Spatial Domain Resource Sharing for Overlapping Cells in Indoor Environment

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.

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 and 8×4 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. Section 2 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 superscript H, 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 hosts U mobile 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 𝐇_𝑘,𝑖∈ℂ^𝑀×𝑁, 𝑘=1,2, and 𝑖=1,2,…,𝑈. The 𝐿_𝑘,𝑖×1 transmit symbol vector for STA 𝑖, 𝐱_𝑘,𝑖, is transmitted using transmission weight 𝐖_𝑘,𝑖∈ℂ^{𝑁×𝐿𝑘,𝑖}. 𝐿_𝑘,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 𝐲_𝑘,𝑖=𝐇_𝑘,𝑖𝐖_𝑘,𝑖𝐱_𝑘,𝑖+𝐧_𝑘,𝑖, (1) where 𝐧_𝑘,𝑖∈ℂ^𝑀×1 is the additive white Gaussian noise vector and the elements of 𝐧_𝑘,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 STA 𝑖, which is communicating with AP 1, and at STA 𝑗, which is communicating with AP 2, are given as 𝐲_1,𝑖=𝐇_1,𝑖𝐖_1,𝑖𝐱_1,𝑖+𝐇_I,2,𝑖𝐖_2,𝑗𝐱_2,𝑗+𝐧_1,𝑖,𝐲_2,𝑗=𝐇_2,𝑗𝐖_2,𝑗𝐱_2,𝑗+𝐇_I,1,𝑗𝐖_1,𝑖𝐱_1,𝑖+𝐧_2,𝑖, (2) where 𝐇_I,𝑙,𝑖∈ℂ^𝑁×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, 𝐇_I,1,𝑖 and 𝐇_I,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, 𝐇^𝐻_𝑘,𝑖𝐇_𝑘,𝑖. By using singular value decomposition (SVD), the eigenvectors are obtained as the right singular vectors of 𝐇_𝑘,𝑖 as 𝐇_𝑘,𝑖=𝐔_𝑘,𝑖𝚺_𝑘,𝑖𝟎𝐕^(s)_𝑘,𝑖𝐕⁽ⁿ⁾_𝑘,𝑖^𝐻, (3) where 𝐕^(s)_𝑘,𝑖∈ℂ^𝑁×𝑀 and 𝐕^(𝑛)_𝑘,𝑖∈ℂ^{𝑁×(𝑁−𝑀)} represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺_𝑘,𝑖 are the square roots of 𝜆_𝑘,1,𝜆_𝑘,2,…,𝜆_𝑘,𝑀, which are the eigenvalues of 𝐇^𝐻_𝑘,𝑖𝐇_𝑘,𝑖. In eigenvector transmission, transmission weight 𝐖_𝑘,𝑖 can be chosen as 𝐿_𝑘,𝑖vectors of 𝐕^(s)_𝑘,𝑖 corresponding to higher eigenvalues. 𝐿_𝑘,𝑖 and the norm of each vectors of 𝐖_𝑘,𝑖 are determined by water pouring strategies subject to power constraint, that is, trace(𝐖^𝐻_𝑘,𝑖𝐖_𝑘,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 𝐖_E,𝑘,𝑖. In (3), 𝐔_𝑘,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 AP 𝑘, the interference channel matrix for STA 𝑗 of the other AP, AP 𝑙, is expressed as

𝐇_I,𝑘,𝑗=𝐔_I,𝑘,𝑗𝚺_I,𝑘,𝑗𝟎𝐕^(s)_I,𝑘,𝑗𝐕⁽ⁿ⁾_I,𝑘,𝑗^𝐻, (4) where 𝐕^(s)_I,𝑘,𝑗∈ℂ^𝑁×𝑀 and 𝐕⁽ⁿ⁾_I,𝑘,𝑗∈ℂ^{𝑁×(𝑁−𝑀)} represent the right singular vectors for the signal space and the null space, respectively. The diagonal elements of 𝚺_I,𝑘,𝑗 are the square roots of 𝜆_𝑘,1,𝜆_𝑘,2,…,𝜆_𝑘,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, 𝐇_𝑘,𝑖𝐕⁽ⁿ⁾_𝑘,𝑗 is decomposed by SVD to yield

