# Spatial Domain Resource Sharing for Overlapping Cells in Indoor Environment

Authors: Riichi Kudo; Yasushi Takatori; Kentaro Nishimori; Takeo Ichikawa; Tomoki Murakami; Masato Mizoguchi; Masahiro Morikura
Journal: International Journal of Digital Multimedia Broadcasting
 (2010)

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## Abstract

As microcell wireless systems become more widespread, intercell interference among the access points will increase due to the limited frequency resource. In the overlapping cell scenario, radio resources should be shared by multiple cells. Although time and frequency resource sharing has been described in many papers, there is no detailed report on dynamic spatial resource sharing among multiple cells for microcell wireless systems. Thus, we present the effectiveness of spatial resource sharing among two access points. We introduce two scenarios based on the zero forcing method; one is the primary-secondary AP scenario and the other is the cooperative AP scenario. To evaluate the transmission performance of spatial resource sharing, channel matrices are measured in an indoor environment. The simulation results using the measured channel matrices show the potential of spatial resource sharing.


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## Body

## 1. Introduction

The rapid increase in data traffic has led to strong demands for large-capacity transmission systems. Wireless local area networks (WLAN) and cellular systems are two major wireless access systems that are being targeted to achieve even higher data rates. Orthogonal frequency division multiplexing (OFDM) and multiple input multiple output (MIMO) have been recognized as effective ways to attain higher throughput for IEEE 802.11n [1] and 3G Long term evolution (LTE) [2]. Unfortunately, the recent advances in these techniques still lag the demands being made, so bandwidth of each carrier is being increased from one generation to the next [1, 2]. Another trend in wireless access systems is the rapid increase in the number of wireless devices. The total number of cellular phone subscribers reached 100 million at the end of December in 2007 in Japan and exceeded the number of land phone subscribers [3]. The number of WLAN chip shipments in each year is also increasing and it reached to 200 million in 2008 [4]. It is thought that people will start putting wireless devices on machines in the near future. This changes the usage of wireless access from people to people (P-to-P) or people to machine (P-to-M) communication to machine to machine (M-to-M) communication and a huge growth in this market can be anticipated [1, 2].The above trends bring new challenges for wireless technologies because both the larger bandwidth and the larger number of wireless devices may cause significant shortages in the frequency channels. One example is the ongoing standardization for very high throughput (VHT) wireless LANs in bands below 6 GHz, that is, IEEE802.11ac, which is expected to be the next standard after IEEE802.11n. It has been virtually agreed that IEEE802.11ac will double the maximum bandwidth of IEEE802.11n from 40 MHz to 80 MHz to achieve 1 Gbps throughput at the median access control (MAC) service access point (SAP) [5]. Since the microwave frequency band has been already assigned to various radio systems, it is difficult to expand the frequency bands allocated for wireless LANs into the microwave band. Thus, the number of available frequency channels would be half that of IEEE802.11n and is more likely that a frequency channel will be used at a nearby basic service set (BSS), which consists of access point (AP) and associated stations (STAs). Therefore, how APs and STAs behave in the overlapping cell among BSS is important [6].In the overlapping cell scenario, radio resources should be shared by multiple cells. There are three resources to be shared, time, frequency, and spatial resources. The first one, time resource sharing is realized by carrier sense multiple access collision avoidance (CSMA/CA) or request to send/clear to send (RTS/CTS) protocols [7, 8]. It allocates different time durations to each access to avoid inter-cell-interference (ICI). Dynamic resource sharing in the time domain is actualized by making transmission opportunity proportional to traffic load at each cell. The second one, frequency resource sharing, allocates a different frequency band to each cell to prevent intercell interference. The dynamic channel assignment (DCA) scheme was proposed to improve the spectrum efficiency [9]. The DCA concept has been extended to support the heterogeneous multiple radio system scenario and is considered as a type of cognitive radio technology. The drawback, the frequency domain method is the complexity of the resource allocation procedure. In the following, we will focus on the last radio resource, spatial resource, to improve the spectrum efficiency further.Compared to time and frequency resource sharing, spatial resources sharing research is relatively immature especially for the overlapping cell scenario. MIMO technology which uses spatial signal processing is employed by the latest wireless access standards such as 3 G long term evolution (LTE) [10] and IEEE802.11n [11]. It increases the channel capacity between one transmitter and one receiver by using spatial domain. MIMO technology has been extended to multiuser MIMO (MU-MIMO) to attain high channel capacity even for multiple simple wireless terminals [12, 13]. Many spatial resource sharing methods for MU-MIMO were proposed to take into account various QoS conditions for isolated cells but not for overlapping cells [14, 15]. On the other hand, ICI suppression using spatial domain technology, for example, beamforming or smart antennas, was extensively studied to shorten the frequency reuse distance [16, 17]. It improves the spectrum efficiency in total system level and can be interpreted as one approach for spatial resource sharing. Recently, femto-cell technology was developed to actualize umbrella cells where multiple femto-cells are created inside a macrocell by transmission power adjustments [18]. Although these techniques realize spatial resource sharing even in autonomous systems, they are effective only for static resource allocation, and it remains hard to respond to dynamic traffic changes in each cell. The cooperation of multiple APs was proposed to attain the highest spectrum efficiency for a multiple overlapping cell scenario [19, 20]. In this method, all APs are connected to an access controller which manages all spatial resources using the channel state information (CSI) of all AP- station (STA) links. Unfortunately, this approach cannot be applied to the general case, for example, overlapping cells in a WLAN, where multiple APs are connected to different wired networks. To the best of our knowledge, no detailed report has examined dynamic spatial resource sharing among multiple cells where each cell is connected to a different network. Thus, this paper focuses on this scenario and presents the throughput improvement obtained by spatial resource sharing for overlapping cells. In spatial resource sharing, AP allocates spatial resources to STAs if the spatial resources are not consumed by the other AP. The conventional AP waits for another time duration even when only one spatial stream is used at the overlapped cells. Therefore, spatial resource sharing for overlapped cell enables dynamic spatial resource allocation and further improvements in spectrum efficiency.In this paper, two scenarios (both based on the zero forcing method) for spatial resource sharing are considered. One is the primary-secondary AP scenario and the other is the cooperative AP scenario. To evaluate the effectiveness of these methods, a channel state information measurement experiment is conducted in a large office and8×4 MIMO OFDM channel matrices for 48 subcarriers are obtained using the short and long preambles based on the IEEE802.11a standard. Although the measurement environment is a large room, we consider the two-room scenario by separating two APs with a “virtual" wall. The simulation results confirm the potential of spatial resource sharing.This paper is organized as follows. Section2 describes eigenvector transmission and the impact of spatial resource sharing in channel capacity. In Section 3, we introduce the experimental setup and the measurement environment. Section 4 presents simulation results. Section 5 summarizes the paper.Throughout the paper, superscript * and superscriptH, denote the complex conjugate, and the Hermitian transposition, respectively. Term |A| is the determinant of A.


