Adaptive Beamforming in Mitigating Interference in 4G networks

Table of Contents

Abstract 5

Chapter One: Introduction. 6

Objective. 7

Background. 8

What is Beamforming?. 9

Beamforming Techniques. 13

Technological Convergence. 16

Various Combining Techniques. 18

Approach. 20

List of Figures

Figure 1: Angle-Doppler with N-dependent Antenna Channels from [6] 11

Figure 2: Schematic of GSM Modulation from [12]. 13

Figure 3: Schematic of a MIMO Wireless Channel from [13] 15

Figure 4: Evolution of 4G Networks from [12] 17

Figure 5: Q √ó L MIMO-OFDM System from [11]. 19

List of Abbreviations/Acronyms

1-D One Dimensional
2-D Two Dimensional
3-D Three Dimensional
1G: First Generation
2G: Second Generation
3G: Third Generation
4G: Fourth Generation
AWGN additive white Gaussian noise
BSs: Base stations
CO: Control office
CRC Cyclic redundancy check bits
DAB: Digital audio broadcasting
DARPA: Defense Advanced Research Projects Agency
DOAs: Directions-of-arrival
DSB-SC: Double-sideband suppressed-carrier transmission
DSRC: Dedicated short range communications
DVB-T: Digital video broadcasting
ELINT: Electronic-intelligence
ESM: electronic surveillance measures radar
FDMA: frequency domain multiple access technique
GSM: Global System for Mobile communication
HDTV: High Definition TV
IEEE: Institute of Electrical and Electronics Engineers
IT: information technology
LAN: Local Area Network
LTE: Long Term Evolution
MAI: Multiple access interference
MAN: Metropolitan area network
MIMO: Multiple-input multiple-output
MTI: moving target indicator radar
OFDM: Orthogonal Frequency Division Multiplexing
PBR: passive bistatic radar
PCR: passive covert radar
PCL: passive coherent location systems
QAM: Quadrature Amplitude Modulator
QPSK/4-PSK: Quadrature Phase Shift Keyed
SIGINT: signal-intelligence
STAP: space-time adaptive processing
SNR: signal-to-noise ratio
TDMA: Time domain multiple access technique
WDM: wavelength division multiplexed
WLAN: Wireless Local Area Network


Adaptive beamforming techniques have been implemented in numerous industrial capacities, such as military operations and technological capacities, as a means of improving communication over long and short distances.  In modern technological capacities, the use of adaptive beamformers has been implemented for use with 4G (fourth generation) wireless applications as a means of combating many technical issues related to diminishing the interference encountered when transmitting data over 4G networks.  The purpose of this discourse is to highlight the types of applications that have benefitted from the use of adaptive beamforming techniques through a comprehensive exploration of the origins of adaptive beamforming, the other technologies and beamforming techniques that complement or are compatible with adaptive beamforming, and the ways 4G technology can benefit from the use of adaptive beamforming.  The swift evolution of current technologies has mandated the equally swift transformation of adaptive beamforming techniques that parallel the demands of such innovations

Adaptive Beamforming in Mitigating Interference in 4G networks

Chapter One: Introduction

The increasing dissemination of wireless technologies has placed a growing demand on mobile networks to support data applications that perform at higher throughputs and the emergence of spectral efficiencies has facilitated the necessity to create Orthogonal Frequency Division Multiplexing (OFDM) centered fourth generation (4G) networks, including WiMAX and 3GPP Long Term Evolution (LTE) [1].  Correlative research in the field of IT (information technology) has demonstrated that spectral efficiency can be significantly increased through the application of multiple antenna arrays at both the transmitter and receiver sites, particularly when using rich-scattering devices in conjunction with both narrowband and wideband channels for wireless communication [2].  Adaptive beamforming is a manner of spatial filtering used in the process of transmitting or receiving sound and can be combined with other air-interface solutions that facilitate communication through next generation wireless local area networks (WLANs) and 4G mobile communication systems, such as Multiple-input multiple-output (MIMO) wireless technology amalgamated with orthogonal frequency division multiplexing (MIMO-OFDM) [3, 4].  The recent advances in communications applications such as OFDM and MIMO have presented opportunities for improvement in 4G networks, making them more reliable transmitters of data for wireless applications.  This dissertation will discuss the principles of adaptive beamforming in regards to mitigating interference in 4G networks, with this introductory chapter presenting the background of adaptive beamforming, a discussion of the objectives of this research, and presentation of the overall approach this dissertation will adapt in researching adaptive beamforming.