𝐇_𝑘,𝑖𝐕⁽ⁿ⁾_I,𝑘,𝑗=𝐔_N,𝑘,𝑖𝚺_N,𝑘,𝑗𝟎𝐕^(s)_N,𝑘,𝑗𝐕⁽ⁿ⁾_N,𝑘,𝑗^𝐻, (5) where 𝐕^(𝑠)_N,𝑘,𝑗∈ℂ^{(𝑁−𝑀)×𝑀} and 𝐕^(𝑛)_N,𝑘,𝑗∈ℂ^{𝑁−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 𝐖_𝑘,𝑖 can be chosen as 𝐿_𝑘,𝑖 vectors of 𝐕^(𝑛)_I,𝑘,𝑖𝐕^(𝑠)_N,𝑘,𝑖 corresponding to the higher eigenvalues of 𝜆_N,𝑘,𝑖. 𝐿_𝑘,𝑖 and the norm of each vector of 𝐖_𝑘,𝑖 is determined by water pouring strategies using 𝜆_N,𝑘,𝑖. The transmission weight is expressed as 𝐖_Z,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 AP 𝑘 and is expressed as 𝐇_𝑘,𝑖=𝐇_𝑘,𝑖+𝐄_𝑘,𝑖,𝐇_I,𝑘,𝑗=𝐇_I,𝑘,𝑗+𝐄_I,𝑘,𝑗, (6) where 𝐄_𝑘,𝑖 and 𝐄_I,𝑘,𝑗 are all i.i.d zero-mean complex Gaussian with variance of 𝜎²_𝑒. Thus, the transmission weight is calculated using the imperfect channel matrix, 𝐇_𝑘,𝑖 and 𝐇_I,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 AP 𝑘 and STA 𝑖 is expressed using the eigenvector transmission weight as

𝐶_S,𝑘,𝑖=log₂|𝐈_𝑀+𝐇_𝑘,𝑖𝐖_E,𝑘,𝑖𝐖^𝐻_E,𝑘,𝑖𝐇^𝐻_𝑘|, (7) 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

𝐶_M,𝑖,𝑗=log₂|𝐈_𝑀+𝐇_1,𝑖𝐖_1,𝑖𝐖^𝐻_1,𝑖𝐇^𝐻₁𝐈_𝑀+𝐇_I,2,𝑖𝐖_2,𝑗𝐖^𝐻_2,𝑗𝐇^𝐻_I,2,𝑖|+log₂|𝐈_𝑀+𝐇_2,𝑗𝐖_2,𝑗𝐖^𝐻_2,𝑗𝐇^𝐻_2,𝑗𝐈_𝑀+𝐇_I,2,𝑖𝐖_1,𝑖𝐖^𝐻_1,𝑖𝐇^𝐻_I,2,𝑗|, (8) 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 𝐕^(𝑠)_𝑘,𝑖 while AP 𝑙(𝑙≠𝑘) uses the transmission weight based on the ZF using 𝐕^(𝑛)_I,𝑘,𝑖𝐕^(𝑠)_N,𝑘,𝑖. 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

𝐶_{PSZ,𝑘,𝑖,𝑗}=log₂|𝐈_𝑀+𝐇_𝑘,𝑖𝐖_E,𝑘,𝑖𝐖^𝐻_E,1,𝑖𝐇^𝐻₁𝐈_𝑀+𝐇_I,2,𝑖𝐖_Z,2,𝑗𝐖^𝐻_Z,2,𝑗𝐇^𝐻_I,2,𝑖|+log₂|𝐈_𝑀+𝐇_𝑙,𝑗𝐖_Z,2,𝑗𝐖^𝐻_Z,2,𝑗𝐇^𝐻_𝑙,𝑗𝐈_𝑀+𝐇_I,𝑙,𝑖𝐖_E,𝑘,𝑖𝐖^𝐻_E,𝑘,𝑖𝐇^𝐻_I,𝑙,𝑗|, (9) where AP 𝑘(𝑘=1,2) is the primary AP. If there is no channel estimation error at the AP, (9) is rewritten as

