Antenna Placement for Downlink Distributed Antenna Systems with Selection Transmission

Transcription

1 Antenna Placement for Downlink Distributed Antenna Systems with Selection Transmission unsung Park, Student Member, I, and Inkyu Lee, Senior Member, I School of lectrical ng., Korea University, Seoul, Korea mail: kupes, inkyu@korea.ac.kr Abstract In this paper we propose new algorithms to determine the antenna location for downlink distributed antenna systems (DAS) with selection transmission (ST). ST h some advantages for DAS since the feedback overhead is quite small and other-cell interference can be reduced compared to other transmission schemes. For the single-cell ce, we consider a circular antenna layout with or without a center antenna and divide a cell into regions with the same physical area. Then, we formulate the optimization problem of distributed antenna (DA) port locations which maximizes the lower bound of the expected signal to noise ratio in each region. Also, for the two-cell DAS, we maximize the lower bound of the expected signal to leakage ratio to identify the optimum DA positions. In order to solve the problem, we propose an iterative method by deriving the gradient of the cost function for a gradient cent algorithm. The DA locations obtained from our proposed method are compared with conventional solutions. Simulation results show that the proposed algorithms offer a large capacity gain over the centralized antenna systems in single-cell and twocell environments. I. INTODUCTION In recent years, distributed antenna systems (DAS) have gained interests because of its ability to extend the cell coverage and incree the system capacity. The DAS w first introduced for indoor wireless communication systems to enhance the coverage. Unlike conventional centralized antenna systems (CAS) where all antenn are co-located at the cell center, distributed antenna (DA) ports in the DAS are separated geographically. Thus, the DAS can reduce the access distance, the transmit power and co-channel interference, which result in the improved cell-edge performance. The locations of DA ports are significant in the system performance of DAS. In many papers, the performance analysis w conducted for DAS with random or fixed antenna layout. In 4, the outage probability of DAS with random antenna layout w analyzed. Also, the ymptotic ergodic capacity w derived by applying random matrix theory for DAS with random and circular antenna layout in 5 and 6, respectively. In 7, the optimal antenna layout w studied for space time block coded orthogonal frequency division multiplexing systems in the linear cell DAS where a be station (BS) h two antenn. For the uplink DAS in singlecell, the squared distance criterion (SDC) w proposed in 8 in order to find antenna locations which maximize the cell averaged ergodic capacity. Since the algorithm of the SDC is equivalent to a codebook design in vector quantization 9, an iterative method is required. In, the SDC w applied to the downlink DAS with selection transmission (ST) where one antenna is selected to transmit data to a mobile station (MS). However, this algorithm is not suitable for DAS in multicell since it does not take other-cell interference (OCI) into consideration. This work w supported by the National esearch Foundation of Korea (NF) grant funded by the Korea government (MST) (No. -799). The ST allows quite simple structure since a MS only feeds back the antenna index to the BS. In contrt, other closed loop systems such maximum ratio transmission (MT) requires much higher feedback overhead since the BS should know full channel state information. Also, for the DAS with a large number of cells, the ST exhibits an increed capacity gain over the MT since the ST can reduce the OCI 4. Therefore, we focus on the antenna location design for DAS with ST. In this paper, we consider the composite fading channel which includes both small scale fadings and large scale fadings, and propose new algorithms to identify the antenna locations for the downlink DAS with ST in single-cell and two-cell. For arbitrary path loss exponents in single-cell, we consider a circular antenna layout with or without a center antenna, and each