMA systems through power control, multiuser detection, and beamforming[END_REF] has focused on this problem in order to obtain the benefits of both power allocation and MUD.

The main contributions of this paper are:

1) The design of a conceptually simple, iterative algorithm that minimizes the sum power of all users subject to outage constraints. The optimization is performed on choice of user powers and linear multiuser receivers. This problem reduces to that considered in [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF] if background noise is neglected and linear receivers fixed. 2) A new sub-optimal iterative PCA-MUD where outage constraints are first mapped to average SIR threshold constraints. Such a mapping permits the use of a variant of an existing combined PCA and MMSE MUD given in [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF]. 3) A decentralized non-iterative PCA-MUD for medium to large systems of users using a recent result that transforms complex expressions for SIR into a compact and decoupled form. Simulation results are also provided comparing each method with established receivers such as the matched filter and decorrelating receiver.

II. SYSTEM MODEL

In this paper, we consider the uplink in a synchronous direct sequence CDMA communications system with K users and a processing gain of N . We assume a BPSK modulation scheme and a N -dimensional chip matched filter vector for each symbol interval, given by

r i = K j=1 G ij F ij P j b j s j + n (1)
where G ij F ij P j is the received power power from user j, with transmit power P j . G ij F ij represents the instantaneous channel gain of user j to the assigned Base Station (BS) of user i. The data bits b j take on values of ±1 with equal probability, s j is the N -dimensional spreading sequence of user j, and n is AWGN with zero mean and covariance σ 2 I. We assume fixed spreading sequences, with elements of s j taking values ±1/ √ N . Following the conventions of [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF], we assume G ij is the positive slow-varying path gain of user j to the assigned Base Station (BS) of user i, excluding any fading. The analysis that follows holds only over a time scale where factors affecting G ij do not change significantly. The terms F ij model fast time-scale Rayleigh fading and are assumed to be unit mean independent exponentially distributed random variables.

Let c i denote the receiver filter coefficients for user i at its assigned BS and c = [c 1 , . . . , c K ]. The filter output of user i at its assigned BS is given by

y i = c i r i = K j=1 G ij F ij P j (c i s j )b j + ñi (2)
where ñi = c i n is N (0, σ 2 c i c i ).

III. OUTAGE PROBABILITY AND CERTAINTY-EQUIVALENT MARGIN WITH NOISE

To simplify notation in this section, we shall drop the receiver filter terms (c i s j ) 2 without a loss of generality (since we can absorb them into the G ij terms). They will become important in Section IV.

A. SIR and Outage Probability

The SIR, γ, of the ith mobile is given by

γ i = G ii F ii P i j =i G ij F ij P j + σ 2 (3)
The outage probability of user i, denoted O i , is defined as the proportion of time that some SIR threshold γ th i is not met for sufficient reception at the BS receiver. By careful choice of γ th i , we can set a QoS for each user. O i is given by

O i = P r γ i ≤ γ th i = P r   G ii F ii P i ≤ γ th i    j =i G ij F ij P j + σ 2      .
The outage probability for the ith user is given by (see [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF])

O i = 1 -exp -σ 2 γ th i G ii P i j =i 1 1 + γ th i Gij Pj GiiPi . (4)

B. Certainty-Equivalent Margin with Noise

The Certainty-Equivalent Margin (CEM) was defined in [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF] without noise. It represents a margin of error for average SIR when representing the system by a certainty-equivalent form (with all statistical variation in signal and noise power ignored and replaced with their expected values.)

We will take average SIR (denoted SIR) to mean the expected value of the i th mobile received power over the expected value of the interference from the K -1 other mobiles and background noise. This is also the certainty-equivalent SIR and is given by

SIR i = γ ce i = E[G ii F ii P i ] E[ j =i G ij F ij P j + σ 2 ] = G ii P i j =i G ij P j + σ 2 .
(5) As with [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF], we also define the CEM (with noise, denoted CEM σ ) as the ratio of the certainty-equivalent SIR to the average SIR threshold,

CEM σ i = γ ce i γ th i = GiiPi γ th i { j =i Gij Pj +σ 2 } . (6)

C. Relation Between the CEM σ and Outage Probability

Using the following result, we briefly sketch the derivation of upper and lower bounds on outage probability in terms of the CEM σ . The full development can be found in [START_REF] Papandriopoulos | Iterative power control and multiuser detection with outage probability constraints[END_REF]. For z 1 , ..., z n ≥ 0 it can be shown that the inequalities

1 + k + n i z i ≤ e k n i (1 + z i ) ≤ e k+ n i zi (7)
hold, where k is some constant.

From (4), we have

O i = 1 - 1 exp σ 2 γ th i GiiPi j =i 1 + γ th i Gij Pj GiiPi
Using the left-hand side inequality in [START_REF] Julian | Robust and QoS constrained optimization of power control in wireless cellular networks[END_REF], it can be shown that

O i ≥ 1 1 + CEM σ i .
It can also be shown that the right-hand side inequality in [START_REF] Julian | Robust and QoS constrained optimization of power control in wireless cellular networks[END_REF] leads to

O i ≤ 1 -e -1/CEM σ i .
The upper and lower bounds on outage are thus,

1 1 + CEM σ i ≤ O i ≤ 1 -e -1/CEM σ i (8)
which have the same form and tightness in the region of interest as the noiseless case in [START_REF] Kandukuri | Optimal power control in interferencelimited fading wireless channels with outage-probability specifications[END_REF].

Note that CEM σ i (or average SIR with a fixed γ th i ) and outage probability are inversely proportional. As we increase the CEM σ i (or SIR), we get a lower outage probability and viceversa.