𝐶_{PSZ,𝑘,𝑖,𝑗}=log₂|𝐈_𝑀+𝐇_𝑘,𝑖𝐖_E,𝑘,𝑖𝐖^𝐻_E,1,𝑖𝐇^𝐻₁|+log₂|𝐈_𝑀+𝐇_𝑙,𝑗𝐖_Z,2,𝑗𝐖^𝐻_Z,2,𝑗𝐇^𝐻_𝑙,𝑗𝐈_𝑀+𝐇_I,𝑙,𝑖𝐖_E,𝑘,𝑖𝐖^𝐻_E,𝑘,𝑖𝐇^𝐻_I,𝑙,𝑗|. (10)

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

𝐶_CZ,𝑖,𝑗=log₂|𝐈_𝑀+𝐇_𝑘,𝑖𝐖_Z,𝑘,𝑖𝐖^𝐻_Z,𝑘,𝑖𝐇^𝐻_𝑘,𝑖𝐈_𝑀+𝐇_I,𝑘,𝑖𝐖_Z,𝑙,𝑗𝐖^𝐻_Z,𝑙,𝑗𝐇^𝐻_I,𝑘,𝑖|+log₂|𝐈_𝑀+𝐇_𝑙,𝑗𝐖_Z,𝑙,𝑗𝐖^𝐻_Z,𝑙,𝑗𝐇^𝐻_𝑙,𝑗𝐈_𝑀+𝐇_I,𝑙,𝑖𝐖_Z,𝑘,𝑖𝐖^𝐻_Z,𝑘,𝑖𝐇^𝐻_I,𝑙,𝑗|. (11) If there is no channel estimation error at the AP, (11) is given as

𝐶_CZ,𝑖,𝑗=log₂|𝐈_𝑀+𝐇_𝑘,𝑖𝐖_Z,𝑘,𝑖𝐖^𝐻_Z,𝑘,𝑖𝐇^𝐻_𝑘,𝑖|+log₂|𝐈_𝑀+𝐇_𝑙,𝑗𝐖_Z,𝑙,𝑗𝐖^𝐻_Z,l,𝑗𝐇^𝐻_𝑙,𝑗|. (12)

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, 𝐇_I,𝑘,𝑖, as 𝛾_I to show the characteristics of the ICI. When the eigenvector transmission is applied, the ICI power, 𝐼_𝐸, is expressed as

𝐼_E=trace(𝐖^𝐻_E,𝑘,𝑖𝐇^𝐻_I,𝑙,𝑗𝐇_I,𝑙,𝑗𝐖_E,𝑘,𝑖)=trace(𝐖^𝐻_E,𝑘,𝑖𝐕^(𝑠)_Z,𝑙,𝑗𝚺^(𝑠)_I,𝑙,𝑗𝐔^𝐻_I,𝑙,𝑗𝐔_I,𝑙,𝑗𝚺^(𝑠)_I,𝑙,𝑗𝐕^(𝑠)𝐻_Z,𝑙,𝑗𝐖_E,𝑘,𝑖)=trace(𝐖^𝐻_E,𝑘,𝑖𝐕^(𝑠)_Z,𝑙,𝑗𝚺^(𝑠)2_I,𝑙,𝑗𝐕^(𝑠)𝐻_Z,𝑙,𝑗𝐖_E,𝑘,𝑖)=trace(𝐀^𝐻𝚺^(𝑠)2_I,𝑙,𝑗𝐀), (13) where 𝚺^(𝑠)_I,𝑙,𝑗∈ℂ^𝑀×𝑀 is the diagonal matrix for the signal space and 𝐀=𝐕^(𝑠)𝐻_Z,𝑙,𝑗𝐖_E,𝑘,𝑖. Since the 𝐕^(𝑠)_Z,𝑙,𝑗 is not correlate to 𝐖_E,𝑘,𝑖, 𝐼_E is determined by 𝛾_I regardless of the channel estimation error.