cell is divided into regions with the same physical area. Then, in each region, we find the location of DA ports which maximize the lower bound of the expected signal to noise ratio (SN). As this optimization problem is convex, we can obtain a closed form solution for the DA locations. We confirm from simulations that the DA positions obtained from the proposed algorithm are the same the conventional SDC results in 8, while the computational complexity of the proposed algorithm is much lower than the conventional SDC algorithm. For the two-cell DAS, we employ the criterion which maximizes the lower bound of the expected signal to leakage ratio (SL) for simple analysis. This SL criterion is suitable for DAS in multi-cell environments, since it takes the leakage interference into consideration. In this ce, we develope an iterative algorithm which finds the locations of DA ports by deriving the gradient of the cost function and applying a gradient cent algorithm. Simulation results demonstrate that DAS with the antenna locations obtained from the proposed algorithm outperforms CAS. II. SYSTM MODL In this section, we describe a system model for the downlink DAS with ST. We consider that each cell h N DA ports and a single MS. We sume that all DA ports and MSs are equipped with a single antenna and all MSs are uniformly distributed in each cell. Also, a circular cell with a radius of is sumed with circular antenna layout with or without a center antenna and the distance between centers of two cells is set to. Since DA ports are largely separated in DAS, the channel model encompses not only the small scale fading (i.e. ayleigh fading) but also the large scale fading including shadowing and pathloss 4. In this paper, we focus on ST where all DA ports first transmit the pilot signals to a MS and the MS chooses one DA port which h the largest received signal strength (SS) and feeds back the selected DA port index 4. Denoting n(l) the index of the DA port selected in the l-th cell, the received //$6. I

2 signal of the MS in the m-th cell for the L-cell DAS can be expressed L sn(l),m L y m = h n(l),m d α x n(l) +n m = g n(l),m x n(l) +n m n(l),m l= where h n(l),m and s n(l),m equal the coefficients of the small scale fading and the shadowing fading, respectively, d n(l),m stands for the distance between the DA port selected in the l-th cell and the MS in the m-th cell, α is the path loss exponent, x n(l) represents the transmitted signal from the DA port selected in the l-th cell with (x n(l) x n(l) ) = P, and n m indicates the additive complex Gaussian noise variable with zero mean and variance σn. Here, the superscript ( ) stands for conjugate. The coefficient of the small scale fading h n(l),m is an independent and identically distributed (i.i.d.) complex Gaussian random variable with zero mean and unit variance and the shadowing fading s n(l),m h a log-normal distribution, i.e., log s n(l),m is a Gaussian random variable with zero mean and standard deviation σ s. Then, at cell, the ergodic capacity for DAS in single-cell (C SC ) and two-cell (C TC ) can be expressed ( C SC = h,s,p log + P ) gn(), σn ( C TC = h,s,p log + P ) g n(), σn + P gn(), where h,s,p represents the expectation with respect to the small scale fading, the shadowing fading and the MS position. It is quite complicated to derive a solution which maximizes the ergodic capacity C SC and C TC. Instead, utilizing the Jensen s inequality log ( + X) log ( + X), we P g n(), attempt to maximize the expected SN h,s,p σ and n P g n(), expected SIN h,s,p for single-cell and twocell, respectively, to simplify the σn +P g n(), analysis. III. ANTNNA LOCATION DSIGN In this section, we propose new algorithms which determine the antenna locations for the downlink DAS with ST. First, we briefly review the conventional SDC algorithm in 8 for the single-cell DAS. Then, we propose a non-iterative algorithm which maximizes the lower bound of the expected SN and a layout selection method in single-cell. Also, in two-cell, an iterative algorithm which maximizes the lower bound of the expected SL is introduced. A. Single-Cell DAS In 8 and, the SDC algorithm for antenna location designs were studied in the uplink