Multiple-input multiple-output (MIMO) communication

Chapter 1

1 Introduction

1.1 Project Overview

The Multiple-Input Multiple-Output (MIMO) communication technique have been an important area of interest for next-generation wireless systems because of their potential for high capacity, increased diversity, and interference suppression. It enhances the reliability of a wireless channel without any increase in the transmitted signal power and bandwidth. However, the capacity of MIMO system is highly dependent on the nature of its propagation environment and antennas. The capacity of MIMO system increases linearly with the number of antennas used in scattering environment. Multipath fading limits the channel capacity, reliability and reduces the spectral efficiency. MIMO is a newest technique used to exploit multipath fading, showing such attractive features as high increase in capacity without any increase in transmission power and/or channel bandwidth. This feature makes it deal for modern wireless systems, particularly in indoor cellular and WLAN communications. Different type of these antennas have been designed and evaluated at at different institutes/universities of the world. The need is to enhance the portability of the antennas through new designs and higher performance capability.

1.2 Project Objective

Our aim of the project is to design a compact ISM band 3-element triangular patch antenna for 802.11n applications with a carrier frequency of 2450 MHz. Basically we have focused on handheld devices like laptops, where size and better performance is the crucial issue. Better performance in small size antenna is desired. We have designed a 3x3 MIMO antenna which is constructed on Arlon AD450 substrate of thickness 1.6mm. Its dielectric constant is 4.50 with maximum dimensions of 90x120mm. From simulation at -6dB return loss (3:1 VSWR) bandwidth is observed to be from 2.39-2.47 GHz with input impedence of 50? at the resonance point.

The intermediate objectives of the project are as follows:

  • Inverstigate and understand the characteristics of our antenna using Ansoft HFFS v9.0
  • Obtain maximum gain
  • Obtain good radiation pattern and meet the standards to omni-directional antenna
  • Obtain better performance in small size as small size of antenna is desired in handheld devices
  • Make it power efficient

1.3 Report Outline

Chapter 2 presents a concise literature review to develop an understanding of the topics related to our project. The chapter starts with the brief historical advancement of antenna followed by the concept of radiation mechanism. The fundamental parameters of antennas like radiation pattern, directivity, beamwidth, return loss, radiation intensity, gain etc are then explained to give a better understanding of antenna theory. Then multipath propagation and fading concept are explained briefly to give readers the basic knowledge so that they can understand the following topic, which is the need of multiple antennas and the concept of MIMO technology.

Chapter 2

2 Background

2.1 Introduction

This chapter provides a concise literature review to develop an understanding of the topics related to our project. The chapter starts with the brief historical advancement of antenna followed by the concept of radiation mechanism. The fundamental parameters of antennas like radiation pattern, directivity, beamwidth, return loss, radiation intensity, gain etc are then explained to give a better understanding of antenna theory. Then multipath propagation and fading concept are explained briefly to give readers the basic knowledge so that they can understand the following topic, which is the need of multiple antennas and the concept of MIMO technology.

2.2 Radiation Mechanism

Radiation mechanism is of the most basic element of antenna propagation. It mainly comprises of two words radiation and mechanism. Radiation is defined and the waves that are radiated from antenna or these are disturbances in the electromagnetic field that propagate away from the source and mechanism is simply the procedure my which these waves radiate. The diagram below shows how the waves radiate when they are produced from the source. Source or generator generates waves, it passes through transmission line and then through tapered transition area. These waves after passing through tapered transition creates disturbances in the medium that moves he molecules and wave is radiated.

There are three types of radiation mechanism given below:

  • Single Wire
  • Two Wires
  • Dipole

In a single wire, waves are radiated using a circular wire of specific diameter. The wires used are conducting wires which have most prominent characteristics of conduction of electric charges. These charges are evenly distributed in a circular wire with the following parameters and are related by equations given below:

Js = q Vs

Is = q Vz

where q = charge, Vs is velocity and Iz is current in columb.