Then, the ICI power for ZF weight, 𝐼_Z, is expressed as

𝐼_Z=trace(𝐖^𝐻_Z,𝑙,𝑗𝐇^𝐻_I,𝑙,𝑗𝐇_I,𝑙,𝑖𝐖_Z,𝑙,𝑗)=trace(𝐕^(𝑠)𝐻_N,𝑙,𝑖𝐕^(𝑛)𝐻_Z,𝑙,𝑖𝐕^(𝑠)_Z,𝑙,𝑖𝚺^(𝑠)2_I,𝑙,𝑖𝐕^(𝑠)𝐻_Z,𝑙,𝑖𝐕^(𝑛)_Z,𝑙,𝑖𝐕^(𝑠)_N,𝑙,𝑖)=trace(𝐁^𝐻𝚺^(𝑠)2_I,𝑙,𝑖𝐁), (14) where 𝐕^(𝑛)_Z,𝑘,𝑗∈ℂ^{𝑁×(𝑁−𝑀)} and 𝐕^(𝑠)_N,𝑘,𝑗∈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=𝐕^(𝑠)𝐻_Z,𝑙,𝑖𝐕^(𝑛)𝐻_Z,𝑙,𝑖𝐕^(𝑠)_N,𝑙,𝑖. In the case without the channel estimation error, 𝐼_Z=0 since 𝐕^(𝑠)𝐻_Z,𝑘,𝑗𝐕^(𝑛)_Z,𝑘,𝑗=𝟎. Since the norm of 𝐁 increases as the channel estimation error becomes large, 𝐼_Z is affected by 𝛾_I and channel estimation error, 𝜎²_𝑒. The ratio of channel estimation error, 𝜎²_𝑒, to 𝛾_I increases as 𝛾_I decreases. Therefore, the norm of 𝐁 and 𝛾_I have inverse correlation. Figure 1 shows 𝐼_Z versus 𝛾_I when the estimation error, 𝜎²_𝑒, 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 𝛾_I of the local maximal become large the channel estimation error increases. When 𝛾_I≫0 dB, ZF works well since 𝐼_Z mitigation is proportional to the interference channel norm, 𝛾_I. However, when 𝛾_I 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, 𝐇_I, in an actual indoor environment and evaluated the effectiveness of space resource sharing by using the measured channel.

Figure 1 

Intercell interference power versus 𝛾I.

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 the 40×26×3 [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 1.0 λ 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 Figure 3 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 𝐇_1,1,𝐇_1,2,…,𝐇_1,15, and 𝐇_I,1,1,𝐇_I,1,2,…,𝐇_I,1,15, respectively. In AP 2, 𝐇_2,1,𝐇_2,2,…,𝐇_2,15 and 𝐇_I,2,1,𝐇_I,2,2,…,𝐇_I,2,15, are obtained between AP 2 and the right STAs and left STAs, respectively.

Table 1 

Parameters of MIMO-OFDM testbed.

Figure 3 

Block diagram of the MIMO testbed.

(a)

(b)

Figure 4 

SNR distribution in an experimental environment corresponding to (a) AP 1 and (b) AP 2.

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 as 𝛼𝐇_I,2,1.  𝛼 [dB] is the attenuation level of the virtual wall. When 𝛼=0 dB, we use measured channel matrix, 𝐇_I,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 that 𝐇_𝑘,𝑖 is a complex Gaussian variable with zero mean (random i.i.d.). The variance of elements of 𝐇_𝑘,𝑖, 𝛾_S, is set to be 30 or 10 dB, and the variance of elements of 𝐇_I,𝑘,𝑖, 𝛾_I, is determined from −5 to 30 dB. Since we assumed a noise variance of one, 𝛾_S and 𝛾_I express the expectation of the received signal to noise ratio (SNR) and interference to noise ratio (INR). Hereinafter, we take 𝛾_s and 𝛾_I as the SNR and INR, respectively. The achievable transmission bit rate corresponding to 𝛾_I is calculated as the median value of 1,000 trials.

Figure 5(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 𝐶_S, 𝐶_PSZ, and 𝐶_CZ, respectively. The solid, dashed, and dotted lines represent the achievable transmission bit rate without channel estimation error and with channel estimation error, 𝜎²_𝑒=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, 𝐶_CZ is 1.72 times greater than 𝐶_𝑆. When the INR is less than 2.8 dB, 𝐶_PSZ without channel estimation error outperforms 𝐶_CZ 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 𝐶_S is negligible. We can see that the intersection of 𝐶_PSZ and 𝐶_CZ becomes larger as channel estimation error increases. The range where 𝐶_PSZ outperforms 𝐶_CZ 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 𝐶_S. Therefore, the difference between 𝐶_PSZ and 𝐶_S 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.