## 2. System Model

We consider a downlink MIMO system for a single AP and STA in the overlapping cell scenario. To evaluate the effectiveness of spatial resource sharing, we compare the two overlapping cell scenario to the single cells scenario using time resource sharing. In this section, we describe the channel conditions and two scenarios of spatial domain resource sharing; the primary-secondary AP scenario and the cooperative AP scenario. Furthermore, we focus on the CSI error and show the relationship between CSI and ICI.


### 2.1. Channel Model for Time Resource Sharing

It is assumed that the number of APs is two, each hostsUmobile stations (STAs) and each AP and STA have N transmit antennas and M receive antennas, respectively. We denote this as the N>Msystem. Here, transmission from  AP k, k = 1, 2, is considered. The channel state between AP k and STA i (being hosted by AP k) is represented by channel matrix Hk,i∈ℂM×N, k=1,2, and i=1,2,…,U. The Lk,i×1 transmit symbol vector for STA i, xk,i, is transmitted using transmission weight Wk,i∈ℂN×Lk,i. Lk,i is the number of data streams transmitted simultaneously to STA i from AP k. The signal vector received at STA i is given as
(1)yk,i=Hk,iWk,ixk,i+nk,i,
where nk,i∈ℂM×1 is the additive white Gaussian noise vector and the elements of nk,i are assumed to have a variance, σ2. In this paper, σ2 is set to be one for all STAs. Even if every STA has a different noise variance, we can consider the same situation by normalizing the norm of the channel matrix without loss of generality.


### 2.2. Channel Model for Spatial Resource Sharing

When spatial resource sharing is active, the two APs can transmit in the same time slot. The received signal vectors at STAi, which is communicating with AP 1, and at STA j, which is communicating with AP 2, are given as
(2)y1,i=H1,iW1,ix1,i+HI,2,iW2,jx2,j+n1,i,y2,j=H2,jW2,jx2,j+HI,1,jW1,ix1,i+n2,i,
where HI,l,i∈ℂN×M is the interference channel matrix between AP l and STA i of AP k, where l is 1 or 2 and l≠k. Therefore, HI,1,i and HI,2,j are the channel matrices between AP 1 and STAj of AP 2, and between AP 2 and STA i of AP 1, respectively.


### 2.3. Eigenvector Transmission

As the transmission weight for the time resource sharing scenario, we employ eigenvector transmission [21] and the water pouring strategies [22]. This is because these techniques maximize the mutual information when the channel state information is available at AP. In eigenvector transmission, the transmission weight at AP k for STA i is calculated as the eigenvectors of the correlation matrix, Hk,iHHk,i. By using singular value decomposition (SVD), the eigenvectors are obtained as the right singular vectors of Hk,i as
(3)Hk,i=Uk,i(𝚺k,i0)(Vk,i(s)Vk,i(n))H,
where Vk,i(s)∈ℂN×M and Vk,i(n)∈ℂN×(N-M) represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺k,i are the square roots of λk,1,λk,2,…,λk,M, which are the eigenvalues of Hk,iHHk,i. In eigenvector transmission, transmission weight Wk,i can be chosen as Lk,ivectors of Vk,i(s) corresponding to higher eigenvalues. Lk,i and the norm of each vectors of Wk,i are determined by water pouring strategies subject to power constraint, that is, trace(Wk,iHWk,i) is one. By using the right singular vectors as the transmission weight, high SNRs corresponding to the eigenvalues can be obtained. We define the transmission weight in eigenvector transmission as WE,k,i. In (3), Uk,i denotes the left singular vectors and corresponds to the reception weight at STA i in eigenvector transmission.


### 2.4. ZF Transmission for Interference AP

When there are two APs using the same frequency and the same time slot, the interference from the other AP degrades the transmission performance. Thus, we consider the transmission weight that prevents the interference to the other AP. In APk, the interference channel matrix for STA j of the other AP, AP l, is expressed as(4)HI,k,j=UI,k,j(𝚺I,k,j0)(VI,k,j(s)VI,k,j(n))H,
where VI,k,j(s)∈ℂN×M and VI,k,j(n)∈ℂN×(N-M) represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺I,k,j are the square roots of λk,1,λk,2,…,λk,M, which are the null space eigenvalues. To obtain the transmission weight that does not interfere with the transmission of AP l, the null space channel matrix, Hk,iVk,j(n) is decomposed by SVD to yield(5)Hk,iVI,k,j(n)=UN,k,i(𝚺N,k,j0)(VN,k,j(s)VN,k,j(n))H,
where VN,k,j(s)∈ℂ(N-M)×M and VN,k,j(n)∈ℂN-M×(N-2M) represent the null space right singular vectors for the signal space and the null space, respectively. In ZF transmission, the transmission weight Wk,i can be chosen as Lk,i vectors of VI,k,i(n)VN,k,i(s) corresponding to the higher eigenvalues of λN,k,i. Lk,i and the norm of each vector of Wk,i is determined by water pouring strategies using λN,k,i. The transmission weight is expressed as WZ,k,i.


### 2.5. Channel State Informationat AP And STA

The CSI is obtained at the transmitter and the receiver. We assume that the STA holds the perfect CSI while the CSI at the AP has some estimation error. The channel matrix obtained at APk and is expressed as
(6)H̅k,i=Hk,i+Ek,i,H̅I,k,j=HI,k,j+EI,k,j,
where Ek,i and EI,k,j are all i.i.d zero-mean complex Gaussian with variance of σe2. Thus, the transmission weight is calculated using the imperfect channel matrix, H̅k,i and H̅I,k,j.