The purpose of this research project is to determine the most effective implementations of adaptive beamforming to mitigate interference in 4G networks.  The primary objectives of this introductory chapter are to discuss:

  • what adaptive beamforming constitutes;
  • the purposes and uses are for this technology; and
  • how adaptive beamforming can be combined with other algorithmic configurations to improve the performance of various elements of wireless technology

In addition, this chapter will define the current understanding of the numerous elements relevant to adaptive beamforming, such as MIMO, OFDM, WLAN, LAN, 1G-4G, and various other technologically derived terms associated with this subject.  The integration of adaptive beamforming into wireless technological functioning is an example of technological convergence, which will also be discussed in order to:

  • examine the advantages and disadvantages of advanced beamforming
  • determine the weaknesses of adaptive beamforming
  • identify how convergence strengthens the vulnerable aspects of beamforming and
  • analyze the effectiveness of adaptive beamforming in provisioning reliable service to 4G wireless networks

The main goal of the project is to evaluate adaptive beamforming techniques and their efficacy in mitigating the interference experienced when transmitting data over 4G wireless networks with the intention of providing additional contributory information to the existing frame of reference on the subject. To achieve the objectives, this research will amalgamate existing knowledge to provide deliverables in the form of a literature survey of current beamforming protocols used on wireless networks, an explanation of the beamforming and adaptive beamforming, discussion of the current problems existing in wireless data transfer, and analysis of how adaptive beamforming addresses the identified problems.


Beamforming is an omnipresent aspect in array signal processes that is incorporated into numerous other applications, such as sonar, radar, acoustics, seismology, astronomy, medical-imaging, and communications [5].  The delay-and-sum approach is included amongst the standard data-independent beamformers as well as various weight vectors for side lobe control methods, which chooses the weight vector as a function of the information to enhance the performance relative to various constraints based on the data-dependent or adaptive beamformers [5].  However, adaptive beamformers tend to have improved resolution and interference rejection proficiency over the data-independent beamformers, although adaptive beamformers are more vulnerable to errors, such as the array steering vector errors resulting from inaccurate sensor calibrations, than data-independent beamformers [2, 5].  These sensitivities have facilitated attempts to fabricate more robust adaptive beamformer techniques.

According to the Institute of Electrical and Electronics Engineers (IEEE) standard implemented in 1997, called the IEEE 802.11, a specific number of MAC (Medium Access Control) protocols in addition to Physical Layers (PHYs), two of which are based on radio communicative properties and infrared light, all of which support data rates of 1-2 Mbps [6].  This improved the provision of WLAN as well as 2.5 GHz and other frequencies.  Furthermore, military electronics systems such as electronic surveillance measures (ESM) radar, electronic-intelligence (ELINT), and signal-intelligence (SIGINT) systems also employ beamforming networks in commercial communications systems that employ MIMO antenna techniques, such as 4G cellular communications systems, to diminish the effects of interference and distortion [7].

Military installations have also been using passive bistatic radar (PBR), also called passive radar systems, passive covert radar (PCR), or passive coherent location (PCL) systems since 1935, which has facilitated a reinvigoration in the potential uses of PCL systems from defense, industry, and academic communities due to the convergence of numerous causative factors, including: (a) the expansion of high dynamic range receiver technology and convergence computing and digital signal processing proficiencies that permit real-time maneuver of practical systems, (b) the proliferation of illuminators that amalgamate high bandwidth and power to deliver more appropriate waveforms for PCL systems, predominantly presented by an cumulative shift towards digital broadcasting networks as well as the foundations for navigation and communication and (c) the development in high performance adaptive processing techniques, predominantly the advancement of vigorous array processing algorithms examined within the radar community for target discovery in addition to parameter approximation in rapidly changing disturbance environments typically encountered by real-world systems [8].  Moreover, beamforming techniques have also been used in up to date applications that have implemented the diversity of the methods.