D. Special Case: Decorrelator

Recall that for K < N , the decorrelator nulls out all users other than the one of interest, at the expense of enhanced receiver noise power. The resulting expression for the decorrelator SNR is given by

γ i = G ii F ii P i σ 2 R -1 ii where R -1
ii is the (i, i) th element of the inverted K × K signature sequence cross-correlation matrix R. The corresponding CEM σ i is given by

CEM σ i = G ii P i γ th i σ 2 R -1 ii . (9)
By definition, the outage expression is given by

O i = P r γ i ≤ γ th i = P r F ii ≤ γ th i σ 2 R -1
ii

G ii P i = 1 -exp -γ th i σ 2 R -1 ii G ii P i
or by substituting [START_REF] Bui | Optimal power control in CDMA over markov fading channels[END_REF],

O i = 1 -e -1/CEM σ i . (10)

IV. POWER CONTROL ALGORITHM

A. Problem Definition

The aim of the PCA is to find the powers, P i , and filter coefficients, c i for i = 1, ..., K, such that the total power transmitted by all users is minimized while all outage constraints are met. Formulating this as an optimization problem, we have min

P,c K i=1 P i s.t. 1 -e -σ 2 (c i c i )γ th i G ii (c i s i ) 2 P i j =i 1 1+ γ th i G ij (c i s j ) 2 P j G ii (c i s i ) 2 P i ≤ O t i , P i ≥ 0, c i ∈ R N i = 1, ..., K
where we used (4) with the receiver filter included and O t i are target outage probability constraints. It can be shown that this problem is equivalent to the following, where the inner optimization has been inserted into the constraint set. See [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF] for a similar refinement.

min P K i=1 P i s.t. min ci∈R N    1 -e -σ 2 (c i c i )γ th i G ii (c i s i ) 2 P i j =i 1 1+ γ th i G ij (c i s j ) 2 P j G ii (c i s i ) 2 P i    ≤ O t i , P i ≥ 0 i = 1, ..., K (11)

B. Optimal Power Control

In this section we describe an iterative algorithm to solve the optimization problem [START_REF] Grandhi | Constrained power control[END_REF].

Taking the log of the outage constraint from [START_REF] Grandhi | Constrained power control[END_REF] and rearranging yields

w i + GiiPi γ th i j =i log 1 + Gij Pj Gii P i γ th i GiiPi γ th i ≤ log 1 1 -O t i with w i = σ 2 (c i c i ), Gij = G ij (c i s j ) 2 ,

and finally

P i ≥ w i + G ii P i j =i log 1 + Gij Pj GiiPi G ii log 1 1-O t i ( 12
)
where

G ii = Gii γ th i .
If we view [START_REF] Ulukus | Stochastic power control for cellular radio systems[END_REF] as representing a set of quasi-interference constraints on the power vector P, we can define a new PCA where each user i iteratively attempts to compensate for the interference. At convergence, we would like each of the outage constraints to be met.

We define

I i (P, c i ) = w i + G ii P i j =i log 1 + Gij Pj GiiPi G ii log 1 1-O t i (13) T i (P) = min ci I i (P, c i ) (14)
where we let I i (P, c i ) = P i be (12) replaced with equality.

We shall now refer to I i (P, c i ) as the interference function to maintain consistency with the framework in [START_REF] Yates | A framework for uplink power control in cellular radio systems[END_REF]. Furthermore, we propose the PCA

P(n + 1) = T(P(n)) (15)
where T(P) = [T 1 (P), . . . , T K (P)] and is initialized with powers set to the receiver noise level P i (0) = σ 2 , ∀i and matched filter coefficients c i (0) = s i , ∀i. This PCA is similar in form to that in [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF], however we are dealing with outage and average quantities on a slower time scale. In Section IV-C, we will see how a sub-optimal variant of ( 13)-( 15) can be reduced to a PCA that is similar in form to [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF].

Since our PCA ( 15) is of the standard form given by [START_REF] Yates | A framework for uplink power control in cellular radio systems[END_REF], Theorem 1 proposes that ( 14) is a standard interference function and thus the PCA converges to a fixed solution. The proof is based on the three properties of a standard interference function given in [START_REF] Yates | A framework for uplink power control in cellular radio systems[END_REF], repeated below: Definition 1: Interference function I(P) is standard if for all P ≥ 0 the following properties are satisfied.

• Positivity I(P) > 0.

• Monotonicity If P ≥ P , then I(P) ≥ I(P ).

• Scalability For all α > 1, αI(P) > I(αP). Theorem 1: T(P) is a standard interference function. The proof of Theorem 1 is given in [START_REF] Papandriopoulos | Iterative power control and multiuser detection with outage probability constraints[END_REF].

Since T(P) is a standard interference function, the PCA (15) converges to a final solution P * = T(P * ). This solution is the minimum power required to meet the outage constraints [START_REF] Ulukus | Stochastic power control for cellular radio systems[END_REF]. The filter coefficients converge to a new type of MUD, the Minimum Outage Probability (MOP) receiver. As such, we shall refer to the PCA (15) as the optimal MOP-PCA.

C. Average SIR and Outage Probability

To meet our outage probability constraints, we require that O i ≤ O t i for all i. Combining this inequality with the upper bound in (8), we can define a new constraint on CEM σ i that when met, will guarantee that our original outage constraints are also met:

O i ≤ 1 -e -1/CEM σ i ≤ O t i i = 1, . . . , K. (16)
Rearranging the right-hand inequality of ( 16) yields,

1 CEM σ i ≤ log 1 1 -O t i γ i ≥ γ th i log 1 1-O t i (17) = Γ th i (18)
where we have used the definition of CEM σ i from (6) and defined a new quantity,

Γ th i = γ th i log 1 1-O t i (19)
called the outage-mapped average SIR threshold. We can now define a new problem, min P,c

K i=1 P i s.t. P i ≥ Γ th i Gii j =i Gij (c i sj ) 2 Pj +σ 2 (c i ci) (c i si) 2 P i ≥ 0, c i ∈ R N i = 1, ..., K
where we have rearranged [START_REF] Foschini | A simple distributed autonomous power control algorithm and its convergence[END_REF] to form a SIR constraint. This problem is mathematically equivalent to the power control problem in [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF], however we consider average channel gains and the outage-mapped average SIR threshold Γ th i as parameters.