### 2.6. Achievable Bit Rate

When two APs transmit signals in different time slots, that is, time resource sharing systems, the mutual information between APk and STA i is expressed using the eigenvector transmission weight as(7)CS,k,i=log2|IM+Hk,iWE,k,iWE,k,iHHkH|,
where k is 1 or 2 and i=1,2,…,U.In this scenario, the simultaneous transmission at both APs is avoided. CSMA/CA and RTS/CTS/ACQ in MAC enables this scenario.We describe the channel capacity in a spatial resource sharing system with two APs as(8)CM,i,j=log2|IM+H1,iW1,iW1,iHH1HIM+HI,2,iW2,jW2,jHHI,2,iH|+log2|IM+H2,jW2,jW2,jHH2,jHIM+HI,2,iW1,iW1,iHHI,2,jH|,
where i=1,2,…,U, and j=1,2,…,U. We consider two scenarios for spatial resource sharing. One is primary-secondary AP method based on zero forcing (PSZ) and the other is cooperative AP method based on zero forcing (CZ). In PSZ mode, AP k determines the transmission weight based on the eigenvector transmission using Vk,i(s) while AP l(l≠k) uses the transmission weight based on the ZF using VI,k,i(n)VN,k,i(s). Thus, the transmission of AP l suffers interference from the transmission of AP k and the signal power is degraded due to the null space beamforming, although the transmission of AP k is expected to have the high channel capacity, see (7), due to the suppressed interference at AP l. The achievable transmission bit rate in the PSZ method is given as(9)CPSZ,k,i,j=log2|IM+Hk,iWE,k,iWE,1,iHH1HIM+HI,2,iWZ,2,jWZ,2,jHHI,2,iH|+log2|IM+Hl,jWZ,2,jWZ,2,jHHl,jHIM+HI,l,iWE,k,iWE,k,iHHI,l,jH|,
where AP k(k=1,2) is the primary AP. If there is no channel estimation error at the AP, (9) is rewritten as(10)CPSZ,k,i,j=log2|IM+Hk,iWE,k,iWE,1,iHH1H|+log2|IM+Hl,jWZ,2,jWZ,2,jHHl,jHIM+HI,l,iWE,k,iWE,k,iHHI,l,jH|.In the cooperating mode, both APs uses the transmission weight based on ZF. This case is expected to yield the high capacity among two APs although the signal powers at the destination STAs are degraded due to ZF beamforming. The achievable transmission bit rate in CZ method is given as(11)CCZ,i,j=log2|IM+Hk,iWZ,k,iWZ,k,iHHk,iHIM+HI,k,iWZ,l,jWZ,l,jHHI,k,iH|+log2|IM+Hl,jWZ,l,jWZ,l,jHHl,jHIM+HI,l,iWZ,k,iWZ,k,iHHI,l,jH|.
If there is no channel estimation error at the AP, (11) is given as(12)CCZ,i,j=log2|IM+Hk,iWZ,k,iWZ,k,iHHk,iH|+log2|IM+Hl,jWZ,l,jWZ,l,jHHl,jH|.


### 2.7. Intercell Interference

In spatial resource sharing, the ICI determines the channel capacity in (9) and (11). Therefore, the ICI is analyzed by numerical approach. We define the variance of elements of the interference channel matrix, HI,k,i, as γI to show the characteristics of the ICI. When the eigenvector transmission is applied, the ICI power, IE, is expressed as(13)IE=trace(WE,k,iHHI,l,jHHI,l,jWE,k,i)=trace(WE,k,iHVZ,l,j(s)𝚺I,l,j(s)UI,l,jHUI,l,j𝚺I,l,j(s)VZ,l,j(s)HWE,k,i)=trace(WE,k,iHVZ,l,j(s)𝚺I,l,j(s)2VZ,l,j(s)HWE,k,i)=trace(AH𝚺I,l,j(s)2A),
where 𝚺I,l,j(s)∈ℂM×M is the diagonal matrix for the signal space and A=VZ,l,j(s)HWE,k,i. Since the VZ,l,j(s) is not correlate to WE,k,i, IE is determined by γI regardless of the channel estimation error.Then, the ICI power for ZF weight,IZ, is expressed as(14)IZ=trace(WZ,l,jHHI,l,jHHI,l,iWZ,l,j)=trace(V̅N,l,i(s)HV̅Z,l,i(n)HVZ,l,i(s)𝚺I,l,i(s)2VZ,l,i(s)HV̅Z,l,i(n)V̅N,l,i(s))=trace(BH𝚺I,l,i(s)2B),
where V̅Z,k,j(n)∈ℂN×(N-M) and V̅N,k,j(s)∈ℂ(N-M)×LK,j are the right singular vectors for null space and null space right singular vectors for signal space calculated by using the channel matrices with channel estimation error. B=VZ,l,i(s)HV̅Z,l,i(n)HV̅N,l,i(s). In the case without the channel estimation error, IZ=0 since VZ,k,j(s)HV̅Z,k,j(n)=0. Since the norm of B increases as the channel estimation error becomes large, IZ is affected by γI  and channel estimation error, σe2. The ratio of channel estimation error, σe2, to γI increases as γI decreases. Therefore, the norm of B and γI have inverse correlation. Figure 1 shows IZ versus γI when the estimation error, σe2, is set to be 0.5, 1.0, and 5.0 times the noise variance, σ2, of one. We can see that the local maximal value and γI of the local maximal become large the channel estimation error increases. When γI≫0 dB, ZF works well since IZ mitigation is proportional to the interference channel norm, γI. However, when γI is less than 5 dB, the transmission performance of spatial resource sharing based on ZF may be degraded. To estimate the realistic transmission performance, we measured the channel matrices, H, and the interference channel matrices, HI, in an actual indoor environment and evaluated the effectiveness of space resource sharing by using the measured channel.Figure 1
Intercell interference power versusγI.Figure 2
Experimental environment.