By differentiating the equation, we finally derived the equation relating current and charges which is also known as fundamental relation of electromagnetic radiation. This fundamental relation states that to create radiation, there must be time varying current or acceleration or deceleration of charges. The fundamental relation is given below:

L dI/dt = lq dVz / dt = lqaz

For the two wires, voltage source is connected to a two conductor transmission line which is connected to antenna. The voltage is applied to conductor and due to this, charges starts moving among two wires. The electric lines of forces have tendency to act on free electrons associated with each conductor and force them to be displaced. This is how radiations are emitted by using two wires.

In dipole case, electric lines of forces are detached from antenna to form free-space waves. During the first quarter lambda\4, the waves are emitted in a form of three half circular lines. During the next quarter period three more half circular waves are emitted to complete the radiation. The end result is that there are three lines pointing upwards and thee lines pointing downwards in the second phase, completing the radiation pattern in a form of circles.


Some of the fundamental parameters of antenna are discussed briefly below:


Theradiation patterndescribes the relative strength of the radiated field in various directions from the antenna, at a constant distance (Far field region). The radiation pattern is a reception pattern as well, since it also describes the receiving properties of the antenna. The radiation pattern is three-dimensional, but usually the measured radiation patterns are a two-dimensional slice of the three-dimensional pattern. These pattern measurements are presented in either arectangularor apolarformat.


It is a plot of the power radiated from an antenna per unit solid angle, or its radiation intensity U [watts per unit solid angle]. U r2 S where S is the power density at distance r. this shows that radiation pattern is the same at all distances provided that r is in the far field region.

The radiation pattern in the near field and far field is different. The term near-field means the field pattern that exists close to the antenna, while the term far-field means the field pattern at large distances. The far-field is also called the radiation field. Mostly, it is the radiated power that is of interest, and so antenna patterns are usually measured in the far-field region. For measuring the radiation pattern it is important to choose a distance sufficiently large to be in the far-field. The minimum permissible distance depends on the dimensions of the antenna in relation to the wavelength.

The properties of radiation are power flux density, radiation intensity, field strength, directivity, phase or polarization will be discussed later in this chapter. A trace of received electric (magnetic) field at a constant distance is known as Amplitude field pattern whereas the graph of spatial variation of the power density along a constant radius is called Amplitude power pattern.

Normalized field and power patterns are usually considered by normalizing the field and power patterns with respect to their maximum values. RADIATION PATTERN LOBES

Parts of the radiation pattern which has lobe like shape are called Lobes. A proper definition for radiation lobe is portion of radiation pattern bounded by relatively radiation intensity. These lobes are further categorized in two ways.

  1. Major lobes which include the main lobe.
  2. Minor lobes which include side lobes and back lobes
  • Major lobe:
  • Also called the main lobe, is defined as the radiation lobe containing the direction of maximum radiation . Normally there is one major lobe in an antenna radiation pattern but antenna do have more than one major lobe in their radiation pattern.

  • Minor lobes:
  • Minor lobes represent the radiation pattern which is mostly undesirable so they are not desirable.

  • Side lobe:
  • The radiation lobe in any direction other than the main lobe or the major lobe is called side lobe.

  • Back lobe:
  • A back lobe is a radiation lobe whose axis makes an approximate angle of 180o with the major lobe. Is occupies the space opposite to the major lobe. ISOTROPIC, DIRECTIONAL & OMNIDIRECTIONAL RADIATION PATTERN

Radiation pattern of isotropic antenna is isotropic radiation pattern, this radiation patterns consists of radiations in all directions. Normally it is an ideal radiation pattern and only used as a reference for expressing the directives properties of actual antennas.

A directional antenna is the one which has the power to receive and transmit radiations in one direction more efficiently than other directions. So the radiation pattern of directional antenna is the radiation in one particular direction. PRINCIPAL PATTERN

Performance of linearly polarized antenna is defined in terms of its principle E-plane and H-plane patterns. The E-plane and H-plane are reference planes for linearly polarized antennas.