In a similar fashion to [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF], the problem is equivalent to

min P K i=1 P i s.t. P i ≥ Γ th i Gii min ci∈R N j =i Gij (c i sj ) 2 Pj +σ 2 (c i ci) (c i si) 2 P i ≥ 0 i = 1, ..., K
with an associated PCA given by,

Ĩi (P, c i ) = Γ th i G ii j =i G ij (c i s j ) 2 P j + σ 2 (c i c i ) (c i s i ) 2 Ti (P) = min ci Ĩi (P, c i ) (20)

P(n + 1) = T(P(n))

where T(P) = T1 (P), . . . , TK (P) . We shall refer to this PCA as the outage-mapped MMSE-PCA.

In [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF], it was shown that the MMSE filter coefficients c i minimize ( 20) and so we have the following iterative algorithm for the above problem:

ĉi = S i D i S i + σ 2 I -1 s i (21)
P i (n + 1) = Γ th i G ii j =i P j (n)G ij (ĉ i s j ) 2 + σ 2 (ĉ i ĉi ) (ĉ i s i ) 2 (22)
where S i = [s 1 , . . . , s i-1 , s i+1 , . . . , s K ], and D i is a (K -1)×(K -1) diagonal matrix with entries P 1 G 11 , . . . , P K G KK , omitting P i G ii . The filter coefficients estimate ĉi is updated on each iteration. The PCA is initialized with powers set to the noise level and matched filter coefficients. The convergence proof of this PCA mirrors that in [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF].

Since we have used the upper bound on O i in the derivation above, the solution is sub-optimal, however we guarantee the outage constraints from the right-hand side of [START_REF] Madhow | Minimum mean squared error interference suppression for direct-sequence spread-spectrum code-division multipleaccess[END_REF]. Recall that in the region of interest, the outage bounds are tight, and so we expect that this PCA will result in near-optimal performance as compared to the optimal MOP PCA.

V. LARGE SYSTEM ANALYSIS

The linear receiver that achieves the minimal power allocation in the previous problem is the linear MMSE receiver. It does this by minimizing the interference function [START_REF] Almutairi | Power control algorithm for MMSE receiver based CDMA systems[END_REF], or equivalently, maximizing the average SIR of user i. The corresponding maximal SIR for user i is given by

SIR i = P i G ii s i S i D i S i + σ 2 I -1 s i , (23)
which we can use to restate the optimization problem of section IV-C as follows:

min P K i=1 P i s.t. SIR i ≥ Γ th i P i ≥ 0 i = 1, ..., K. (24)
The solution to this problem (if it exists) occurs when all users meet their outage-mapped average SIR constraint with equality. This problem is then equivalent to solving

P i G i s i S i D i S i + σ 2 I -1 s i = Γ th i ( 25
)
for all i = 1, . . . , K.

The Large System Analysis (LSA) in [START_REF] Tse | Linear multiuser receivers: Effective interference, effective bandwidth and user capacity[END_REF] derives a closed form expression that the left-hand side of (25) converges to, in probability, as N → ∞, K → ∞ and the number of users per degree of freedom, α ≡ K N , remains fixed. This SIR, in the limit, is a deterministic quantity for each user i denoted

β * i .
Somewhat surprisingly, the result enables the uncoupling of each user in the SIR expression above, by representing each user with an effective interference.

The result allows us to approximate the average SIR for a given user i, denoted β i , in a finite sized system with MMSE receivers. The average SIR approximation is given by

β i ≈ P i G ii σ 2 + 1 N K j=1 I(P j G jj , P i G ii , β i ) (26)
where I(P j G jj , P i G ii , β i ) is the effective interference term contributed from the j th user, and is defined as

I(P j G jj , P i G ii , β i ) ≡ P j G jj P i G ii P i G ii + P j G jj β i . (27)
Combining ( 26) and (27) yields

β i ≈ P i G ii σ 2 + 1 N K j=1 Pj Gjj PiGii PiGii+Pj Gjj βi . ( 28
)
For the remaining analysis, we shall assume (28) holds with equality. Let α * i = βi PiGii . Equation (28) becomes

α * i P i G ii = P i G ii σ 2 + 1 N K j=1 Pj Gjj 1+Pj Gjj α * i or α * = 1 σ 2 + 1 N K j=1 Pj Gjj 1+Pj Gjj α * (29) since α * i does not depend on i. Substituting P j G j = βj α * = Γ th j α * into (29) gives α * = 1 σ 2 + 1 N K j=1 β j α * 1+ β j α * α * = 1 σ 2 + 1 α * 1 N K j=1 Γ th j 1+Γ th j (30)
The non-trivial solution to the fixed point equation ( 30) is given by

α * = 1 -1 N K j=1 Γ th j 1+Γ th j σ 2 = Γ th i P i G ii
where again,

P i G ii = Γ th i α * .
Rearranging the left-hand side for P i gives the power solution of the i th user,

P i = Γ th i G ii σ 2 1 -1 N K j=1 Γ th j 1+Γ th j ( 31
)
where we have the necessary and sufficient condition

1 N K j=1 Γ th j 1 + Γ th j < 1 (32)
for a solution to exist. The expression (31) allows for a totally decentralized and non-iterative PCA since we have a closed form expression that only requires the gain of the user of interest and the outagemapped SIR thresholds for all users -all these parameters are known (or can be measured) at the base station receiver.

We shall refer to this PCA as the LSA-PCA.