What is Beamforming?

Adaptive beamforming is comparable to frequency domain analysis of temporal signals such that time/frequency filtering indicates the content of a time signal using its Fourier transform, which maps the function as a signal that is defined in a specific domain, like space or time, into another domain as a wavelength or frequency [9].  The Fourier transform (see Equation 1) exemplifies the function in terms of sines and cosines, providing the formulaic equation of the flexibility of an integral transform that is used within multiple branches of science, with the equation being expressed as the form:  [Equation 1]

where the limits of integration are from –‚ąě to +‚ąě and the function F is the transform of the function f¬†[9].¬† The angular or directional spectrum of a signal in beamforming is exposed by Fourier analysis in regards to the manner in which the different parts of the set of transducers become excited, allowing for this technology to be implemented in a variety of ways¬†[7].¬† Beamforming can be accomplished physically by shaping and repositioning a transducer, electrically by using analog delay circuitry, or mathematically through digital signal processing¬†[8]. ¬†In terms of directivity, using the spatial filtering technique of beamforming can be used to block most of the external noise oppositional to the directions of interest to increase the signal-to-noise ratio¬†[6].¬† ¬†Although no filter is ideal for side-lobe control, the relative main lobe directivity and side-lobe levels must be balanced, especially when using beam steering since some degradation in performance is expected due to electronic course-plotting¬†[5].

Beamformers can also effectively impede the influences of jammers through reconfiguration of the antenna pattern from an arrangement of radiating components in both land and space-based communication systems [7].   Initial specifications were usually for fixed-beam constructions, although modern formations include multifaceted adaptive beamforming networks that can be formed with either passive or active configurations [7].  The far-zone field-strength pattern of a dipole element and a pattern of collinear array of dipoles can be calculated using Equation 2 for highly directive arrays using the element pattern that may be replaced by unity, which can be expressed in the equation:

    [Equation 2] [10]

such that replacing the element patterns is similar to having isotropic elements, which means that only the array factor is represented  [10].  This can be compared with the discrete Fourier transform in Equation 3,

         [Equation 3] [10]

where (2ŌÄm/N)i corresponds in wave number space to (ksinőł)zi in Equation 2 ¬†[10]. ¬†¬†This means that a long antenna on the z-axis will transmute in the far field to a shorter patterned narrow beam-width in wave number space (ksin), which must be compensated for when considering the directivity patterns of high-gain antennas ¬†[10].

Patterns of beamformer functionality are frequency dependent, meaning that the primary lobe tapers with accumulative frequency [6].   Beamformers made of discrete hydrophones can produce spatial aliasing, also called grating lobes, which can transpire when the hydrophones are one wavelength apart or greater in spatial distance [6].  Beamforming networks may also be used to combine signals from a set of non-directional antennas to simulate the behavior of a single, larger antenna with greater gain [7].  Named for airborne multichannel moving target indicator (MTI) radar, space-time adaptive processing (STAP) has been accepted in many disciplines involving joint adaptive sensor temporal and spatial processing are performed [6].

As demonstrated in Figure 1, there are N-independent antenna channels used in the space-time beamformer configuration that consists of M pulses, which comprise the CPI [6].  A specific angle-Doppler pattern is obtained by judicious selection of the complex linear combiner weights [10].  As with ordinary one-dimensional (1-D) spatial-only beamforming, a 2-D angle-Doppler space-time beam configuration can be shaped by an astute selection of the multifaceted linear combiner weights {wi} [6].  As discussed in current research, maximization of the rejoinder and/or signal-to-noise ratio (SNR) to a uniform narrowband plane wave analogous to a given angle and Doppler, the linear combiner weight vector w = vec (w1,… , wNM ) (where vec ( ) is the vector operator that basically forms a NM-dimensional column vector from the NM elements w1, . . . , wNM ) should be set equal to the anticipated structure of the desired signal s; that is, w = s [6].