## 2.1. Channel Model for Time Resource Sharing

It is assumed that the number of APs is two, each hostsUmobile stations (STAs) and each AP and STA have N transmit antennas and M receive antennas, respectively. We denote this as the N>Msystem. Here, transmission from  AP k, k = 1, 2, is considered. The channel state between AP k and STA i (being hosted by AP k) is represented by channel matrix Hk,i∈ℂM×N, k=1,2, and i=1,2,…,U. The Lk,i×1 transmit symbol vector for STA i, xk,i, is transmitted using transmission weight Wk,i∈ℂN×Lk,i. Lk,i is the number of data streams transmitted simultaneously to STA i from AP k. The signal vector received at STA i is given as
(1)yk,i=Hk,iWk,ixk,i+nk,i,
where nk,i∈ℂM×1 is the additive white Gaussian noise vector and the elements of nk,i are assumed to have a variance, σ2. In this paper, σ2 is set to be one for all STAs. Even if every STA has a different noise variance, we can consider the same situation by normalizing the norm of the channel matrix without loss of generality.


## 2.2. Channel Model for Spatial Resource Sharing

When spatial resource sharing is active, the two APs can transmit in the same time slot. The received signal vectors at STAi, which is communicating with AP 1, and at STA j, which is communicating with AP 2, are given as
(2)y1,i=H1,iW1,ix1,i+HI,2,iW2,jx2,j+n1,i,y2,j=H2,jW2,jx2,j+HI,1,jW1,ix1,i+n2,i,
where HI,l,i∈ℂN×M is the interference channel matrix between AP l and STA i of AP k, where l is 1 or 2 and l≠k. Therefore, HI,1,i and HI,2,j are the channel matrices between AP 1 and STAj of AP 2, and between AP 2 and STA i of AP 1, respectively.


## 2.3. Eigenvector Transmission

As the transmission weight for the time resource sharing scenario, we employ eigenvector transmission [21] and the water pouring strategies [22]. This is because these techniques maximize the mutual information when the channel state information is available at AP. In eigenvector transmission, the transmission weight at AP k for STA i is calculated as the eigenvectors of the correlation matrix, Hk,iHHk,i. By using singular value decomposition (SVD), the eigenvectors are obtained as the right singular vectors of Hk,i as
(3)Hk,i=Uk,i(𝚺k,i0)(Vk,i(s)Vk,i(n))H,
where Vk,i(s)∈ℂN×M and Vk,i(n)∈ℂN×(N-M) represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺k,i are the square roots of λk,1,λk,2,…,λk,M, which are the eigenvalues of Hk,iHHk,i. In eigenvector transmission, transmission weight Wk,i can be chosen as Lk,ivectors of Vk,i(s) corresponding to higher eigenvalues. Lk,i and the norm of each vectors of Wk,i are determined by water pouring strategies subject to power constraint, that is, trace(Wk,iHWk,i) is one. By using the right singular vectors as the transmission weight, high SNRs corresponding to the eigenvalues can be obtained. We define the transmission weight in eigenvector transmission as WE,k,i. In (3), Uk,i denotes the left singular vectors and corresponds to the reception weight at STA i in eigenvector transmission.


## 2.4. ZF Transmission for Interference AP

When there are two APs using the same frequency and the same time slot, the interference from the other AP degrades the transmission performance. Thus, we consider the transmission weight that prevents the interference to the other AP. In APk, the interference channel matrix for STA j of the other AP, AP l, is expressed as(4)HI,k,j=UI,k,j(𝚺I,k,j0)(VI,k,j(s)VI,k,j(n))H,
where VI,k,j(s)∈ℂN×M and VI,k,j(n)∈ℂN×(N-M) represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺I,k,j are the square roots of λk,1,λk,2,…,λk,M, which are the null space eigenvalues. To obtain the transmission weight that does not interfere with the transmission of AP l, the null space channel matrix, Hk,iVk,j(n) is decomposed by SVD to yield(5)Hk,iVI,k,j(n)=UN,k,i(𝚺N,k,j0)(VN,k,j(s)VN,k,j(n))H,
where VN,k,j(s)∈ℂ(N-M)×M and VN,k,j(n)∈ℂN-M×(N-2M) represent the null space right singular vectors for the signal space and the null space, respectively. In ZF transmission, the transmission weight Wk,i can be chosen as Lk,i vectors of VI,k,i(n)VN,k,i(s) corresponding to the higher eigenvalues of λN,k,i. Lk,i and the norm of each vector of Wk,i is determined by water pouring strategies using λN,k,i. The transmission weight is expressed as WZ,k,i.


## 2.5. Channel State Informationat AP And STA

The CSI is obtained at the transmitter and the receiver. We assume that the STA holds the perfect CSI while the CSI at the AP has some estimation error. The channel matrix obtained at APk and is expressed as
(6)H̅k,i=Hk,i+Ek,i,H̅I,k,j=HI,k,j+EI,k,j,
where Ek,i and EI,k,j are all i.i.d zero-mean complex Gaussian with variance of σe2. Thus, the transmission weight is calculated using the imperfect channel matrix, H̅k,i and H̅I,k,j.


## 2.6. Achievable Bit Rate

When two APs transmit signals in different time slots, that is, time resource sharing systems, the mutual information between APk and STA i is expressed using the eigenvector transmission weight as(7)CS,k,i=log2|IM+Hk,iWE,k,iWE,k,iHHkH|,
where k is 1 or 2 and i=1,2,…,U.In this scenario, the simultaneous transmission at both APs is avoided. CSMA/CA and RTS/CTS/ACQ in MAC enables this scenario.We describe the channel capacity in a spatial resource sharing system with two APs as(8)CM,i,j=log2|IM+H1,iW1,iW1,iHH1HIM+HI,2,iW2,jW2,jHHI,2,iH|+log2|IM+H2,jW2,jW2,jHH2,jHIM+HI,2,iW1,iW1,iHHI,2,jH|,
where i=1,2,…,U, and j=1,2,…,U. We consider two scenarios for spatial resource sharing. One is primary-secondary AP method based on zero forcing (PSZ) and the other is cooperative AP method based on zero forcing (CZ). In PSZ mode, AP k determines the transmission weight based on the eigenvector transmission using Vk,i(s) while AP l(l≠k) uses the transmission weight based on the ZF using VI,k,i(n)VN,k,i(s). Thus, the transmission of AP l suffers interference from the transmission of AP k and the signal power is degraded due to the null space beamforming, although the transmission of AP k is expected to have the high channel capacity, see (7), due to the suppressed interference at AP l. The achievable transmission bit rate in the PSZ method is given as(9)CPSZ,k,i,j=log2|IM+Hk,iWE,k,iWE,1,iHH1HIM+HI,2,iWZ,2,jWZ,2,jHHI,2,iH|+log2|IM+Hl,jWZ,2,jWZ,2,jHHl,jHIM+HI,l,iWE,k,iWE,k,iHHI,l,jH|,
where AP k(k=1,2) is the primary AP. If there is no channel estimation error at the AP, (9) is rewritten as(10)CPSZ,k,i,j=log2|IM+Hk,iWE,k,iWE,1,iHH1H|+log2|IM+Hl,jWZ,2,jWZ,2,jHHl,jHIM+HI,l,iWE,k,iWE,k,iHHI,l,jH|.In the cooperating mode, both APs uses the transmission weight based on ZF. This case is expected to yield the high capacity among two APs although the signal powers at the destination STAs are degraded due to ZF beamforming. The achievable transmission bit rate in CZ method is given as(11)CCZ,i,j=log2|IM+Hk,iWZ,k,iWZ,k,iHHk,iHIM+HI,k,iWZ,l,jWZ,l,jHHI,k,iH|+log2|IM+Hl,jWZ,l,jWZ,l,jHHl,jHIM+HI,l,iWZ,k,iWZ,k,iHHI,l,jH|.
If there is no channel estimation error at the AP, (11) is given as(12)CCZ,i,j=log2|IM+Hk,iWZ,k,iWZ,k,iHHk,iH|+log2|IM+Hl,jWZ,l,jWZ,l,jHHl,jH|.