  • For a linearly polarized antenna, this is the plane containing the electric field vector and the direction of maximum radiation. The electric field or "E" plane determines the polarization or orientation of the radio wave. For a vertically-polarized antenna, the E-plane usually coincides with the vertical/elevation plane. For a horizontally-polarized antenna, the E-Plane usually concide with the horizontal/azimuth plane.

  • In the case of the same linearly polarized antenna, this is the plane containing the magnetic field vector and the direction of maximum radiation. The magnetic field or "H" plane lies at a right angle to the "E" plane. For a vertically-polarized antenna, the H-plane usually coincides with the horizontal/azimuth plane. For a horizontally-polarized antenna, the H-plane usually coincides with the vertical/elevation plane. FIELD REGIONS

In simple words, the field region is the region around antenna where the radiation propagates. The field region is further subdivided into three regions.

  1. Reactive near field
  2. Radiating near field (Fresnel)
  3. Far field (Fraunhofer)
  • The region in near field immediately around the antenna is called reactive near field because the reactive field predominates here. The outer boundary of this region is normally taken at distance R < 0.62vD3/ from the antenna surface. Where the wavelength and D is the largest dimension of antenna.

  • The region of the field between reactive near field and the far field is called radiating near field where the radiative field predominates and the angular field distribution depends upon the distance from antenna. For an antenna having maximum dimension not large compared to the wavelength then this radiating near field region dont exists and for an antenna focused at infinity, this region is called Fresnel region.

  • Thefar-field regionis the region outside the near-field region, where the angularfielddistribution is essentially independent of distance from the source. In the far field, the shape of the antenna pattern is independent of distance. If the source has a maximum overall dimensionD that is large compared to the wavelength?, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D2/(4?), S > 1. For abeamfocused at infinity, the far-field region is sometimes referred to as theFraunhofer region.


Directivity can de defined as the ratio of the radiated intensity (of the non-isotropic) antenna over that of the isotropic source. It is a dimensionless quantity. Directivity for an isotropic antenna will be unity. Mathematically it can be expressed as

D = U/Uo

Also D =4?U/ Prad


D = Directivity

U = radiation intensity (unit: W/unit solid angle)

Uo = radiation intensity of isotopic source (unit: W/unit solid angle)

Prad = total radiated power (unit: W)

2.3.3 GAIN

The gain of antenna and its directivity are closely related to each other; however there is one major difference in between them. The gain of the antenna is always in some specific direction and it depends upon efficiency and directional capabilities whereas directivity only describes directional properties of antenna.

The gain of antenna is defined as the ratio of the intensity in some specific direction to the radiation intensity of reference antenna. The reference antenna normally used is isotropic antenna that has unity gain. Gain in its equation form can be expressed as:

Gain = 4p (radiation intensity / Total input accepted power) = 4p U (?, ?) / Pin

The term gain is dimensionless. Another term normally used in place of gain is its relative gain that mainly depends upon its input power compared with the power of lossless isotropic antenna. Relative gain is defined as the ratio of power gain in a specific direction to the power gain of reference antenna (specific direction). If direction is not specified, the power gain is usually taken in the direction where there is maximum radiation. Maximum radiation region is taken because the major loab lies in this region and maximum power is transferred. Relative gain in its equation form is given as:

Gain = 4p U (?, ?) / Pin (lossless isotropic source)

In the antenna radiation, two types of power losses occurs which are losses arising from input mismatching which is also known as reflection loss and loss due to polarization mismatching. Both relative gain and simple gain does not include these two losses.

Gain and directivity are closely related by the equation given below, where evd is the antenna radiation efficiency.

Gain (?, ?) = evd D (?, ?)

The maximum value of the gain related to maximum directivity of antenna as:

Gain (?, ?)max = evd D (?, ?)max = evd Do

Whenever the antenna is connected to transmission line, reflection or mismatch losses occurs. While calculating gain, the reflection or mismatch losses can be handled by

Introducing mismatch efficiency factor as er and is represented as ( 1 I?I ). Including reflection loss, absolute gain can be written as:

Gain (?, ?) = evd D (?, ?) ] = ( 1 I?I ) G (?, ?)

