Random Array Theory and Collaborative Beamforming

Random Array Theory and Collaborative Beamforming

Hideki Ochiai (Yokohama National University, Japan), Patrick Mitran (University of Waterloo, Canada), H. Vincent Poor (Princeton University, USA) and Vahid Tarokh (Harvard University, USA)
DOI: 10.4018/978-1-59904-988-5.ch005
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In wireless sensor networks, the sensor nodes are often randomly situated, and each node is likely to be equipped with a single antenna. If these sensor nodes are able to synchronize, it is possible to beamform by considering sensor nodes as a random array of antennas. Using probabilistic arguments, it can be shown that random arrays formed by dispersive sensors can form nice beampatterns with a sharp main lobe and low sidelobe levels. This chapter reviews the probabilistic analysis of linear random arrays, which dates back to the early work of Y. T. Lo (1964), and then discusses recent work on the statistical analysis of two-dimensional random arrays originally derived in the framework of wireless sensor networks.
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Wireless sensor networks have recently attracted much attention in the communication engineering community (e.g., Yao, 1998). In many such networks, tiny communicating nodes, each equipped with a single antenna, are distributed randomly. These nodes not only gather information but also communicate over a wireless channel. Some nodes may relay the received information to nearby nodes or directly transmit to the destination (or fusion center). In order to deliver information to the fusion center, provided neighboring nodes possess the same information and are able to synchronize, it is also possible for these nodes to beamform collaboratively. We refer to this kind of distributed beamforming as collaborative beamforming (Ochiai, 2005).

In wireless communications, beamforming enables an efficient implementation of space-division multiple access (SDMA), which has the potential to significantly increase communication rates over multiple access channels. SDMA by means of collaborative beamforming is also a powerful approach in the framework of wireless ad hoc sensor networks where several clusters operate asynchronously.

Let us consider the scenario illustrated in Figure 1, where the sensor nodes in two separate clusters A and B are communicating with respective distant fusion centers located in different directions. In this case, intra-cluster communication among sensor nodes for information sharing may be realized by low-cost short distance broadcast-type communication. Therefore, the main challenge is fair channel allocation for long distance communication links between the clusters and the fusion centers. Since synchronization among nodes in different clusters may not be easily established, random access is commonly used. With limited available spectrum resources, however, random access typically requires additional overhead such as collision detection. Furthermore, an increase in the number of communicating clusters considerably reduces the overall throughput.

Figure 1.

Collaborative beamforming in ad hoc wireless sensor networks

On the other hand, with collaborative beamforming depicted in Figure 1, cognition of the other communicating clusters is not necessary, provided that the direction of the fusion center is different. Due to the random nature of ad hoc sensor networks, it is highly unlikely that the sensor nodes in the distinct clusters are transmitting in the same direction. Therefore, collaborative beamforming has the potential to become a low-cost SDMA implementation.

A question that arises in this scenario is whether or not collaborative sensors can form a nice beampattern. Since the distribution of the sensor nodes is typically random by nature, it is reasonable to consider arrays formed by the sensor nodes as random arrays and to treat them using probabilistic arguments.

Probabilistic analysis of antenna arrays dates back to the early work of Lo (1964), who first developed a comprehensive theory of linear random arrays. Using statistical arguments, Lo showed that a random array can form a nice average beampattern without the major grating lobes that are observed in a typical periodic array. He also derived the distribution of the beampattern based on a Gaussian approximation. Later, Steinberg (1972), Agrawal & Lo (1972), as well as Donvito & Kassam (1979) analyzed the distribution of the maximum of the sidelobe peaks associated with linear random arrays. An excellent overview and analytical treatment of linear random arrays can be found in (Steinberg, 1976).