## 2.7. Intercell Interference

In spatial resource sharing, the ICI determines the channel capacity in (9) and (11). Therefore, the ICI is analyzed by numerical approach. We define the variance of elements of the interference channel matrix, HI,k,i, as γI to show the characteristics of the ICI. When the eigenvector transmission is applied, the ICI power, IE, is expressed as(13)IE=trace(WE,k,iHHI,l,jHHI,l,jWE,k,i)=trace(WE,k,iHVZ,l,j(s)𝚺I,l,j(s)UI,l,jHUI,l,j𝚺I,l,j(s)VZ,l,j(s)HWE,k,i)=trace(WE,k,iHVZ,l,j(s)𝚺I,l,j(s)2VZ,l,j(s)HWE,k,i)=trace(AH𝚺I,l,j(s)2A),
where 𝚺I,l,j(s)∈ℂM×M is the diagonal matrix for the signal space and A=VZ,l,j(s)HWE,k,i. Since the VZ,l,j(s) is not correlate to WE,k,i, IE is determined by γI regardless of the channel estimation error.Then, the ICI power for ZF weight,IZ, is expressed as(14)IZ=trace(WZ,l,jHHI,l,jHHI,l,iWZ,l,j)=trace(V̅N,l,i(s)HV̅Z,l,i(n)HVZ,l,i(s)𝚺I,l,i(s)2VZ,l,i(s)HV̅Z,l,i(n)V̅N,l,i(s))=trace(BH𝚺I,l,i(s)2B),
where V̅Z,k,j(n)∈ℂN×(N-M) and V̅N,k,j(s)∈ℂ(N-M)×LK,j are the right singular vectors for null space and null space right singular vectors for signal space calculated by using the channel matrices with channel estimation error. B=VZ,l,i(s)HV̅Z,l,i(n)HV̅N,l,i(s). In the case without the channel estimation error, IZ=0 since VZ,k,j(s)HV̅Z,k,j(n)=0. Since the norm of B increases as the channel estimation error becomes large, IZ is affected by γI  and channel estimation error, σe2. The ratio of channel estimation error, σe2, to γI increases as γI decreases. Therefore, the norm of B and γI have inverse correlation. Figure 1 shows IZ versus γI when the estimation error, σe2, is set to be 0.5, 1.0, and 5.0 times the noise variance, σ2, of one. We can see that the local maximal value and γI of the local maximal become large the channel estimation error increases. When γI≫0 dB, ZF works well since IZ mitigation is proportional to the interference channel norm, γI. However, when γI is less than 5 dB, the transmission performance of spatial resource sharing based on ZF may be degraded. To estimate the realistic transmission performance, we measured the channel matrices, H, and the interference channel matrices, HI, in an actual indoor environment and evaluated the effectiveness of space resource sharing by using the measured channel.Figure 1
Intercell interference power versusγI.Figure 2
Experimental environment.


## 3. Channel Condition

### 3.1. Measured Channel Matrix

We measured the channel matrices in an actual indoor environment using the testbed for MIMO-OFDM transmission. The measurement environment is the40×26×3 [m] room shown in Figure 2. We used the channel matrices measured in an actual environment to evaluate the transmission performance of spatial resource sharing systems.In the experiment, we used a circular array of eight antennas with element spacing of 1.0λ and a four-antenna linear array with element spacing of 0.5 λ as the transmit antennas and the receive antennas, respectively. Therefore, we obtained 8×4 MIMO channel matrices. We consider 8×4 and 8×2 MIMO systems and8×2 MIMO channel matrices are obtained using the center two receive antennas of the linear array. The AP was established on a 2.5 m pole and located at points AP 1, and AP 2 in Figure 2. The receive antenna array was attached to a laptop computer on a desk 0.7 m high that was placed at the star marks in Figure 2. The partitions are made of metal and partition height is 1.9 m. The each desk is separated by 1.4 m metal barriers.A block diagram of the experimental testbed is shown in Figure3 and the main parameters for this testbed are given in Table 1. The center radio frequency is 4.85 GHz and the OFDM signal is transmitted in 20 MHz bandwidth. The AP transmits the preamble based on the short and long preambles in the IEEE 802.11a standard [10]. The STA estimates the channel matrices of the 48 sub-carriers from the received signals at 30 STA positions. We assume that the left 15 STAs and right 15 STAs communicate with AP 1 and AP 2, respectively. Thus, the measured channel matrices at AP 1 corresponding to the right 15 STAs and the left 15 STAs are H1,1,H1,2,…,H1,15, and HI,1,1,HI,1,2,…,HI,1,15, respectively. In AP 2, H2,1,H2,2,…,H2,15 and HI,2,1,HI,2,2,…,HI,2,15, are obtained between AP 2 and the right STAs and left STAs, respectively.Table 1
Parameters of MIMO-OFDM testbed.
Number of antennas8 (Tx), 4 (Rx)Radio frequency4.85 GHzBandwidth20 MHzTotal transmission power10 dBmSensitivity-20 to -70 dBmSampling rate20 MHz (A/D), 80 MHz (D/A)Number of FFT points64Number of subcarriers48 (Information) + 4 (Pilot)Short preamble length0.8μsec×10=8μsecOFDM symbol length3.2× 2 μs + 1.6 μs (GI)Figure 3
Block diagram of the MIMO testbed.SNR distribution in an experimental environment corresponding to (a) AP 1 and (b) AP 2.
(a)(b)In this experiment, a virtual wall is considered between the AP 1’s STAs and AP 2’s STAs. Thus, we define the interference channel matrices asαHI,2,1.  α [dB] is the attenuation level of the virtual wall. When α=0 dB, we use measured channel matrix, HI,k,i as the interference channel matrix. By using α, we can evaluate the performance of spatial resource sharing corresponding to the distance between two APs or the attenuation level of the wall. The averaged SNRs at STA corresponding to the two APs are shown in Figures 4(a) and 4(b). We assume that the measured channel matrices are accurate regardless of their SNR since the measured channel matrices are obtained by averaging a sufficient number of channel matrices.