The partial gain of antenna is related to its polarization is some specific direction. The partial gain of an antenna is defined as polarization of radiation intensity of some specific part to the ratio of total radiation intensity of the isotropic antenna. By adding the loss due to polarization, total gain is equal to sum of both of the components ? and ? and is given as:

Total gain = Go = G? + G?


Beamwidth of an antenna is defined as Angular separation between two identical points on opposite side of the radiation patterns maximum. In antennas perspective there are number of beamwidths used. Two of the most common used are Half Power Beamwidth (HPBW) and First Null Beamwidth (FNBW). Half Power Beamwidth is defined by IEEE as In a plane containing the direction of the maximum of a beam, the angle between the two directions in which the radiation intensity is one-half the value of the beam. And First Null Beamwidth is defined as the angular separation between first Nulls of the radiation pattern. Many other Beamwidth are used depend on the point of separation from the maximum like -10dB etc. For HPBW -3dB point in taken as power become half the maximum at this point.

No antenna can radiate energy in just one direction. Some of the energy is radiated in some other directions and these are called side lobes. As the side lobes decreases, Beamwidth increases. Resolution of an antenna can also be calculated from Beamwidth.


In the antenna parameters, there are many different beamwidths as mentioned above. One of the beamwidth among them is half power beamwidth which is defined as in a plane containing the direction of maximum beam, the angle between the two directions in which radiation intensity is one half value of beam. Half power beamwidth may also be physical size of projection of angle or at the location where measurement is taken.

2.3.5 Return Loss

2.3.6 VSWR

VSWR (Voltage Standing Wave Ratio) is the measure of impedence matching of a load to the source. This is expressed in ratio. When an antenna is fed with a signal, some part of it may reflect back to the transmitter. This happens in the case of impedence mismatching of the antenna and cable. Like in the case if our antenna is 50 Ohm and the Cable is 70 Ohm. Our objective is to achieve the VSWR of 1:1. This means all energy from the transmitter is getting into antenna and nothing is reflecting back. But practically it is not possible to achieve 1:1 VSWR because antenna is usually located at a distance from the transmitter and thats why we need to use a feed-line to transfer power. And for 1:1 VSWR there should be no feedline loss and feedline should match both the transmitters output impedance and antennas input impedance. And practically it is not possible, so our goal is always to gain VSWR as close to 1:1 as possible.


The bandwidth of antenna is another important parameter. It is the aim of every antenna to transmit n receives at its maximum bandwidth. Bandwidth is defined as the range of frequencies at which antenna can transmit and receives. It is always considered at the both sides according to the center frequency. The center frequency mainly chosen is the resonant frequency and the bandwidth is equally divided as upper bandwidth and lower bandwidth. This concept of upper and lower bandwidth is used in broadband antennas. For broadband antenna, the bandwidth is normally expressed as a ratio of upper and lower frequencies of acceptable operation. The bandwidth of an antenna depends upon the following parameters given below:

  • Gain
  • Side loab level
  • Beamwidth
  • Polarization
  • Beam direction
  • Pattern characteristics

In the early days antenna with the ratio of 2:1 were designed but now a days due to technological advancements, the ratio of 40:1 or greater can be achieved. Another important factor on which bandwidth depends is the dimension of antenna. By changing the length and width of antenna, bandwidth can be varied. The most common example is the antenna of car radio or rabbit ears of television. Both of these antennas have adjustable length and the can be tuned to give better reception. So from this we can see that by changing antenna length, better performance can be achieved.


Another antenna parameter is its input impedance that depends upon its terminals. Input impedance is defined as ratio of the voltage to the current pair of terminals or ratio of components of magnetic and electric field. In the case of antenna, input impedance mainly depends upon its terminals with no load attached. The input impedance of antenna is represented as Za given in equation below:

Za = Ra + jXa

In the above equation jXa is the antenna resistance at both of its terminals and Ra is the resistive part which is sum of radiation resistance Rr and loss resistance Rl. The total power that is delivered to the antenna, some part is radiated through the mechanism of radiation resistance and other is dissipated as a heat and this heat n radiation resistance influences the overall efficiency of antenna. If the antenna terminals are correctly matched to its transmission line, then these losses can be reduced but heat dissipation is always there. This heat dissipation loss can never be minimized.