Figure 1: Angle-Doppler with N-dependent Antenna Channels from [6]

A multi-channel receiver is used to digitally compile an orientation beam in the direction of the dominant signal emitted from the transmitter to estimate a complex scaled, time-delayed and potentially Doppler shifted form of the radiated source waveform over a coherent processing interval (CPI) [8].  Under ideal conditions, the reference beam endeavors to diminish corruption in the waveform estimate produced by the superimposition of unwelcome transmitter signal multipath components, co-channel interloping due to other range users unrelated to the source of interest, and target echoes that may enter the orientation beam through the antenna pattern side-lobes [8]. One or more surveillance beams are then digitally formed using the same time-segment of array data in pre-determined direction(s) selected for target search. Ideally, the surveillance beam provides maximum gain for target echoes, while cancelling all direct-wave signals from the transmitter (including multipath components) collectively referred to as direct-wave clutter, as well as additive interference from other co-channel emitters [8].

Beamforming Techniques

GSM (Global System for Mobile communication) belongs to the second mobile phone generation and was first established in 1992 in Europe. The user channels are separated on the one hand in the frequency domain using the frequency domain multiple access technique (FDMA) and on the other hand in the time domain using the time domain multiple access technique (TDMA). The time frame with the length 60/13 m/sec is divided into 8 time slots which are assigned to different users. In addition the frequency band is divided into different channel each having 200 kHz bandwidth. Adjacent base stations are not allowed to use the same frequencies [11].  This type of configuration is modeled in Figure 2, which demonstrates how the modulation data are produced from the encoded speech data [12].

Figure 2: Schematic of GSM Modulation from [12]

As the model in Figure 2 illustrates, speech data are constructed through the encoding of the speech samples with intervals of 20 m/sec into 260 bit blocks that corresponds to 13 kb/s¬†[12]. ¬†These 260 bits data blocks are allocated into two classes such that Class I is comprised of 182 bits that are sensitive to bit errors and are considered as important, so they are encoded using convolutional coding with a constrain length 4 and the rate of ¬Ĺ¬†[12]. The 182 bits are further divided into 50 bits, designated Class Ia, and 132 bits, called Class Ib such that the block encoder generates three cyclic redundancy check bits (CRC) that are integrated with the class Ia bits and ¬†four tail bits are incorporated into the Class Ib bits prior to convolutional encoding¬†[12].¬† Data blocks that comprise Class II contain less important 78 bits, which are transmitted without protection¬†[12]. ¬†Digital beamforming antennas are flexible enough to provide beams to singular users on demand by amalgamating both adaptive and suited resource allocation processes to ensure the best use of available capacity, such as in the use of space division multiple access beamforming antennae (SDMA)¬†[13].

Another technique known as on-board satellite multiple beam antennas (MBA) have been efficaciously employed for either personal or military communications as well as Internet applications since they enable multiple adjacent patterns covering an extended zone, which insures high gains  [13].  They also are capable of increasing the accessible capacity for a given bandwidth through the introduction of frequency reuse on non-adjacent beams [13].  In their standard configuration, MBA provide a static coverage range with contiguous beams typically crossing three to four dB beneath maximum gain level with typical 1:3 or 1:4 frequency reuse schemes on a fixed bandwidth to beam allocation  [13].  The frequency is reused on one beam over three or four, while on classical payloads beamforming is executed prior to channelization function in radio frequency domain, typically in a digitized baseband or on transitional frequencies [13].  Digital beamforming allows the integration of fully flexible beamforming by presenting digital beamforming networks related to transparent or regenerative processors, allowing the insertion of a considerably improved multi-beam antenna [13].