## 3.1. Measured Channel Matrix

We measured the channel matrices in an actual indoor environment using the testbed for MIMO-OFDM transmission. The measurement environment is the40×26×3 [m] room shown in Figure 2. We used the channel matrices measured in an actual environment to evaluate the transmission performance of spatial resource sharing systems.In the experiment, we used a circular array of eight antennas with element spacing of 1.0λ and a four-antenna linear array with element spacing of 0.5 λ as the transmit antennas and the receive antennas, respectively. Therefore, we obtained 8×4 MIMO channel matrices. We consider 8×4 and 8×2 MIMO systems and8×2 MIMO channel matrices are obtained using the center two receive antennas of the linear array. The AP was established on a 2.5 m pole and located at points AP 1, and AP 2 in Figure 2. The receive antenna array was attached to a laptop computer on a desk 0.7 m high that was placed at the star marks in Figure 2. The partitions are made of metal and partition height is 1.9 m. The each desk is separated by 1.4 m metal barriers.A block diagram of the experimental testbed is shown in Figure3 and the main parameters for this testbed are given in Table 1. The center radio frequency is 4.85 GHz and the OFDM signal is transmitted in 20 MHz bandwidth. The AP transmits the preamble based on the short and long preambles in the IEEE 802.11a standard [10]. The STA estimates the channel matrices of the 48 sub-carriers from the received signals at 30 STA positions. We assume that the left 15 STAs and right 15 STAs communicate with AP 1 and AP 2, respectively. Thus, the measured channel matrices at AP 1 corresponding to the right 15 STAs and the left 15 STAs are H1,1,H1,2,…,H1,15, and HI,1,1,HI,1,2,…,HI,1,15, respectively. In AP 2, H2,1,H2,2,…,H2,15 and HI,2,1,HI,2,2,…,HI,2,15, are obtained between AP 2 and the right STAs and left STAs, respectively.Table 1
Parameters of MIMO-OFDM testbed.
Number of antennas8 (Tx), 4 (Rx)Radio frequency4.85 GHzBandwidth20 MHzTotal transmission power10 dBmSensitivity-20 to -70 dBmSampling rate20 MHz (A/D), 80 MHz (D/A)Number of FFT points64Number of subcarriers48 (Information) + 4 (Pilot)Short preamble length0.8μsec×10=8μsecOFDM symbol length3.2× 2 μs + 1.6 μs (GI)Figure 3
Block diagram of the MIMO testbed.SNR distribution in an experimental environment corresponding to (a) AP 1 and (b) AP 2.
(a)(b)In this experiment, a virtual wall is considered between the AP 1’s STAs and AP 2’s STAs. Thus, we define the interference channel matrices asαHI,2,1.  α [dB] is the attenuation level of the virtual wall. When α=0 dB, we use measured channel matrix, HI,k,i as the interference channel matrix. By using α, we can evaluate the performance of spatial resource sharing corresponding to the distance between two APs or the attenuation level of the wall. The averaged SNRs at STA corresponding to the two APs are shown in Figures 4(a) and 4(b). We assume that the measured channel matrices are accurate regardless of their SNR since the measured channel matrices are obtained by averaging a sufficient number of channel matrices.


## 4. Numerical Results

### 4.1. Achievable Transmission Bit Rate for i.i.d Channel

First, we consider thatHk,i is a complex Gaussian variable with zero mean (random i.i.d.). The variance of elements of Hk,i, γS, is set to be 30 or 10 dB, and the variance of elements of HI,k,i, γI, is determined from -5 to 30 dB. Since we assumed a noise variance of one, γS and γI express the expectation of the received signal to noise ratio (SNR) and interference to noise ratio (INR). Hereinafter, we take γs and γI as the SNR and INR, respectively. The achievable transmission bit rate corresponding to γI is calculated as the median value of 1,000 trials.Figure5(a) plots the median value of the achievable transmission bit rate for 8×4 MIMO systems versus the INR when the SNR is set to be 30 dB. The achievable transmission bit rate for the eigenvector transmission in the time resource sharing scenario and two spatial resource sharing scenarios, PSZ and CZ methods, are shown as CS, CPSZ, and CCZ, respectively. The solid, dashed, and dotted lines represent the achievable transmission bit rate without channel estimation error and with channel estimation error, σe2=1 and 5, respectively. It is found that the spatial resource sharing systems have much higher achievable transmission bit rate than that in time resource sharing systems. When the INR is 30 dB, CCZ is 1.72 times greater than CS. When the INR is less than 2.8 dB, CPSZ without channel estimation error outperforms CCZ without channel estimation error. When there are channel estimation error, the achievable transmission bit rates in spatial resource sharing degrade while the degradation by the channel estimation error in CS is negligible. We can see that the intersection of CPSZ and CCZ becomes larger as channel estimation error increases. The range where CPSZ outperforms CCZ becomes large with large channel estimation error. When there is no channel estimation error, the achievable transmission bit rate of the primary AP in PSZ equals that in CS. Therefore, the difference between CPSZ and CS denotes the achievable transmission bit rate of the secondary AP in PSZ. Since the interference from the primary AP decreases as the INR becomes small, the achievable transmission bit rate in PSZ increases.Median value of achievable transmission bit rate versus INR for8×4 MIMO systems  (a) when SNR is 30 dB and (b) when SNR is 10 dB.
(a)(b)Figure5(b) plots the median value of the achievable transmission bit rate when SNR is 10 dB. In Figure 5(b), CCZ is 1.42 times greater than CS for the INR are 30 dB. The intersection of CPSZ and CCZ with channel estimation error decreases compared to that in Figure 5(a). We can see that the local minimal value of CCZ with channel estimation error in Figures 5(a) and 5(b) corresponds to the local maximal of Iz in Figure 1 and that the degradation is large when the SNR is small.Figures6(a) and 6(b) plot that the median values of the achievable transmission bit rate for 8×2 MIMO systems for SNR values of 30 dB and 10 dB, respectively. Figures 6(a) and 6(b) shows that CCZ is 1.91 times and 1.80 times greater than CS when the INR is 30 dB and 10 dB, respectively. Spatial resource sharing is more effective in 8×2 MIMO systems than in 8×4 MIMO systems. This is because the fewer receive antennas of the STA corresponding to the interference channel matrix increases the dimension of VI,k,j(n)∈ℂN×(N-M) in (4). VI,k,j(n) with large dimension values prevents the null space eigenvalues in (5) from decreasing compared to the eigenvalues in (3).Median value of achievable transmission bit rate versus INR for8×2 MIMO systems (a) when SNR is 30 dB and (b) when SNR is 10 dB.
(a)(b)