The radiation intensity can be defined as The power radiated from an antenna from unit solid angle in a given direction. If U is Radiation Intensity in W/unit solid angle and Wrad is Radiation density in W/m2 then Radiation Intensity will be

U = r2 Wrad


The antenna efficiency eo is important to consider as it helps in evaluating losses at the input terminals and within the antennas structure. These losses are due to; reflections because of the mismatch of the antenna and the transmission line and I2R losses in conduction and dielectric. Mathematically it can be written as

eo = er ec ed


eo = total efficiency

er = mismatch efficiency

ec = conduction efficiency

ed = dielectric efficiency

(All quantities are dimensionless)


Polarization is one another antenna parameter that also depends upon direction of transmission or reception. Polarization state of an antenna in some specific direction is defined as the polarization of wave radiated by antenna. Direction must always be specified for polarization and if it is not given, polarization is taken into direction of maximum gain. Polarization can be in X , Y and Z direction. Below is the figure showing polarization in both X and Y directions.

There are two types of polarizations. They are given below:

  • Linear polarization
  • Circular or elliptical polarization

Linear polarization at a given point or space is defined as if the electrical or magnetic field at that point is always oriented along the straight line at that specific instant. This means that the wave that is moving always move in some specific direction or axis such as X , Y or Z axis. Circular polarization occurs when the wave is travelling in both X and Y direction and the magnitude of both of the vectors is equal, electric or magnetic field at that point traces a circle as a function of time, whereas in elliptical polarization, wave is travelling on both X and Y axis but with different magnitudes so both electric and magnetic traces an elliptical locus in space. For a wave to be linearly polarized, the time phase difference between two components.

Similarly for circular polarization, the magnitude of two components is same and time phase difference between two components is odd multiple of 1/2.

For elliptical polarization, the time phase difference between two components is odd multiple of 1/2 and their magnitude are not same.


Beam efficiency of an antenna is the measure of how much of the power is radiated in its major loab. This is one another antenna parameter which depends upon the major loab. Beam efficiency is defined as the ratio of power transmitted (received) within the cone angle to the power transmitted (received) by antenna. Beam efficiency in equation form is given below:

Beam Efficiency = P transmitted in cone angle / P transmitted by the antenna

To compare the amount of power in the major loab, the angle theta is chosen as the angle where first null or minimum occurs. High efficiency beam antenna are used in radiometry, astronomy, radar etc.


In triangular patch antenna, triangle shaped patch is used to emit radiations. They are found to provide the radiation characteristics similar to that of rectangular patch but less than as compared to rectangular shaped patch. By using equilateral triangle, the circular polarization is almost similar to that of square patch. To enhance the power emitted by antenna, slots or slits are added or shortening pin can be used. By using these, antenna size can also be reduced. Other factors regarding triangular patch antenna are given below:

  • Field Representation
  • To calculate the field, a cavity model is used in which triangle is surrounded by magnetic wall. The relative permivitty and thickness are kept constant, there are no variations in Z direction and TM mode is used. By duality property, the TM field patterns with magnetic boundary conditions are same. Using the basic equations we found that the wave number and resonant frequency remains the same. The fields for TM10 mode are symmetrical about the bisector line.

  • Resonant Frequency
  • To calculate the resonant frequency, the triangular patch is surrounded by a perfect magnetic wall. For resonant frequency, the length side a is replaced by effective value of ae but the dielectric value remains unchanged. The equation used to calculate resonant frequency is given below:

    Fr = ckmn / 2?ver = 2c vm2 + mn + n2 / 3av er


Radio wave does not travel only in Line Of Sight (LOS) path even if directional antenna is used. It spreads out in different angles and encounters other objects on its way like hills, buildings, water, vehicles etc and may encounter different mechanisms like reflection, diffraction and scattering. So they arrive at the receiving end at different instants of time. This result in multiple copies of the transmitted signal at the receiver end, and this phenomenon is called multipath fading.