and downlink single-cell DAS. The SDC algorithm tries to optimize the cell averaged ergodic capacity by minimizing the expectation of the squared distance from a randomly distributed MS to the nearest antenna port. This criterion is similar to a codebook design in vector quantization 9, and needs an iterative method. In order to reduce the computational complexity, we propose a noniterative algorithm. For the single-cell DAS, the expected SN is given Psn(), h n(), h,s,p SN = h,s,p. l= d α n(), σ n.5.5 w/ a center antenna w/o a center antenna.5.5 Fig.. Cell regions for circular antenna layouts with N =7 Since the small scale fading, the shadowing fading and the MS position are independent, the expected SN can be represented Psn(), hn(), h,s,p SN = h,s p σ n d α n(), P σn h,s s hn(), n(), α.() p d n(), where the lower bound of the expected SN follows from the Jensen s inequality. In (), we consider that h,s s n(), h n(), is a constant value since it is independent of the antenna layout. Then, the lower bound of the expected SN is maximized by minimizing the expected squared distance p d n(),. We sume that a cell is divided into N regions with the same physical area considering a circular antenna layout with or without a center antenna. The i-th DA location can be expressed DA i = i exp (jθ i ) () for a,i i b,i, θ a,i θ i θ b,i where i and θ i are the magnitude and the phe, a,i and b,i denote the minimum and the maximum value of the magnitude, and θ a,i and θ b,i represent the minimum and the maximum value of the phe in the i-th DA location, respectively. For example, Figure shows two ces with N =7. For the layout with a center antenna, the parameters for the region of the center antenna are a,i =, b,i = / 7, θ a,i =and θ b,i =π while those of the regions of the circular antenn equal a,i = / 7, b,i = and θ b,i θ a,i = π/. Also, the regions of the antenna for the layout without a center antenna have a,i =, b,i = and θ b,i θ a,i =π/7. Let us denote p the MS location in the single-cell. Assuming that the MS is located in the i-th DA region, p can be expressed by p = r exp (jφ ) () for a,i r b,i, θ a,i φ θ b,i where r and φ indicate the magnitude and the phe of the MS position. Then, defining Ξ i SC p d i, we can formulate the antenna location problem ˆi, ˆθ i = arg min Ξi SC i,θ i (4) subject to a,i i b,i, θ a,i θ i θ b,i.

3 Using () and (), the squared distance can be computed by d i = i + r i r cos (φ θ i ). (5) Since the MS is uniformly distributed, it is straightforward to obtain the expected squared distance Ξ i SC = p d i. After some derivations, the cost function can be computed by (6) which ( is located at ) the next page, where A = / (θ b,i θ a,i ) b,i a,i. The cost function is convex, if the second partial derivatives of the cost function with respect to i and θ i are non-negative. The first and second partial derivatives are expressed Ξ i ( SC = A i b,i a,i) (θb,i θ a,i ) i ( b,i a,i ) sin (θb,i θ i ) sin (θ a,i θ i ) = A ( i b,i a,i ) cos (θb,i θ i ) cos (θ a,i θ i ) Ξ i SC i = A ( b,i a,i) (θb,i θ a,i ) Ξ i SC θi = A i( b,i a,i) sin (θb,i θ i )+sin(θ i θ a,i ). Ξ i SC i Since b,i a,i and θ b,i θ a,i, is always nonnegative. For a center antenna ce, θ a,i =and θ b,i =π. Thus, we have sin (θ b,i θ i )+sin(θ i θ a,i )=.Also,for circular antenn, θ b,i θ i and θ i θ a,i are always smaller than π. So, sin (θ b,i θ i )+sin(θ i θ a,i ) always becomes nonnegative, and the cost function becomes convex. Therefore, we can obtain the unique ˆ i and ˆθ i which minimize the expected i= Ξ. i α/ SC B. Two-Cell DAS Since the conventional SDC algorithm does not take the OCI into account, the DA locations from the SDC algorithm are not suitable for the two-cell DAS. In order to optimize the ergodic capacity C TC for the two-cell DAS, we should maximize the expected SIN. However, this criterion is quite complicated for determining the DA locations due to the coupled nature of the corresponding optimization problem. Thus, we adopt an alternative approach bed on the expected SL which considers the leakage interference and offers simple analysis. In this subsection, we propose an iterative algorithm which maximizes the lower bound of the expected SL. Defining the SL at