For use in wireless technology, OFDM has become a popular technique used for transmission of signals over wireless channels and has been adopted in several wireless standards, such as digital audio broadcasting (DAB), digital video broadcasting (DVB-T), the IEEE 802.11a local area network (LAN) standard and the IEEE 802.16a metropolitan area network (MAN) standard [11].  OFDM is also being pursued for dedicated short range communications (DSRC) for road side to vehicle communications and as a potential candidate for the fourth generation (4G) mobile wireless systems.  OFDM converts a frequency selective channel into a parallel collection of frequency flat sub-channels [11].  Additionally, M Multiple Receive antenna communication is now a key component of practically every up-to-date high-rate wireless standard, such as LTE, 802.11n, and WiMax [10].  Furthermore, conclusions by Foschini and Gans inspired the investigation of a MIMO wireless channel, depicted in Figure 3, for the purpose of communication since the achievable throughput of a point-to-point MIMO channel scale is linearly with the minimum of the number of transmit and receive antennas [14].

Figure 3: Schematic of a MIMO Wireless Channel from [14]

The schematic in Figure 3 demonstrates how the input /output configuration is expressed in a relation of a narrow band single-user MIMO wireless link that is moderated by a composite baseband vector notated as: Y=HX+ n [Equation 4] such that N and the channel matrix is the additive white Gaussian noise (AWGN) vector at a given instant in time channel noise [14].  The approaching Fourth generation (4G) mobile communication systems are projected to solve still remaining problems of 3G (third generation) systems and to provide a wide variety of new services, from high quality voice to high-definition video to high-data-rate wireless channels [13].  The term 4G is used broadly to include several types of broadband wireless access communication systems aside from cellular telephone systems and was originally created by the Defense Advanced Research Projects Agency (DARPA), which is the same business that established the wired Internet [13].  The 4G network will allow the user to be in control decide aspects of the system, including the right terminal for each application as well as for each mobility and coverage environment [13].  The multifaceted integrative capabilities of 4G applications has prompted the acronym MAGIC being associate with this type of technology, meaning Mobile multimedia, Anytime anywhere, Global mobility support, Integrated wireless solution, and Customized personal service, since services can be delivered at expected data rates for high mobility, calculated at 100Mbps and 1Gbp for Nomadic  [13].

Addressing the challenge of limited spectrum, coupled with increasing consumer demand for bandwidth, requires innovation, so that consumer hunger can be satiated while carrier’s business models perform effectively [14].  New solutions must be developed that: use available spectrum with the utmost efficiency to allow higher data throughput over the wireless link; support a greater number of users within individual cells and significantly enhance the user experience; and reduce the carrier cost of transporting megabit-rate traffic and carry that lower carrier cost through to the consumer [14].

Technological Convergence

Tremendous consumer interest in multimedia applications requires high data rates in mobile communication system. With the advent of 4G mobile communication systems, many broadband wireless applications can be supported like Video Conferencing, Wireless Scada and HDTV.  High capacity and variable bit rate information transmission with high bandwidth efficiency are the key requirements that the modern transceivers have to meet in order to provide a variety of new high quality services to be delivered to the customers [4].  Technological convergence is the merging of singular technological entities into new technologies that bring together a myriad of media into a single device that originally handled only one medium or accomplished one or two tasks.  Technological convergence allows devices to present and interact with a wide array of media, increasing the variations of devices present in homes due to the continued advancement in available technologies, necessitating strong frequencies to support such devices.

The most common example of technological convergence is the cell phone, which was originally conceived as mobile telephones, but now are complex instruments, able to perform many functions of telephones, desktop PCs, music players, and even digital video cameras, all in small, pocket-sized devices. Mobile networks have evolved through more than three generations, shown in Figure 4, starting with the analogue or first-generation (1G) networks deployed in the early 1980s, and moving on to the digital second-generation (2G) networks deployed in the early 1990s. Operators started to deploy third generation (3G) networks in 2001-03, and 3.5G networks from around 2005. Networks still in the design phase include 3.9G and 4G systems [12].