Complete Chapter List

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Table of Contents
Jack H. Winters
Chen Sun, Jun Cheng, Takashi Ohira
Chapter 1
Constantin Siriteanu, Steven D. Blostein
This chapter unifies the principles and analyses of conventional signal processing algorithms for receive-side smart antennas, and compares their... Sample PDF
Eigencombining: A Unified Approach to Antenna Array Signal Processing
Chapter 2
Zhu Liang Yu, Meng Hwa Er, Wee Ser, Chen Huawei
In this chapter, we first review the background, basic principle and structure of adaptive beamformers. Since there are many robust adaptive... Sample PDF
Robust Adaptive Beamforming
Chapter 3
Sheng Chen
Adaptive beamforming is capable of separating user signals transmitted on the same carrier frequency, and thus provides a practical means of... Sample PDF
Adaptive Beamforming Assisted ReceiverAdaptive Beamforming
Chapter 4
Thomas Hunziker
Many common adaptive beamforming methods are based on a sample matrix inversion (SMI). The schemes can be applied in two ways. The sample covariance... Sample PDF
On the Employment of SMI Beamforming for Cochannel Interference Mitigation in Digital Radio
Chapter 5
Hideki Ochiai, Patrick Mitran, H. Vincent Poor, Vahid Tarokh
In wireless sensor networks, the sensor nodes are often randomly situated, and each node is likely to be equipped with a single antenna. If these... Sample PDF
Random Array Theory and Collaborative Beamforming
Chapter 6
W. H. Chin, C. Yuen
Space-time block coding is a way of introducing multiplexing and diversity gain in wireless systems equipped with multiple antennas. There are... Sample PDF
Advanced Space-Time Block Codes and Low Complexity Near Optimal Detection for Future Wireless Networks
Chapter 7
Xiang-Gen Xia, Genyuan Wang, Pingyi Fan
Modulated codes (MC) are error correction codes (ECC) defined on the complex field and therefore can be naturally combined with an intersymbol... Sample PDF
Space-Time Modulated Codes for MIMO Channels with Memory
Chapter 8
Javier Vía, Ignacio Santamaría, Jesús Ibáñez
This chapter analyzes the problem of blind channel estimation under Space-Time Block Coded transmissions. In particular, a new blind channel... Sample PDF
Blind Channel Estimation in Space-Time Block Coded Systems
Chapter 9
Chen Sun, Takashi Ohira, Makoto Taromaru, Nemai Chandra Karmakar, Akifumi Hirata
In this chapter, we describe a compact array antenna. Beamforming is achieved by tuning the load reactances at parasitic elements surrounding the... Sample PDF
Fast Beamforming of Compact Array Antenna
Chapter 10
Eddy Taillefer, Jun Cheng, Takashi Ohira
This chapter presents direction of arrival (DoA) estimation with a compact array antenna using methods based on reactance switching. The compact... Sample PDF
Direction of Arrival Estimation with Compact Array Antennas: A Reactance Switching Approach
Chapter 11
Santana Burintramart, Nuri Yilmazer, Tapan K. Sarkar, Magdalena Salazar-Palma
This chapter presents a concern regarding the nature of wireless communications using multiple antennas. Multi-antenna systems are mainly developed... Sample PDF
Physics of Multi-Antenna Communication Systems
Chapter 12
MIMO Beamforming  (pages 240-263)
Qinghua Li, Xintian Eddie Lin, Jianzhong ("Charlie") Zhang
Transmit beamforming improves the performance of multiple-input multiple-output antenna system (MIMO) by exploiting channel state information (CSI)... Sample PDF
MIMO Beamforming
Chapter 13
Biljana Badic, Jinho Choi
This chapter introduces joint beamforming (or precoding) and space-time coding for multiple input multiple output (MIMO) channels. First, we explain... Sample PDF
Joint Beamforming and Space-Time Coding for MIMO Channels
Chapter 14
Zhendong Zhou, Branka Vucetic
This chapter introduces the adaptive modulation and coding (AMC) as a practical means of approaching the high spectral efficiency theoretically... Sample PDF
Adaptive MIMO Systems with High Spectral Efficiency
Chapter 15
Joakim Jaldén, Björn Ottersten
This chapter takes a closer look at a class of MIMO detention methods, collectively referred to as relaxation detectors. These detectors provide... Sample PDF
Detection Based on Relaxation in MIMO Systems
Chapter 16
Wolfgang Utschick, Pedro Tejera, Christian Guthy, Gerhard Bauch
This chapter discusses four different optimization problems of practical importance for transmission in point to multipoint networks with a multiple... Sample PDF
Transmission in MIMO OFDM Point to Multipoint Networks
Chapter 17
Salman Durrani, Marek E. Bialkowski
This chapter discusses the use of smart antennas in Code Division Multiple Access (CDMA) systems. First, we give a brief overview of smart antenna... Sample PDF
Smart Antennas for Code Division Multiple Access Systems
Chapter 18
Aimin Sang, Guosen Yue, Xiaodong Wang, Mohammad Madihian
In this chapter, we consider a cellular downlink packet data system employing the space-time block coded (STBC) multiple- input-multiple-output... Sample PDF
Cross-Layer Performance of Scheduling and Power Control Schemes in Space-Time Block Coded Downlink Packet Systems
Chapter 19
Yimin Zhang, Xin Li, Moeness G. Amin
This chapter introduces the concept of multi-beam antenna (MBA) in mobile ad hoc networks and the recent advances in the research relevant to this... Sample PDF
Mobile Ad Hoc Networks Exploiting Multi-Beam Antennas
Chapter 20
Toru Hashimoto, Tomoyuki Aono
The technology of generating and sharing the key as the representative application of smart antennas is introduced. This scheme is based on the... Sample PDF
Key Generation System Using Smart Antenna
Chapter 21
Nemai Chandra Karmakar
Various smart antennas developed for automatic radio frequency identification (RFID) readers are presented. The main smart antennas types of RFID... Sample PDF
Smart Antennas for Automatic Radio Frequency Identification Readers
Chapter 22
Konstanty Bialkowski, Adam Postula, Amin Abbosh, Marek Bialkowski
This chapter introduces the concept of Multiple Input Multiple Output (MIMO) wireless communication system and the necessity to use a testbed to... Sample PDF
Field Programmable Gate Array Based Testbed for Investigating Multiple Input Multiple Output Signal Transmission in Indoor Environments
Chapter 23
Masahiro Watanabe, Sadao Obana, Takashi Watanabe
Recent studies on directional media access protocols (MACs) using smart antennas for wireless ad hoc networks have shown that directional MACs... Sample PDF
Ad Hoc Networks Testbed Using a Practice Smart Antenna with IEEE802.15.4 Wireless Modules
Chapter 24
Monthippa Uthansakul, Marek E. Bialkowski
This chapter introduces the alternative approach for wideband smart antenna in which the use of tapped-delay lines and frequency filters are... Sample PDF
Wideband Smart Antenna Avoiding Tapped-Delay Lines and Filters
Chapter 25
Jun Cheng, Eddy Taillefer, Takashi Ohira
Three working modes, omni-, sector and adaptive modes, for a compact array antenna are introduced. The compact array antenna is an electronically... Sample PDF
Omni-, Sector, and Adaptive Modes of Compact Array Antenna
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