cell P g n(),, the expected SL P g n(), at cell is expressed h,s,p,p SL = h,s,p,p s n(), hn(), /d α n(), s n(), h n(), /d α n(), where p and p denote the expectation with respect to the MS positions in cell and, respectively. Since the small scale fading, the shadowing fading, and the MS positions in cell and cell are independent, the expected SL is given sn(), hn(), h,s,p,p SL= h,s s hn(), n(), p p d α n(), h,s sn(), h n(), s n(), h n(), d α n(), p d n(), α p d α n(), where the lower bound of the expected SL is obtained by applying the Jensen s inequality. Suppose that the i-th DA location and the MS position in cell are denoted by () and (), respectively. Also, the MS position in cell is expressed p = r exp (jφ )+ for r, φ π. (9) Then, we can formulate the problem for the i-th DA at cell ˆi, ˆθ i p d α i = arg max i,θ i squared distance by calculating Ξi SC i =and Ξi p d SC i =. α/ subject to As a result, for the single-cell DAS, the i-th DA location a,i i b,i, θ a,i θ i θ b,i can be obtained by where d i is expressed ( ) b,i ˆ a,i sin (θ b,i ˆθ ) ( ) i +sin ˆθi θ a,i i = ( ) d (7) i = i +r + i r cos(φ θ i )+ (r cosφ i cosθ i ). () b,i a,i (θ b,i θ a,i ) However, the cost function p d α i cannot be computed p d and i α/ ( ) for α > in general. Thus, we change the cost function cos θb,i cos θ a,i to ln ˆθ p dα i since the maximization of ln p i = arctan. (8) p d sin θ a,i sin θ i α/ d α i is p d i α/ b,i not only equivalent to the maximization of p d α i,but Finally between circular antenna layouts with and without p d i α/ a center antenna, we choose the one which h a larger value also makes it ey to deal with the path loss exponent α. of Again applying the Jensen s inequality, the lower bound of ln N p dα i can be computed p d i α/ Ω= ln p d α i p d i α/ = ln p d α i ln p d i α/ p ln ( d ) α/ i ln p d α/ i = α ( ) p ln d i ln p d i. Defining Ξ i TC ( ) p ln d i ln p d i, the problem for i-th DA can be written ˆi, ˆθ i = arg max Ξi TC i,θ i () subject to a,i i b,i, θ a,i θ i θ b,i.

4 Ξ i ( SC=A i b,i a,i ) (θb,i θ a,i ) ( i b,i a,i ) sin(θb,i θ i ) sin(θ a,i θ i )+ ( 4 4 b,i a,i 4 ) (θb,i θ i ) (6) Assuming that ( the ) MS in cell is uniformly distributed we can obtain p ln d i similar to the single-cell ce in Section III-A ( ) π p ln d i = ln ( d ) i r π dr dφ = π π r ln ( d i) dr dφ. Using π ln(+acos φ+bsin φ)dφ =πln + a b ( ) for a b 5, p ln d i is computed ( ) p ln d i = ln + γ for γ< ln γ for γ where γ = i + i cos θ i. Then, the cost function can be represented Ξ i TC = ln + γ ln Ξ i SC for γ< ln γ ln Ξ i SC for γ. () Here, γ is always smaller than if <θ i < or < θ i < 6 and cos θ i cos θ i < i <. Otherwise, we have γ. In order to obtain the DA locations which maximize the cost function, we apply a gradient cent algorithm which iteratively updates the DA locations in the direction of the gradient of the cost function. Then, the gradients of the cost function with respect to i and θ i are derived i Ξ i TC= θi Ξ i TC = ( i cos θ i ) i /Ξ i SC for γ< γ ( i cos θ i ) i /Ξ i SC for γ i sin θ i Ξi SC /Ξ i SC for γ< γ i sin θ i Ξi SC /Ξ i SC for γ. With the derived gradient expressions, our algorithm which solves () is summerized follows: Initialization: ) Initialize i and θ i for the i-th DA in cell a,i i b,i and θ a,i θ i θ b,i ) Calculate Ξ i TC with the initial values Main Loop: ) Calculate the gradient i Ξ i TC and θ i Ξ i TC 4) Update i i +δ i i Ξ i TC and θ i θ i +δ θi θi Ξ i TC 5) Calculate Ξ i TC with the updated values 6) epeat until convergence In 6, several line search methods were presented for the selection of the step size δ i and δ θi. In our algorithm, we employ Armijo s rule which provides provable convergence. After the DA locations are determined for cell, the DA locations at cell can be simply determined by using the rotational symmetric property between cell and. Fig N =.5.5 N = N = N = Locations of DA ports for DAS in single-cell N = N = TABL I Ω FO DIFFNT CICULA ANTNNA LAYOUTS N Ω w/ a center antenna Ω w/o a center antenna IV. SIMULATION SULTS In this section, simulation results are shown to demonstrate the efficacy of our proposed algorithms. In the simulation, the standard deviation for shadowing and the path loss exponent