(a)

(b)

Figure 5 

Median value of achievable transmission bit rate versus INR for 8×4 MIMO systems (a) when SNR is 30 dB and (b) when SNR is 10 dB.

Figure 5(b) plots the median value of the achievable transmission bit rate when SNR is 10 dB. In Figure 5(b), 𝐶_CZ is 1.42 times greater than 𝐶_S for the INR are 30 dB. The intersection of 𝐶_PSZ and 𝐶_CZ with channel estimation error decreases compared to that in Figure 5(a). We can see that the local minimal value of 𝐶_CZ with channel estimation error in Figures 5(a) and 5(b) corresponds to the local maximal of 𝐼_z in Figure 1 and that the degradation is large when the SNR is small.

Figures 6(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 𝐶_CZ is 1.91 times and 1.80 times greater than 𝐶_S 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 𝐕^(𝑛)_I,𝑘,𝑗∈ℂ^{𝑁×(𝑁−𝑀)} in (4). 𝐕^(𝑛)_I,𝑘,𝑗 with large dimension values prevents the null space eigenvalues in (5) from decreasing compared to the eigenvalues in (3).

(a)

(b)

Figure 6 

Median value of achievable transmission bit rate versus INR for 8×2 MIMO systems (a) when SNR is 30 dB and (b) when SNR is 10 dB.

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, 𝜎²_𝑒=0, 𝜎²_𝑒=1, and 𝜎²_𝑒=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 𝐶_CZ and 𝐶_SPZ are 1.59 and 1.38 times greater than that of 𝐶_S, respectively. The median values of 𝐶_CZ and 𝐶_SPZ in 8×2 MIMO systems without channel estimation error are 1.90 and 1.51 times greater than that of 𝐶_S, 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 𝐶_CZ and 𝐶_PSZ in 8×4 (8×2) MIMO systems with 𝜎²_𝑒 of one and five are 1.41 (1.74) and 1.19 (1.51) times greater than that of 𝐶_S. The decrease in 𝐶_CZ 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, 𝜎²_𝑒 of one or five, high achievable transmission bit rates are obtained compared to 𝐶_S.

Figure 7 

CDF of achievable bit rate using measured 8×4 channel matrix with 𝛼=0.

Figure 8 

CDF of achievable bit rate using measured 8×2 channel matrix with 𝛼=0.

4.3. Virtual Wall Attenuation

Figures 9 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 𝐶_PSZ and 𝐶_CZ of Figures 5 and 6. 𝐶_PSZ becomes large as the virtual wall attenuation factor decreases. In 8×4 MIMO systems without channel estimation error, 𝐶_PSZ outperforms 𝐶_CZ when 𝛼 is less than −10 dB. As the channel estimation error increases, the intersection of 𝐶_PSZ and 𝐶_CZ 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 measured 8×4 channel matrices.

Figure 10 

Median value of achievable bit rate using measured 8×2 channel matrix.

In 8×2 MIMO systems, CZ method is effective. When the estimation error, 𝜎²_𝑒, is one, 𝐶_CZ is greater than 𝐶_PSZ 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, 𝜎²_𝑒, is less than five.

Although Figures 5 and 6 show the local minimum points of 𝐶_CZ corresponding to the local maximum interference power (see Figure 1), C_CZ 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 C_PSZ and C_CZ outperform C_CZ 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 for 8×4 MIMO (8×2 MIMO) systems when there is no channel estimation error. Even though we considered large estimation error, 𝜎²_𝑒 of one, the median values of 𝐶_CZ and 𝐶_PSZ in 8×4 MIMO (8×2 MIMO) systems with 𝜎²_𝑒 of one and five were 1.41 (1.74) and 1.19 (1.51) times greater than that of 𝐶_S. 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.

Acknowledgments

The authors thank Mr. Kazuyasu Okada, the Executive Manager of NTT Network Innovation Laboratories, for his constant encouragement. The authors would also like to thank Mr. Yoshinobu Makise and Mr. Masaaki Ida of NTT Advanced Technology Corporation for their support.