VI. SIMULATION RESULTS Our simulations consider a single circular CDMA cell with radius 1km. We assume uniform location of users within the cell who are subject to distance dependent loss (loss exponent 4) and log-normal (zero mean, 8dB variance) shadowing. Unless otherwise stated, a processing gain of 32 was chosen, corresponding to a chip rate of 1.2288Mcps and an encoder input rate of 38.4kbps under the cdma2000 specification [START_REF]Working document towards submission of RTT candidate to ITU-R, IMT-2000 process 'the cdma2000 RTT candidate submission[END_REF]. Furthermore, an AWGN noise power equal σ 2 = 10 -13 was chosen corresponding to approximately a 1MHz bandwidth.

We define three user classes, each having outage probability and SIR threshold pairs as {(5%, 10dB), (10%, 8dB), (20%, 6dB)}. We assign 25% of users to the first class, 50% to the second and the remaining to the third.

In all simulations that follow, user signature sequences are chosen randomly with elements of s j taking values ±1/ √ N with equal probability. Initial filter coefficients are set to the matched filter and initial user powers are set to the receiver noise power σ 2 = 10 -13 where appropriate.

A. Optimal MOP and Outage-Mapped MMSE PCAs

In this section, we compare the optimal MOP-PCA with the outage-mapped MMSE-PCA.

For K = 4, 8, 16, 32 users, Fig. 1 shows in log scale the sum power of all users as a function of the iteration step. The optimal MOP-PCA and MMSE-PCA are almost indistinguishable, verifying earlier claims on the tightness of the outage probability bounds.

Figure 2 considers a system of 32 users. It shows the convergence of the outage probabilities for each user as a function of the iteration step. We clearly see the three outage probability classes (5%, 10% and 20%) at convergence.

B. MMSE, Matched Filter and Decorrelator PCAs

In this section we compare three standard receivers with outage constraints under power control: the matched filter (MF), decorrelator (DC) and MMSE receivers. Each receiver has an associated outage constraint mapped to an average SIR constraint using [START_REF] Ulukus | Adaptive power control and MMSE interference suppression[END_REF]. We consider 1,000 independent simulation runs for each receiver type. Signature sequences are chosen independently between runs, however sequences are common across simulations for each receiver type and specific value of K.

For K = 2, 3, 4, 16, 32 users, Fig. 3 shows the total power allocation, averaged over each simulation run. Simulations where the solution was not feasible are excluded from this figure -the reason for the MF-PCA plot stopping at K = 4.

To appreciate the relative difficulty of obtaining a feasible solution, Fig. 4 shows the percentage of users that met their outage constraints, averaged over all simulation runs.

Note the reduction in total power for the MF-PCA as K was increased from three to four users. This can be attributed to the low number of feasible solutions (0.425%) in the scenario for K = 4: only those users with "good" signature sequences could attain a feasabile solution. In the scenario where K = 3, there is less competition amongst users (as each has a higher degree of freedom) and a greater number of less-efficient signature sequence combinations were possible, in the sense that more feasible solutions were possible at the expense of a higher total power on average.

C. Large Systems

We now consider the large system results for K = 16, 32, 64, 128, 256, 512 users and compare the LSA-PCA with the MMSE-PCA.

A fixed α = 0.75 was chosen, with other parameters as above. Figure 5 shows in log scale the sum power of all users for each simulation scenario. As the system size is scaled upwards, the LSA-PCA accuracy improves significantly until it becomes indistinguishable from the MMSE-PCA. For mediumsized systems, the approximate result gives excellent performance considering the reduced complexity and decentralized nature of the result.

Figure 6 shows the percentage of users in each simulation scenario that did not meet their outage constraints, using the LSA-PCA. Similar statistics are not shown for the MMSE-PCA, as all users in all scenarios met their outage constraints with equality. Since the closeness of the LSA-and MMSE-PCAs was noted above, a plot is also shown to quantify the average deviation between the outage probability specification and simulated outage probability, for each user not meeting their outage target. For all scenarios, this deviation is small, ranging from 3% to under 1% and improves as the size of the system is scaled upwards. This statistic is important as it validates the LSA method, even for smaller sized systems.

VII. CONCLUSION

This paper introduced a new power control problem that aims to jointly optimize user powers and linear receiver filters according to outage specifications. An iterative algorithm to solve this problem was developed and convergence proved. A bound on the outage probability enabled a mapping to take place between outage and an average SIR threshold. From this, a suboptimal PCA-MUD was developed that utilized the well known MMSE receiver. The approximation to the optimal solution was found to be exceptionally close in the CEM σ region of interest.

Large system approximations were used to decouple complex SIR expressions when the number of users and degrees of freedom approach infinity, with a fixed ratio between the two. This approximation enabled a closed form solution to an outage-mapped, joint power control and MMSE MUD optimization problem. In a finite-sized system, the approximate solution was found to be close to the MMSE-PCA solution, giving excellent results for medium to large finite-sized systems.

Fig. 1 .

 1 Fig. 1. Total transmitter power with 2-32 users.

Fig. 2 .

 2 Fig. 2. Outage probability for MMSE-PCA with 32 users.

Fig. 3 .

 3 Fig. 3. Total transmitter power with 2-32 users, averaged over 1,000 simulations.

Fig. 4 .

 4 Fig. 4. Percentage of users meeting constraints, averaged over 1,000 simulations.

Fig. 5 .

 5 Fig. 5. Comparison between the LSA-PCA and MMSE-PCA with K = 16, . . . , 512 users and α = 0.75.

Fig. 6 .

 6 Fig.6. Performance of the LSA-PCA in meeting user outage probability constraints, and the average deviation between resultant user outage probability and respective targets for those users with an inadequate QoS.

The authors are with the ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne VIC 3010, Australia, email:{jpap, jse, s.dey}@ee.mu.oz.au

This work was supported by the Australian Research Council.


