Eigencombining: A Unified Approach to Antenna Array Signal Processing

Eigencombining: A Unified Approach to Antenna Array Signal Processing

Constantin Siriteanu (Seoul National University, Korea) and Steven D. Blostein (Queen’s University, Canada)
DOI: 10.4018/978-1-59904-988-5.ch001
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This chapter unifies the principles and analyses of conventional signal processing algorithms for receive-side smart antennas, and compares their performance and numerical complexity. The chapter starts with a brief look at the traditional single-antenna optimum symbol-detector, continues with analyses of conventional smart antenna algorithms, i.e., statistical beamforming (BF) and maximal-ratio combining (MRC), and culminates with an assessment of their recently proposed superset known as eigencombining or eigenbeamforming. BF or MRC performance fluctuates with changing propagation conditions, although their numerical complexity remains constant. Maximal-ratio eigencombining (MREC) has been devised to achieve best (i.e., near-MRC) performance for complexity that matches the actual channel conditions. The authors derive MREC outage probability and average error probability expressions applicable for any correlation. Particular cases apply to BF and MRC. These tools and numerical complexity assessments help demonstrate the advantages of MREC versus BF or MRC in realistic scenarios.
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General Perspective. Andrew Viterbi is credited with famously stating that “spatial processing remains as the most promising, if not the last frontier, in the evolution of multiple access systems” (Roy, 1998, p. 339). Multiple-antenna-transceiver communications systems, also known as single-input multiple-output (SIMO), multiple-input single-output (MISO), or multiple-input multiple-output (MIMO) systems, which exploit the spatial dimension of the radio channel, promise tremendous benefits over the traditional single-input single-output (SISO) transceiver concept, in terms of data rate, subscriber capacity, cell coverage, link quality, transmit power, etc. Such benefits can be achieved with smart antennas, i.e., SIMO, MISO, and MIMO systems that combine baseband signals for optimum performance (Paulraj, Nabar, & Gore, 2005).

Herein, we consider receive smart antennas (i.e., the SIMO case) deployed in noise-limited scenarios with frequency-flat multipath fading (El Zooghby, 2005, Section 3.3) (Jakes, 1974) (Vaughan & Andersen, 2003, Chapter 3), for which the following signal combining techniques have conventionally been proposed:

  • Statistical beamforming (BF), i.e., digitally steering a radio beam along the dominant eigenvector of the correlation matrix of the channel fading gain vector (S. Choi, Choi, Im, & Choi, 2002) (El Zooghby, 2005, Eqn. (5.23), p. 126, Eqns. (5.78–80), p. 148) (Vaughan & Andersen, 2003, Section 9.2.2). BF enhances vs. SISO the average, over the fading and noise, signal-to-noise ratio (SNR) by an array gain factor that is ultimately proportional to the antenna correlation and is no greater than the number of antenna elements. Since BF requires the estimation of only the projection of the channel gain vector onto the eigenvector mentioned above, it has low numerical complexity. However, BF is effective only for highly-correlated channel gains, i.e., when the intended signal arrives with narrow azimuth angle spread (AS).

  • Maximal-ratio combining (MRC), i.e., maximizing the output SNR conditioned on the fading gains (Brennan, 2003; Simon & Alouini, 2000). This SNR is computed by averaging over the noise only, i.e., conditioning on the channel gains. When the intended-signal AS is large enough to significantly reduce antenna correlation, MRC can greatly outperform BF as a result of diversity gain and array gain, at the cost of much higher numerical complexity incurred due to channel estimation for each antenna element.

Note that, for fully correlated (i.e., coherent) channel gains, both BF and MRC reduce to the classical notion of “beamforming” whereby a beam is formed towards the intended signal arriving from a discrete direction (Monzingo & Miller, 1980; Trees, 2002; Godara, 2004).

Statistical beamforming and diversity combining principles have traditionally been classified, studied, and applied separately, leading to disparate and limited performance analyses of BF and MRC. Furthermore, since BF and MRC optimize the average SNR and the conditioned SNR, respectively, they have opposing performance-maximizing spatial correlation requirements, as well as significantly different, correlation-independent, numerical complexities (Siriteanu, Blostein, & Millar, 2006; Siriteanu, 2006; Siriteanu & Blostein, 2007). Because correlation varies in practice due to variable AS (Algans, Pedersen, & Mogensen, 2002), BF or MRC performance fluctuates, whereas numerical complexity remains constant. Therefore, MRC can actually waste processing resources and power, whereas BF can often perform poorly (Siriteanu et al., 2006; Siriteanu, 2006; Siriteanu & Blostein, 2007).

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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