Figure 4: Evolution of 4G Networks from [12]

To obtain an increasingly high transmission rate for next generation wireless communications, two major problems have to be addressed, which are the multipath interference and multiple access interference (MAI) [12].  Both obstacles encountered can be surmounted through the use of an antenna array in conjunction with multiuser detection and array signal processing is typically used to identify or anticipate problems when a preferred signal is arrested in the presence of interference and noise [16]. Arrays play an important role in areas like (a) detection of the presence of signal sources, (b) estimation of temporal waveforms or spectral contents of signals, (c) estimation of directions-of-arrival (DOAs) or positions of multiple sources, (d) focusing on specific spatial locations for transmission [16].  Traditionally, they are used in such diverse fields as radar, sonar, transmission systems, seismology, or medical diagnosis and treatment.

Various Combining Techniques

Maximal ratio combining, selection combining, and equal gain combining are all methods for achieving high capacity transmission since they use optical fiber networks, which plays an important role in all of these processes [4].  Broadband millimeter-wave fiber-radio access system can meet demands for wireless first/last hop to the customers, which can support broad-band and portable services and reconcile the shortage of available microwave-band  [4].  For millimeter-wave fiber-radio systems, the only feasible option to connect between the central control office (CO) and the micro- or pico-cellular antenna base stations (BSs) would be an optical generation and transport technique of millimeter-wave RF signals over optical fiber links [4]. In the micro- or pico-cellular fiber-radio access system, more than 1000 BSs are likely to be located under the coverage of a single CO; therefore, it would be desirable to accommodate a large number of BSs, and the promise for support will be wavelength division multiplexed (WDM) technology [4].  Recently, there has been rapid progress in WDM transmission technologies. Dense WDM (DWDM) shows promise to increase the transmission capacity of trunk lines within the spectral regions limited by the gain bandwidths of optical fiber amplifiers [4].

Figure 5: Q √ó L MIMO-OFDM System from [11]

In the model illustrated in Figure 5, Q and L are the number of inputs and outputs, respectively, which helps to deliver a realistic signal received by a mobile receiver moving away from a transmitting base station¬†[11]. ¬†The path loss leads to an overall decrease in signal strength as the distance between the transmitter and the receiver increases. The physical processes which cause it are the outward spreading of waves from the transmit antenna and the obstructing effects of trees, buildings and hills¬†[16]. A typical system may involve variations in path loss of around 150 dB over its designed coverage area. Superimposed on the path loss is the shadowing, which changes more rapidly, with significant variations over distances of hundreds of meters and generally involving variations up to around 20 dB¬†[16]. ¬†Shadowing arises due to the varying nature of the particular obstructions between the base and the mobile, such as particular tall buildings or dense woods. Fast fading involves variations on the scale of a half wavelength (50 cm at 300 MHz, 17 cm at 900 MHz) and frequently introduces variations as large as 35‚Äď40 dB. It results from the constructive and destructive interference between multiple waves reaching the mobile from the base station¬†[16].

Although, as of 2008, broadband service was available in 182 markets and mobile networks exceeded one billion by the start of 2009, more than half the world nations still do not have an Internet Exchange Point, (IXP) primarily where local traffic can be transmitted and pay exorbitant charges, as much as $2,000-$5,000 USD per megabyte (Mb) per month, for transiting traffic information IXP within an improved world (OECD, 2010, p.4).  Data transmission is recognized by technologies that appears in normal everyday life including cell phones and blue tooth technology, wifi, infra-red, and wired technologies, all of which operate as part of each network.  Although originally coined for airborne multichannel moving target indicator (MTI) radar space-time adaptive processing (STAP) has been adopted in many disciplines in which joint adaptive sensor temporal and spatial processing are performed (e.g., multidimensional adaptive filtering).  The need for joint space and time processing in either airborne (or spaceborne) MTI radar arises from the inherent two-dimensional (2-D) nature of ground clutter [6].