are set to σ sh =4dB and α =.75, respectively. Also, we define the SN P/σn. We first compare the locations of DA ports from the proposed algorithm with the conventional SDC algorithm results for DAS in single-cell with various numbers of DA ports. In the single-cell DAS for N =, 4,, 8, the locations of DA ports in (7) and (8) are presented in Figure. In the figure, the dots, the terisks and the circles indicate the locations of DA ports from the SDC algorithm, the proposed algorithm for the layout with a center antenna and the proposed algorithm for the layout without a center antenna, respectively. In Table IV, the values of Ω are listed for both layouts. The table shows that for N =, 4, and 5, the circular layout without a center antenna is preferred, while when N =6, 7, and 8, a center DA port is helpful in terms of the expected SN. Thus, the results of our proposed algorithm are the same the conventional SDC results in. Note that the SDC algorithm requires an iterative method, where our problem h closed form solutions. In Figure, we plot the average capacity curves a function of various numbers of DA ports for DAS and CAS with SN= db in single-cell. For DAS, the locations of DA ports depicted in Figure are employed with ST. Also, in CAS, we use both ST and MT. For the CAS with ST, a MS chooses one antenna which h the largest SS and only the selected antenna transmits the signal to the MS. When N =8, compared to CAS with MT and ST, DAS with ST h the

5 Average Capacity bps/hz 5 4 Average Capacity for DAS and CAS at SN=dB DAS w/ ST CAS w/ MT CAS w/ ST N Average Capacity bps/hz 8 6 Average Capacity for DAS and CAS with N=7 4 DAS w/ ST CAS w/ MT CAS w/ ST SN db Fig.. The average capacity for DAS and CAS in single-cell at SN= db Fig. 5. The average capacity for DAS and CAS with N =7in two-cell Antenna.5.5 Single cell ce Two cell ce Antenna Fig. 4. The locations of DA ports for DAS in two-cell with N =7 capacity gains of 6% and % since the DAS can reduce the access distance by separating the DA ports geographically. It should be emphized that MT requires the full channel state information at the transmitter, and thus is much more complex than ST in terms of the feedback mechanism. In Figure 4, we plot the locations of DA ports for DAS in two-cell with N =7obtained from our proposed solution in Section III. In the figure, the dots and the terisks denote the locations from the proposed algorithms in the single-cell and two-cell ce, respectively. Since our proposed algorithm in the two-cell ce takes the leakage interference into consideration, the DA ports for the two-cell DAS are shifted against to each other in order to reduce the interference. Also, our iterative gradient cent algorithm converges with only to 5 iterations when we employ the single-cell solutions the initial points. In Figure 5, we exhibit the average capacity curves a function of SN for DAS and CAS with N =7in two-cell. The same transmission schemes in the single-cell ce for DAS and CAS are employed. Since the optimized locations of DA ports from the proposed gradient cent algorithm reduce the access distance and the OCI, DAS with ST h the capacity gains of % and 8% over CAS with MT and ST, respectively. V. CONCLUSION In this paper, we have proposed new algorithms which identify antenna locations for DAS in single-cell and two-cell. For the single-cell DAS, in comparison to the conventional SDC algorithm which needs an iterative method, our problem maximizes the lower bound of the expected SN and results in a closed form solution. The simulation results show that the DA locations obtained from our method are the same those of the SDC algorithm for the single-cell DAS. For the two-cell DAS, we have proposed an iterative algorithm which finds the locations of DA ports by deriving the gradient of the cost function and applying the gradient cent algorithm. Since the proposed algorithm takes the leakage interference into consideration, our method is suitable for DAS in multicell. The simulation results confirm that DAS with antenna locations obtained from the proposed algorithm offers a large capacity gain over CAS. FNCS A. A. M. Saleh, A. 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