Reflection can occur due to walls, billboards, even from earth surface. This happens when the incoming signal strikes the surface which is relatively large as compared to the incoming signals wavelength. The diffraction occurs due to the edges of the objects that come on its way. This happens when the incoming signal strikes the relatively large edge as compared to its own wavelength. And the scattering happens due to the rough surface. These three phenomenon are further elaborated.


As discussed earlier, radio wave arrives at the receiver via different paths. So the overall signal at the receiving end is the sum of all signals. At times this comes in phase to the main signal and adds constructively, strengthening the signal. But practically these components add destructively due to Non Line Of Sight (NLOS) environment giving rise to the fading phenomenon, resulting in overall signal strength to reduce. This constructive and destructive interference refers to Rayliegh fading model. And the strong Line Of Sight content give better performance refers to Rician fading model. The figure below shows multipath fading. The wave travels from the different paths, one has direct line of sight while other two are in deep fade.


As we see earlier that the practical world has a very scattering environment and it is not possible that all the time we can have LOS environment, especially in indoor communication. So we have to consider NLOS environment and ultimately we will encounter reflection, diffraction, scattering, fading and other phenomenon. Thats why researchers are working on it since the start of 19th century. Several mechanisms are being introduced to minimize destructive effects or make this mechanism beneficial. Out of these mechanisms one is diversity technique where received multipath components are merged together in an efficient way to increase the signal strength and channel capacity. Multiple antennas on receiving and transmitting end can help in reducing undesired multipath effects and can achieve a higher Signal to Noise Ratio (SNR) at the receiving end, ultimately improving the system performance. If one signal face fading problem then its very possible that the other signal comes at the receiving end with good strength. Practically it has been observed that it is very rare that at the same time both the signals arrive in deep fade. So in late 1990s researchers comes to the conclusion that use of multiple antennas at the receiving and transmitting end can help in better signal performance and reliable communication.

2.* MIMO Systems

In earlier system, single antennas were used at the transmitter and the receiver end, i.e. SISO (Single-Input Single-Output) systems. This system needs to be revised according to the scattering conditions of the site because of multipath propagation. This affects the overall system performance and increase the number of errors. So as discussed above we need to have multiple antennas. At first, the concept of Single-Input Multiple-Output (SIMO) and Multple-Input Single-Output (MISO) come to existence, which gives birth to the newest technology of Multiple-Input Multiple-Output (MIMO).

Using multiple antennas at both ends enhances the transmission power without extra frequency and power resources. Moreover, it exploits the multipath propagation channel and increases the channel capacity, providing the parallel orthogonal transmission channel, especially in rich scattering environment.


MIMO system model is shown in figure **** . to improve the communication performance it uses multiple antennas multiple antennas at both ends. If N is the number of transmitter antennas and M is the number of receiver antennas then the resulting system is shown in the figure

For simplification purposes, we assume that the number of antennas at the transmitter and the receiver side are same. Let this number be represented by n so we can say that: M=N=n

The vectors for the transmitter and receiver are represented by Where [*]t represents the transpose of the vector

If H(t) is the MIMO channel propagation matrix abd v(t) is AWGN additive noise then transmit and received signal vectors have the following relationship.

If i is the number for the receiving antenna and j is the number for the transmitting antenna then for i=1,2,.NR and j=1,2,.,NT , Hij represents the complex path gain from the transmit point to the receive point. Then for frequency fo the frequency response of a narrowband channel is given by Where M denotes the number of propagations paths between the end points. Here fo is operating frequency, LAMBDA=NOT is the wavelength, Pk is the receieved power, Ik is thelength of Kth ray and TAWWWk is the time delay corresponding to the Kth ray.

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