Sana Ben Jamaa

Zwi Altman

Jean-Marc Picard

Benoît Fourestié

Julien Mourlon

Manual and Automatic Design for UMTS Networks

Introduction

The expected commercial opening of UMTS networks in Europe emphasizes the need for high performance design tools and methodology. UMTS networks are interference-limited with frequency resources shared among users [START_REF] Holma | WCDMA for UMTS, Radio Access for Third Generation Mobile Communications[END_REF]. High quality design is therefore crucial to optimally utilize the limited available resources to maximize coverage, capacity, and Quality of Service (QoS). This paper focuses on the design in terms of antenna parameters: antenna tilt, azimuth and type, and common channel powers. The design depends on the objectives defined by the operator: The dimensioning service, the penetration margins, the coverage target for the different services, the pricing or throughput policies, etc. Network optimization is required throughout the lifetime of the network: Roll-out stage and densification of an existing network. The design quality is of particular importance since it impacts the investments of the operator, and the network performance in terms of coverage, capacity and QoS.

Two design strategies are described in this paper: The first one is a manual design guided by an expert system which identifies the most effective modifications for the designer; The second strategy uses a combinatorial optimization approach for an automatic design procedure. A Genetic Algorithm (GA) is adapted to guide an Automatic Cell Planner (ACP). Detailed examples of network optimization illustrate the performance of the design approaches.

Network design

The development of an efficient design methodology requires a deep understanding of UMTS characteristics. Network parameters could be strongly interdependent, and a change of one parameter in a given sector could influence several sectors, in particular its neighbors. The number of parameters to optimize in the network could be large, and typically varies from a few hundreds to a few thousands. The following objectives guide the design process, and will be used by all models described hereafter:

-Satisfy coverage objectives for different services and penetration margins. Both UpLink (UL) and DownLink (DL) coverage of traffic channels and DL coverage of common channels should be considered. -Maximize capacity. For a single service, capacity can be defined as the number of mobiles that can be served. In case of multi-service traffic, one can approximate capacity in terms of global throughput. -Ensure handover (HO) zones (macrodiversity zones). A predefined proportion of the surface of each sector should satisfy HO conditions. HO zones are essential to guarantee continuity of service between the sectors. It also strengthens the radio link against fast fading and shadowing. -Minimize economic cost related to the solution implementation. An economic cost is associated with a modification of each type of parameter.

Manual design strategies

The first approach considered here is a manual design approach based on an expert system developed in FTR&D. At each step of the manual process the expert system analyzes different quality criteria and guides the designer by identifying the most effective parameter modifications to be carried out. It aims at reducing the loads and excess of interference in the loaded sectors. Manual intervention is slow and the number of modifications that could be considered is limited to a few tens. For this reason, the initial network should be well parameterized, and typically one could choose an optimal default (uniform) parameterization that ensures coverage objectives as a starting point.

As an example, a network with 45 sectors in a dense urban environment is considered, with mixed traffic: 80% voice (12.2 kbps) service, 15% 64 kbps service and 5% 144 kbps service, with mixed outdoor and indoor mobiles. The UL and DL load histograms of the initial and optimized network after 20 modifications are presented in Figure 1. The following definitions for theUL load, L UL , and DL load, L DL , are used: where I total stands for the total interference received at the base station, N th is the thermal noise at the receiver, P total is the total power transmitted by the base station and P max is the maximum possible power at the base station.

The reduction of the number of sectors in the higher part of the histogram illustrates the added value of the design process. It is noted that performance degradation (HO failure, blocking and dropped calls, bad BER and BLER etc.) typically occurs at highly loaded sectors and therefore the results are particularly interesting. The network in this example is down link limited, which is often the case in dense urban environment, and for this reason improvements are more significant in DL than in UL. Figures 2 and3 show comparisons between traffic demands as a function of the satisfaction rate for the initial network and those obtained using manual and automatic (Oasys V2, see Sect. 2.2) optimization. The traffic demand is related to the total number of mobiles positioned in the network, namely, to mobiles trying to establish communication. The comparison is carried out using two traffic distributions: voice traffic (12.2 kbps) and high bit rate traffic (144 kbps). In the first case (Figure 2), a capacity gain of more than 6 percents is obtained using both optimization approaches. In the second case (Figure 3), no gain is obtained for the manual optimization, whereas a gain of about 8 percents is achieved for the optimization with Oasys V2. In fact, since the manual optimization is carried out using a mixed traffic with 80% of voice mobiles, it is more adapted to a low bit rate level traffic. In addition it is noted that for larger networks, capacity gain using the ACP is larger (see section 2.2).

Automatic design strategies

The large number of parameters to optimize and the inter-dependency of these parameters make the design process a complex optimization problem that belongs to the class of NP-hard problems and can be solved utilizing a combinatorial optimization technique. An Automatic Cell Planner (ACP), Oasys, has been developed in FTR&D to automatically design UMTS networks. The ACP is orchestrated by a Genetic Algorithm (GA) [START_REF] Goldberg | Genetic Algorithms in Search, Optimization and Machine Learning[END_REF], which simultaneously processes a population of networks, each of which is defined by a set of parameters to be optimized. The GA uses the Darwinian evolution as an optimization model that guides a population of networks towards better solutions through repetitive applications of genetic operators till high performance networks are obtained. The GA can test thousands of network configurations and typically outperforms manually design networks. A block diagram describing the optimization procedure is shown in Figure 4.

UMTS Fast Simulation Engine

Genetic Algorithm Optimization Engine

New set of network parameters Quality Criteria Evaluation Traffic-based model: Traffic distribution is explicitly introduced in the model (using forecasts or measurements). Ultra-rapid evaluation algorithms have been developed, allowing the model to accurately compute basic UMTS quantities such as powers, loads, interferences etc. Based on this model, a second version of the ACP, Oasys V2 has been developed. Non-homogeneous traffic distributions can be introduced via hot spots, linear traffic objects and superposition of surface traffic objects.

Performance analysis is of particular importance in the design process since it allows the designer to evaluate the quality of the network and the improvement brought about by the optimization. A set of deterministic quality criteria has been elaborated based on coverage, capacity, service continuity, and probabilistic quality criteria such as probability of access, link upholding and good quality.