Following this Introductory Chapter, this dissertation will continue with a Literature review that will provide description of Generalized Selection combining, and MRC in addition to four different G.S. combining techniques, which can be implemented in an assemblage that primarily consists of a combination of MRC and S.C.  The Literature review will include diagrams or other visual media where appropriate for clarity as well as equations to illustrate the mathematical principles of adaptive beamforming techniques.  The literature review chapter will additionally present calculations of SNR, SNIR, and other adaptive beamforming techniques to calculate the probability of Signal detection.  Additionally, this chapter will discuss current research regarding the possible implementations of adaptive beamforming in 4G networks that probably employ OFDM, QPSK, QAM and other possible configurations.  The third chapter will that will present the research method employed as a means of deriving answers to the indicated research questions and the fourth chapter will present the aggregate results of the research.  The next chapter will analyze and discuss the findings and determinations followed by a concluding chapter to summarize the whole project, including how the research questions were proven or disproved within the body of the research, limitations in the research methods, gaps in the literature, and possible areas for future research.

Works Cited

[1] G. Boudreau, J. Panicker, N. Guo, R. Chang, N. Wang, S. Vrzic and Nortel, “Interference Coordination and Cancellation for 4G Networks,” IEEE Communications Magazine, April 2009.
[2] C. A. Balanis, Antenna Theory Analysis and Design, 3rd ed., Hoboken, New Jersey: John Wiley & Sons, Inc, 2005.
[3] H. H. Chen and J. S. Lee, “Adaptive joint beamforming and B-MMSE detection under multipath interference,” IEE Proceedings — Communications, vol. 151, no. 6, pp. 605-612, 2004.
[4] S. Nema, A. Goel and R. P. Singh, “Integrated DWDM and MIMO-OFDM System for 4G High Capacity Mobile Communication,” Signal Processing: An International Journal, vol. 3, no. 5, pp. 132-143.
[5] J. Li and P. Stoica, Eds., Robust Adaptive Beamforming, Hoboken, New Jersey: John Wiley & Sons, Inc, 2006.
[6] J. R. Guerci, Space-time adaptive processing for radar, Norwood, MA: Artech House, Inc, 2003 .
[7] K. Greenwood, “Understanding Passive Beamforming Networks,” Electronic Design, vol. 59, no. 14, pp. S18-S24, 2011.
[8] G. G. Fabrizio, F. F. Colone, P. P. Lombardo and A. A. Farina, “Adaptive beamforming for high-frequency over-the-horizon passive radar,” IET Radar, Sonar & Navigation, vol. 3, no. 4, pp. 384-405, 2009.
[9], “Fourier transform,” Collins English Dictionary – Complete & Unabridged, 2009. [Online]. Available: transform. [Accessed 26 February 2013].
[10] K. Siwiak and Y. Bahreini, Radiowave Propagation and Antennas for Personal Communications, 3rd ed., Norwood, MA: Artech House, Inc, 2007.
[11] G. L. St√ľber, J. Barry, S. W. McLaughlin, Y. G. Li, M. A. Ingram and T. G. Pratt, “Broadband MIMO-OFDM Wireless Communications,” Georgia Institute of Technology, Atlanta, GA.
[12] M. Jaloun and Z. Guennoun, “Wireless Mobile Evolution to 4G Network,” Wireless Sensor Network, no. 2, pp. 309-317, April 2010.
[13] J. J. Montesinos, O. O. Besson and C. C. Larue de Tournemine, “Adaptive beamforming for large arrays in satellite communications systems with dispersed coverage,” IET Communications, vol. 5, no. 3, pp. 350-361, 2011.
[14] N. B. Sinha, M. C. Snai and M. Mitra, “Per formance Enhancement of MIMO-OFDM Technology for High Data Rate Wireless Networks,” International Journal of Computer Science and Application, no. 2010, pp. 122-128, 2010.
[15] J. Hoadley, “Building future networks with MIMO and OFDM,” 19 September 2005. [Online]. Available: [Accessed 27 February 2013].
[16] S. R. Saunders and A. Argón-Zavala, Antennas and Propogation for wireless communication systems, 2nd ed., Chichester,West Sussex: JohnWiley & Sons Ltd, 2007.