### 4.2. Achievable Transmission Bit Rate for Indoor Environment

The achievable transmission bit rate is calculated using 2 (AP positions)× 48 (subcarriers) × 10 (MS positions) measured channel matrices. Figures 7 and 8 show the cumulative probability of the achievable transmission bit rate in 8×4 and 8×2 MIMO systems. The solid, dashed, and dotted lines denote the achievable transmission bit rate with channel estimation error, σe2=0, σe2=1, and σe2=5, respectively. In this section, we does not use the virtual wall attenuation, α=0 [dB]. In 8×4 MIMO systems without the channel estimation error, the median values of CCZ and CSPZ are 1.59 and 1.38 times greater than that of CS, respectively. The median values of CCZ and CSPZ in 8×2 MIMO systems without channel estimation error are 1.90 and 1.51 times greater than that of CS, respectively. The degradation in the achievable transmission bit rate due to the channel estimation error in 8×4 MIMO systems is larger than that in 8×2 MIMO systems. Figures 7 and 8 show that the median values of CCZ and CPSZ in 8×4 (8×2) MIMO systems with σe2 of one and five are 1.41 (1.74) and 1.19 (1.51) times greater than that of CS. The decrease in CCZ due to the channel estimation error is large compared to the results in Figures 5 and 6. It is found that the spatial resource sharing with large channel estimation error, σe2 of one or five, high achievable transmission bit rates are obtained compared to CS.Figure 7
CDF of achievable bit rate  using measured8×4 channel matrix with α=0.Figure 8
CDF of achievable bit rate  using measured8×2 channel matrix with α=0.


### 4.3. Virtual Wall Attenuation

Figures9 and 10 show the median value of the achievable transmission bit rate versus the virtual wall attenuation factor, α, for 8×4 and 8×2 MIMO systems, respectively. The tendencies of Figures 9 and 10 are similar to CPSZ and CCZ of Figures 5 and 6. CPSZ  becomes large as the virtual wall attenuation factor decreases. In 8×4 MIMO systems without channel estimation error, CPSZ outperforms CCZ when α is less than -10 dB. As the channel estimation error increases, the intersection of CPSZ and CCZ increases. When there are large channel estimation error, PSZ method becomes effective compared to CZ method.Figure 9
Median value of achievable bit rate using measured8×4 channel matrices.Figure 10
Median value of achievable bit rate using measured8×2 channel matrix.In8×2 MIMO systems, CZ method is effective. When the estimation error, σe2, is one, CCZ is greater than CPSZ when α is larger than -15 dB. Although the spatial resource sharing is affected by channel estimation error, it is found that CZ and PSZ method outperforms time resource sharing method even though there are channel estimation error whose variance, σe2, is less than five.Although Figures5 and 6 show the local minimum points of CCZ corresponding to the local maximum interference power (see Figure 1), CCZ in Figures 9 and 10 has the local minimum points around α=0. This is because there are gaps between the expectations of the channel matrix norm and interference channel matrix norm as shown in Figures 4(a) and 4(b), and the eigenvalue distribution in an actual environment channel is different from that in random i.i.d. channel. It is found that the primary secondary AP is robust against CSI error compared with the cooperative AP scenario, and CPSZ and CCZ outperform CCZ even when α=0.