Consider next a network with 115 sectors in a dense urban environment. 74 sectors are set for possible modifications, whereas the parameters of the remaining 41 sectors are kept unchanged and constitute a buffer zone to minimize the effect of truncation (see Figure 5). The total DL power distribution of the sectors is presented in Figure 9. The ACP strives to reduce the sector powers, and in particular the power of the highly loaded sectors. It is noted that the ACP which includes traffic in the evaluation and optimization process (Oasys V2) further alleviates the power of the most loaded sectors in the network with respect to the Roll-out ACP, Oasys V1. This improvement in resource utilization results in a gain in capacity.

Figure 9. Total DL power distributions for the initial network (black), and the networks optimized using Oasys V1 (gray) and Oasys V2 (white).

One can relate the number of served mobiles to the average UL and DL loads in the network, as shown in Figure 10. For a given average load, the optimized network serves more mobiles, and conversely, for a fixed number of mobiles, the average load of the optimized network is reduced. Since optimizing the common channels affects mainly DL performance, and in addition, the network is DL limited, the decrease in average load values is particularly apparent in DL, although it is also clear in UL. In interference-limited networks, reduction of interference is directly related to gain in capacity and service quality. For this reason, the impact of optimization on interference distribution is of particular interest. In Figure 11 the DL inter-cellular interference maps for the initial and optimized networks are presented. The color of each mesh corresponds to a received power calculated at its center. The optimized networks appear lighter than the initial one due to lower interference levels. Furthermore, Oasys V2, which takes traffic into account in the optimization, allows to further reduce excess of interference with respect to Oasys V1 which uses a fixed load hypothesis. The optimized network requires less radio resources, namely, transmitted power, to achieve the required signal to noise target ratio. Figure 12 presents DL coverage maps of 144 kbps service for traffic channels. The color of each mesh corresponds to the transmitted power of the traffic channel that serves a mobile located at the center of the mesh. It can be seen (see Figure 12e) that the portion of the area with high DL powers, namely in the limit of coverage, is considerably reduced for both optimization models. Probabilistic quality criteria are of particular importance for performance analysis of mobile networks due to random phenomena related to traffic position and mobility, shadowing, fast fading, etc. Figure 13 shows the probability of access for 144 kbps mobiles evaluated at the center of each mesh. Both optimization models reduce the surface of low probability of access. The legend is presented in (d), and the comparison between the surfaces with lower probability of access is shown in (e).

Conclusions

This paper presents efficient manual and automatic design approaches for UMTS networks. The design consists in adjusting antenna types, tilts and azimuths, and common channel powers to improve the network performances: capacity, coverage, QoSe, and service continuity.

Manual design is a complex and a time-consuming task that can be made efficient by the use of an expert system that, by processing quality criteria, identifies the problematic sectors and suggests the most effective parameter modifications. Due to the limited number of modifications that can be treated manually, the expert system focuses on the most loaded and interfered sectors.

An automatic cell planner guided by a genetic algorithm has been developed for automatic optimization. Two models have been considered: a roll out model using fixed load hypothesis, and a traffic based model. The latter includes traffic in the optimization process that allows to accurately evaluate basic UMTS quantities such as powers, loads and interference. The ACP can handle large networks with a number of sectors varying from few tens to several hundreds, corresponding to a few thousands of parameters, and with computational time of several hours. The automatic optimization allows to increase capacity, to reduce excess of interference, and improve quality of service. Further more, the ACP produces cost efficient solutions by including economic cost in the optimization process.

Figure 1 .

 1 Figure 1. Comparison of load histograms for the initial (black) and the manually designed (white) networks.

Figure 4 .

 4 Figure 4. Block diagram describing the GA based ACP. Two models have been studied: Roll-out model: Traffic distribution is not yet known, and is implicitly introduced via fixed UL and DL load values utilizing geo-marketing forecasts. Based on the roll-out model, a first version of the ACP, Oasys V1 has been developed [3-4].

Figure 5 .Figure 6 .Figure 7 .Figure 8 .

 5678 Figure 5. A network with 115 sectors in a dense urban environment.

  Number of served mobiles for the 144 kbps service as a function of the average UL (a) and DL (b) loads of the network sectors.

Figure 11 .

 11 Figure 11. DL inter-cellular interference maps utilizing the initial network (a), Oasys V1 (b) and Oasys V2 (c). The legend is presented in (d) and the comparison between highly interfered surfaces is shown in (e).

  Figure 12. DL coverage maps for traffic channels for the initial network (a), Oasys V1 (b) and Oasys V2 (c). The legend is presented in (d), and the comparison of the surfaces in limit of coverage is shown in (e).

  <= P acces < 1 0,85 <= P acces < 0,95 0 <= P acces < 0,85 (d) (e) Figure 13. Probability of access for the initial network (a), Oasys V1 (b) and Oasys V2 (c).

Satisfaction rate (% mobiles served) Traffic demand

					400
				Initial network Manual optim OaSys_V2	250 300 350	Traffic demand
					200
	100,0%	97,5%	95,0%	92,5%	90,0%
		Satisfaction rate (% mobiles served)
	Figure 2. Traffic demand of as a function of satisfaction rate for voice service
	(12.2 kbps). Traffic demand is related to the total number of mobiles
		in the network trying to establish communication.
					70
					60
					50
					40
					30
				Initial network	20
				Manual optim
				OaSys V2	10
					0
	100,0%	97,5%	95,0%	92,5%	90,0%
	Figure 3. Traffic demand of as a function of satisfaction rate for
			for 144 kbps service.


Filiz Bektas
email: filiz.bektas@siemens.at

Bojan Vondra
email: bojan.vondra@siemens.hr

Peter E Veith
email: peter.veith@siemens.at

Leopold Faltin
email: leopold.faltin@siemens.at

Alfred Pohl
email: alfred.pohl@siemens.at

Arpad L Scholtz
email: arpad.scholtz@tuwien.ac.at

In order to cope with the environmental impacts on Bluetooth data transmission diversity techniques were examined. A Bluetooth antenna diversity demonstrator was developed.