## 4.1. Achievable Transmission Bit Rate for i.i.d Channel

First, we consider thatHk,i is a complex Gaussian variable with zero mean (random i.i.d.). The variance of elements of Hk,i, γS, is set to be 30 or 10 dB, and the variance of elements of HI,k,i, γI, is determined from -5 to 30 dB. Since we assumed a noise variance of one, γS and γI express the expectation of the received signal to noise ratio (SNR) and interference to noise ratio (INR). Hereinafter, we take γs and γI as the SNR and INR, respectively. The achievable transmission bit rate corresponding to γI is calculated as the median value of 1,000 trials.Figure5(a) plots the median value of the achievable transmission bit rate for 8×4 MIMO systems versus the INR when the SNR is set to be 30 dB. The achievable transmission bit rate for the eigenvector transmission in the time resource sharing scenario and two spatial resource sharing scenarios, PSZ and CZ methods, are shown as CS, CPSZ, and CCZ, respectively. The solid, dashed, and dotted lines represent the achievable transmission bit rate without channel estimation error and with channel estimation error, σe2=1 and 5, respectively. It is found that the spatial resource sharing systems have much higher achievable transmission bit rate than that in time resource sharing systems. When the INR is 30 dB, CCZ is 1.72 times greater than CS. When the INR is less than 2.8 dB, CPSZ without channel estimation error outperforms CCZ without channel estimation error. When there are channel estimation error, the achievable transmission bit rates in spatial resource sharing degrade while the degradation by the channel estimation error in CS is negligible. We can see that the intersection of CPSZ and CCZ becomes larger as channel estimation error increases. The range where CPSZ outperforms CCZ becomes large with large channel estimation error. When there is no channel estimation error, the achievable transmission bit rate of the primary AP in PSZ equals that in CS. Therefore, the difference between CPSZ and CS denotes the achievable transmission bit rate of the secondary AP in PSZ. Since the interference from the primary AP decreases as the INR becomes small, the achievable transmission bit rate in PSZ increases.Median value of achievable transmission bit rate versus INR for8×4 MIMO systems  (a) when SNR is 30 dB and (b) when SNR is 10 dB.
(a)(b)Figure5(b) plots the median value of the achievable transmission bit rate when SNR is 10 dB. In Figure 5(b), CCZ is 1.42 times greater than CS for the INR are 30 dB. The intersection of CPSZ and CCZ with channel estimation error decreases compared to that in Figure 5(a). We can see that the local minimal value of CCZ with channel estimation error in Figures 5(a) and 5(b) corresponds to the local maximal of Iz in Figure 1 and that the degradation is large when the SNR is small.Figures6(a) and 6(b) plot that the median values of the achievable transmission bit rate for 8×2 MIMO systems for SNR values of 30 dB and 10 dB, respectively. Figures 6(a) and 6(b) shows that CCZ is 1.91 times and 1.80 times greater than CS when the INR is 30 dB and 10 dB, respectively. Spatial resource sharing is more effective in 8×2 MIMO systems than in 8×4 MIMO systems. This is because the fewer receive antennas of the STA corresponding to the interference channel matrix increases the dimension of VI,k,j(n)∈ℂN×(N-M) in (4). VI,k,j(n) with large dimension values prevents the null space eigenvalues in (5) from decreasing compared to the eigenvalues in (3).Median value of achievable transmission bit rate versus INR for8×2 MIMO systems (a) when SNR is 30 dB and (b) when SNR is 10 dB.
(a)(b)


## 4.2. Achievable Transmission Bit Rate for Indoor Environment

The achievable transmission bit rate is calculated using 2 (AP positions)× 48 (subcarriers) × 10 (MS positions) measured channel matrices. Figures 7 and 8 show the cumulative probability of the achievable transmission bit rate in 8×4 and 8×2 MIMO systems. The solid, dashed, and dotted lines denote the achievable transmission bit rate with channel estimation error, σe2=0, σe2=1, and σe2=5, respectively. In this section, we does not use the virtual wall attenuation, α=0 [dB]. In 8×4 MIMO systems without the channel estimation error, the median values of CCZ and CSPZ are 1.59 and 1.38 times greater than that of CS, respectively. The median values of CCZ and CSPZ in 8×2 MIMO systems without channel estimation error are 1.90 and 1.51 times greater than that of CS, respectively. The degradation in the achievable transmission bit rate due to the channel estimation error in 8×4 MIMO systems is larger than that in 8×2 MIMO systems. Figures 7 and 8 show that the median values of CCZ and CPSZ in 8×4 (8×2) MIMO systems with σe2 of one and five are 1.41 (1.74) and 1.19 (1.51) times greater than that of CS. The decrease in CCZ due to the channel estimation error is large compared to the results in Figures 5 and 6. It is found that the spatial resource sharing with large channel estimation error, σe2 of one or five, high achievable transmission bit rates are obtained compared to CS.Figure 7
CDF of achievable bit rate  using measured8×4 channel matrix with α=0.Figure 8
CDF of achievable bit rate  using measured8×2 channel matrix with α=0.


## 4.3. Virtual Wall Attenuation

Figures9 and 10 show the median value of the achievable transmission bit rate versus the virtual wall attenuation factor, α, for 8×4 and 8×2 MIMO systems, respectively. The tendencies of Figures 9 and 10 are similar to CPSZ and CCZ of Figures 5 and 6. CPSZ  becomes large as the virtual wall attenuation factor decreases. In 8×4 MIMO systems without channel estimation error, CPSZ outperforms CCZ when α is less than -10 dB. As the channel estimation error increases, the intersection of CPSZ and CCZ increases. When there are large channel estimation error, PSZ method becomes effective compared to CZ method.Figure 9
Median value of achievable bit rate using measured8×4 channel matrices.Figure 10
Median value of achievable bit rate using measured8×2 channel matrix.In8×2 MIMO systems, CZ method is effective. When the estimation error, σe2, is one, CCZ is greater than CPSZ when α is larger than -15 dB. Although the spatial resource sharing is affected by channel estimation error, it is found that CZ and PSZ method outperforms time resource sharing method even though there are channel estimation error whose variance, σe2, is less than five.Although Figures5 and 6 show the local minimum points of CCZ corresponding to the local maximum interference power (see Figure 1), CCZ in Figures 9 and 10 has the local minimum points around α=0. This is because there are gaps between the expectations of the channel matrix norm and interference channel matrix norm as shown in Figures 4(a) and 4(b), and the eigenvalue distribution in an actual environment channel is different from that in random i.i.d. channel. It is found that the primary secondary AP is robust against CSI error compared with the cooperative AP scenario, and CPSZ and CCZ outperform CCZ even when α=0.


## 5. Conclusion

We evaluated the transmission performance in spatial resource sharing. This paper introduced the primary-secondary AP scenario based on zero forcing (PSZ) and cooperative AP scenario based on zero forcing (CZ). Simulation results clarify the difference of applicability domain of these scenarios and the achievable transmission bit rate improvement compared to time domain resource sharing scenario. By using the channel matrices measured in an actual indoor environment, CZ and PSZ methods showed that they yielded 1.59 (1.90) times and 1.38 (1.51) times the achievable transmission bit rate of the time domain resource sharing system for8×4 MIMO (8×2 MIMO) systems when there is no channel estimation error. Even though we considered large estimation error, σe2 of one, the median values of CCZ and CPSZ in 8×4 MIMO (8×2 MIMO) systems with σe2 of one and five were 1.41 (1.74) and 1.19 (1.51) times greater than that of CS. By using a virtual wall attenuation factor, it is found that CZ method is effective in the case where mobile stations (STAs) have small number of the receive antennas and the norm of interference channel matrix is large while PSZ method outperforms CZ method when the norm of interference channel matrix becomes small and CSI error increases. We confirmed that spatial resource sharing is very attractive for the overlapping cell scenario.



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*Source: 642542-2010-03-24.xml*