Extensive experimental investigations documenting the significant improvements of data communication employing diversity have been done. It was shown that the effects of multipath and fading can be combated to a large extent by antenna diversity. Thus, antenna diversity was found to be a powerful technique for improving the quality of Bluetooth links.

Introduction

Presently, Bluetooth is the fastest growing wireless communication technology. Operating in the 2.4 GHz ISM-band and based on a frequency hopping physical layer, it enables different types of portable devices to form short-range wireless ad-hoc networks. Mobile phones and PDA's as well as car equipment, refrigerators, even luggage have been published as Bluetooth carrying objects. Bluetooth will be an integral part of the convergence of the wireless and the internet world and will cover preferably, but not only, personal area networks (PAN). It will be the interface to the outer world, in particular to cellular networks and hot spots [START_REF] Bray | Bluetooth, Connect Without Cables[END_REF], [START_REF] Muller | Bluetooth Demystified[END_REF], [START_REF] Robert | Wireless Personal Communications, Bluetooth Tutorial[END_REF].

Industrial plants consist of many devices interconnected in different ways. Simple data collection units, more intelligent devices (sensors with built in intelligence, single loop controllers or programmable controllers) and supervisory systems. These devices are interconnected using many different communication protocols and media, which in some cases be replaced with Bluetooth wireless technology. Serial cable replacement, combination of Bluetooth and Internet technologies, industrial access points, wireless sensors and actuators can be industrial uses of Bluetooth.

Bluetooth involves highly sophisticated methods for packaging, encryption and error correction of data and for radio resource sharing. But, still, Bluetooth transmits data via a radio channel. The application scenarios use their own radio channels due to the individual topology of the radio link.

To examine the performance of Bluetooth, simulations and numerous measurements have been done [START_REF] Bektas | Investigation of Bluetooth Communication in Representative Usage Environments[END_REF], [START_REF] Bektas | The Actual ''Physical Layer" and its Impact to Bluetooth Communication[END_REF]. Also, data rate measurements in different environments have been performed [START_REF] Bektas | Evaluation of Bluetooth Communication[END_REF]. It was found that Bluetooth combines performance characteristics of narrow band transmission with the advantages of spread spectrum communication.

Data communication requires a reproducible Quality of Service (QoS), i.e. negotiated performance is to be granted during operation. Quality of service means a predefined and negotiated data rate, delay, and error rate. Since the error rate and the delay are strongly related to the data rate, we focus our present investigations on the data rate.

A signal passed over a wireless channel is affected by pathloss, narrow and wideband fading, and co-channelinterference [START_REF] Parson | The Mobile Radio Propagation Channel[END_REF], [START_REF] Saunders | Antennas and Propagation for Wireless Communication Systems[END_REF], [START_REF] Jakes | Microwave Mobile Communications[END_REF]. The impulse response of the wireless channel is time variant and depends on the particular location. In general a deterministic approach is not feasible. Estimations can be made with statistical models [START_REF] Bektas | Investigation of Bluetooth Communication in Representative Usage Environments[END_REF], [START_REF] Bektas | The Actual ''Physical Layer" and its Impact to Bluetooth Communication[END_REF].

To cope with multipath fading and also with cochannel interference, BT applies FHSS (Frequency Hopping Spread Spectrum). Single data packets are transmitted using one of 79 carrier frequencies with a spacing of 1 MHz. BT employs a pseudo random hopping sequence with 1600 hops/s, rather fast compared to other FHSS systems in the 2.4 GHz ISM band (802.11, homeRF, etc.). Although BT uses a 83.5 MHz wide frequency band to transmit raw data at a rate of 1 Mbit/s, it only occupies a bandwidth of about 1 MHz while transmitting. As modulation scheme BGFSK (Binary Gaussian Frequency Shift Keying) with a modulation index of 0.28-0.35 is used. The Gaussian pulse shaping reduces the covered bandwidth dramatically [START_REF] Pahlavan | Wireless Information Networks[END_REF].

Most of the short range wireless communication technologies use the 2.45 GHz ISM band and therefore have to cope with interference. Furthermore, indoor communication is strongly affected by shadowing and reflections. This results in radio channels with only statistically predictable parameters variant in time and frequency. Narrow band systems perform only poor under such circumstances.

With Bluetooth, the packets transferred consecutive in time do not use the same frequency, thus avoiding the drawbacks of the narrowband transmission. As has been investigated in [START_REF] Bektas | Investigation of Bluetooth Communication in Representative Usage Environments[END_REF], [START_REF] Bektas | The Actual ''Physical Layer" and its Impact to Bluetooth Communication[END_REF], the link performance obeys the rules for narrow band systems and additionally depends on the fading of the individual channels occupied. Therefore all methods of improving the physical layer have to be frequency agile. As such an approach, we developed a Bluetooth antenna diversity demonstrator. In the following Section the demonstrator is described. Then in Section 3 the setup for our measurements is explained and in Section 4 the results of the experiments are discussed. A conclusion summarizes our work in Section 5.

Bluetooth Diversity Demonstrator

The medium access protocol for Bluetooth communication is a packet-based, Time Division Duplex (TDD) polling scheme. The transmission channel is divided into time slots, each 625µs in length. In the TDD scheme (Fig. 1), master and slave transmit alternatively. In Fig. 2 practical examples for the transmitted and the received signals are given.

Beam steering is the main principle of our Bluetooth diversity module. Diversity is controlled by sampling the received signal during the 'Guard Time' interval. This interval is used to get information about the incoming wave and to choose the optimum antenna configuration. When the receiving module takes over transmission, it uses the same antenna configuration. This procedure is repeated for each slot. Since the beam steering is done during the 'Guard Time', it does not reduce data rate.

A photo of the demonstrator is shown in Fig. 3 and the basic hardware diagram sketched in Fig. 4. The demonstrator has a single base band unit, two radio units, one micro controller unit, an antenna matrix and two antenna connectors. The antenna connectors are separated by λ/2, providing a choice between integrated or external antennas. The demonstrator is physically separated into two PCB modules, the Bluetooth diversity module and the micro controller module. The module supports three operational modes: mode one is normal Bluetooth operation without diversity. The second mode enables space diversity (Fig. 6): the signals coming from the two antennas are compared in strength and the stronger one is chosen by the micro controller for further processing in the baseband. Angle (beam) diversity is the third mode (Fig. 6): the signals from the two antennas are combined in the antenna matrix to obtain two orthogonally directed antenna beams (Fig. 7). As in case of space diversity, the stronger beam signal is processed in the baseband.

The micro controller board, determines the antenna diagram by controlling the position of the four antenna switches in the antenna matrix.

Measurements

The Bluetooth link was established using two notebook computers (hosts) connected to Bluetooth diversity modules via their serial ports. As measurement results we obtained both the data rate of the Bluetooth connection and the magnitude of the received signal. Data rate measurements were performed by means of "HCI Toolbox" software made for BT device test via the host controller interface (HCI). For the field strength measurements the micro controller board was connected to a computer via its serial port. Then, the magnitude of the received field strength was observed, large numbers of samples were taken and stored via hyper-terminal. Finally the statistical distribution of the fluctuating field at the receiver side was derived using these data.

Representative application environments can be found e.g. in offices, living rooms, and laboratories. We performed a series of diversity demonstrator measurements in a laboratory/office room (7m x 13.5m x 3.25m), where different types of obstacles (working desks, computers, RF measurement devices, soldering equipment, wooden office cupboards and a metallic temperature test box) causing reflection, refraction and fading are located.

In order to investigate the performance of the BT diversity demonstrator in an industrial environment, a second series of data rate measurements was done in a factory for assembling of electronic devices (120m x 109m x 7m) (Fig. 8). Here many metallic obstacles such as reflow soldering machines, SMD mounting machines, work places for testing and mounting of electrical circuits, a closed depot, a closed office room and a closed break room can be found. During this measurements we confined our interest to angle diversity.

Results

For the measurements in the laboratory/office room, we installed the transmitter in one corner of the room and performed data rate measurements for different positions of the receiver. The measurement results in the laboratory/office room for space and angle diversity are shown in Fig. 9 and Fig. 10 respectively.

Without diversity, data rate changed remarkably for different locations within a distance range of a few meters. As shown in both Fig. 9 and Fig. 10, a strong variation of data rate can be observed due to severe multipath propagation with an average coherence bandwidth of 7.4 MHz [START_REF] Bektas | Investigation of Bluetooth Communication in Representative Usage Environments[END_REF], [START_REF] Bektas | The Actual ''Physical Layer" and its Impact to Bluetooth Communication[END_REF]. Hopping across the whole 83.5 MHz bandwidth provides signal loss in many hops due to deep fading and shadowing almost independent from the geometric distance between transmitter and receiver.

Essential increase in data rate due to both space and angle diversity can be seen from the figures. Use of diversity overcame the multipath propagation effects and provided almost constant data rate throughout the room.

The cumulative distributions of the signal strength at an arbitrarily chosen point in the room, 6.4m apart from the transmitter, are shown in Fig. 11. The average of the received power increased by 3dB for space diversity and by 8dB for angle diversity. The gain due to space diversity was remarkable in the power range from -71dBm to -85dBm. Here by space diversity 7dB maximum gain was achieved. The improvement by angle diversity was larger. A maximum gain of 12dB was observed.

In the factory the distance between transmitter and receiver was kept constant and the positions of transmitter and receiver were changed along parallel corridors 22.8m apart (Fig. 8). The data rate measurement results are depicted in Fig. 12. The data rate had a strong variation at different positions along the corridor.

The use of angle diversity increased the data rate and reduced the signal strength variations. The improvement achieved for angle diversity can be seen from Fig. 12. Angle diversity suppresses multipath and fading effects to a fairly large extent. The average data rate was 13kbit/s without diversity. It increased to 59kbit/s with angle diversity.

Conclusion

In this paper, a Bluetooth antenna diversity demonstrator was presented. Measurements representing typical indoor scenarios were performed.

As a parameter with high significance for the availability and reliability of a data link, the data rate has been determined. Also, received power has been examined as a second means to quantify the gain due to diversity.

Space and angle diversity were examined. The performance of angle diversity was found to be significantly better than that of space diversity. It was shown that, the degradation in data rate due to impacts of the environment can be suppressed by antenna diversity to a large extent. Thus, significant improvement in the performance of Bluetooth communication links can be obtained.

Figure 1 Figure 2 :

 12 Figure 1: TDD and timing

Figure 3 :Figure 4 :

 34 Figure 3: Bluetooth diversity module

Figure 5 :Figure 6 :

 56 Figure 5: Basic block diagram of the antenna matrix If the Switch0/3 is in the position that connects antenna terminal to ground, it is considered to be in OFF position, otherwise, the switch is in ON position. Switch in OFF position must not load antenna terminals; therefore, the 90 or 4 λ transformers are introduced in the path between switch and corresponding antenna terminal.

Figure 7 :

 7 Figure 7: The beams used in the angle (beam) switching mode of operation

Figure 8 :

 8 Figure 8: Sketch of the measurement scenario in the factory

Figure 9 :

 9 Figure 9: Data rate measurements in the laboratory/office room for space diversity mode

Figure 10 :

 10 Figure 10: Data rate measurements in the laboratory/office room for angle diversity mode

Figure 11 :

 11 Figure 11: The comparison of the theoretical Rayleigh cumulative distribution and the measured data without diversity, with space and with angle diversity

Figure 12 :

 12 Figure 12: Data rate measurements along a corridor in the factory, angle diversity mode