IN THE NAME OF GOD

 

Introduction to MIMO  

By:Mohammad Reza Jabbari

October 2016 1

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INTRODUCTION

Wireless communication has Experienced Several Revolutions, including the appearance of AM and FM communication systems in early twentieth century and the development of the cellular phone systems from its first generation to the four generation in the last few decades.

Higher Performance

Improve Data Rate

Improve Reliability

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SISO MIMO

1990s NOW

Using of Advances coding, such as :1. Turbo2. Low Density Parity Check Codes (LDPC) 3. And … made it feasible to approach the Shannon capacity limit.

Using of Advances reception techniques such as :1. Frequency Sharing2. Space-time Coding3. Beamforming And Antenna Selection have been invented to efficiently achieve the high performance.

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In MIMO Systems:

Spectral Efficiency of MIMO channels grows approximately linearly with the Number Of Antennas (with assuming ideal propagation) .

also benefit from Multiple Path Propagation, or fading, which is traditionally regarded as a disadvantage of a wireless channel.

Important MIMO Systems Limitations :

1.Size

2. Hardware Complexity

3. Processing Power

4. Cost

Cooperative Networks

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MIMO SYSTEMS1. MIMO Systems Model

Let us consider a single point-to-point MIMO system with arrays of nT transmit and nR receive antennas.

The transmitted signals in each symbol period are represented by an nT×1 column matrix X, where i th component xi refers to the transmitted signal from antenna i.

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The channel is described by an nR × nT complex matrix, denoted by H. the i j-th component of the matrix H, denoted by hij, represents the Channel Fading Coefficient from the j th transmit to the i th receive antenna.

By using the Linear Model the received vector can be represented as:

The Noise at the receiver is described by an nR × 1 column matrix, denoted by n. Its components are statistically independent complex zero-mean Gaussian variables, with independent and equal variance real and imaginary parts :

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MIMO SYSTEM CAPACITY The system capacity is defined as the maximum possible transmission rate such that the probability of error is arbitrarily small.

2. MIMO Systems Capacity Derivation

2.1 we assume that the channel matrix is not known at the transmitter, while it is perfectly known at the receiver.

SVD

2.2 we assume that the channel matrix is perfectly known for the receiver and transmitter.

Water-Filling

Transmitter Transmitter ReceiverReceiver

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2.1 Singular Value Decomposition SVD Matrix H can be written as:

the eigenvalue of HHH denoted by are defined as :

Notation: The number of nonzero eigenvalues of matrix HHH is equal to the rank of matrix H, denoted by r.

Thus the equivalent MIMO channel can be consisting of r Uncoupled Parallel Sub-Channels. Each sub-channel is assigned to a singular value of matrix H, which corresponding to the amplitude channel gain. The channel power gain is thus equal to the eigenvalue of matrix HHH.

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Note that in the equivalent MIMO channel capacity modeled by the uncoupled sub-channels are their capacities add up. We can estimate the overall channel capacity, denoted by C, by using the Shannon capacity formula:

where W is the bandwidth of each sub-channel and Pri is the received signal power in the i th sub-channel.

Q is the Wishart Matrix defined as:

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2.2 Water Filling

Let us consider a MIMO channel where the channel parameters are known at the transmitter. The allocation of power to various transmitter antennas can be obtained by a “water-filling” principle. The power allocated to channel i is given by :

COOPERATIVE NETWORKS

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Recently, a new class of methods called Cooperative Communication has been proposed that enables single antenna mobiles in a multi-user environment to Share Their Antennas and generate a Virtual Multiple-Antenna transmitter that allows them to achieve transmit diversity and creates a virtual MIMO system. Cooperation Protocols:1.Amplify and forward (AF) : Relays act as Analog Repeaters2.Decode-and-forward (DF) :Relays act as Digital Regenerative Repeaters 3.Compress-and-forward (CF) : Relays Quantize and Compress (Source Coding)

COGNITIVE NETWORK (CN)

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Cognitive Network is a data communication network, which consist of Intelligent Devices. Intelligence means that they are aware of everything happening inside the device and in the network they are connected to.

Cognitive Network is the collection of elements that make up the network observes network conditions and then, using prior knowledge gained from previous interactions with the network, plans, decides and acts on this information.

Learning loop by Col John Boyd

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Spectrum pooling and Space Pooling

However, in some regions, some of the valuable spectrum are under low-efficiency, This is mainly because the currently fixed Spectrum Allocation policy of today’s wireless networks.

Cognitive radio (CR) technology is widely considered to be one of the most promising technologies for highly efficient spectrum, which allows the Spectrum Sharing among primary and secondary users in an Opportunistic Manner .

In spectrum pooling, the spectrum from different owners is merged into a common pool, and allowing secondary radio networks to access the already licensed frequency bands.

f1

f2

f4

f3

f6

f5

f7

fn

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Space Pooling

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PREFACE We describe a Non-Cooperative Interference Alignment (IA) technique which allows an opportunistic multiple input multiple output (MIMO) link (secondary) to harmlessly coexist with another MIMO link (primary) in the same frequency band.

Assuming perfect channel knowledge at the primary receiver and transmitter, capacity is achieved by transmitting along the Spatial Directions (SD) associated with the singular values of its channel matrix using a Water-filling Power Allocation (PA) scheme.

Often, power limitations (such as low SNR) lead the primary transmitter to leave some of its SD unused.

So Secondary Systems, opportunistically access certain portions of spectrum left unused by other radio Primary Systems, at a given time or geographical area.

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Notation: Secondary users should be such that as soon as the primary user wants to use its bandwidth, bandwidth back to the original owner.

These pieces of unused spectrum, known as White-Spaces, appear mainly when either transmissions in the primary network are sporadic, i.e., there are periods over which no transmission takes place, or there is no network infrastructure for the primary system in a given area, for instance, when there is no primary network coverage in a certain region. In the case of dense networks, a white-space might be a rare and short-lasting event

Private Massage : Each transmitter sends independent messages only to its respective receiver and no cooperation between them is allowed, i.e., there is no message exchange between transmitters.

Only One Destination Node Is Able To Decode It.

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SYSTEM MODEL

• matrix Vi is called Pre-Processing Matrix.

Notation: we assume that the primary terminals (transmitter and receiver) have perfect knowledge of the matrix H11 while the secondary terminals have perfect knowledge of all channel transfer matrices H11, H12, H21 and H22.

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INTERFERENCE ALIGNMENT STRATEGY1. Primary Link Performance

primary link must operate at its highest transmission rate in the absence of interference. with singular value decomposition (SVD) for : 𝐻11=𝑈 𝐻11

𝐴𝐻11𝑉 𝐻11

𝐻

So we can show the optimal pre-processing and post-processing schemes for the primary link to achieve capacity are given by :

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Let denote the number of transmit dimensions used by the primary User, we know that:

1≤𝑚1≤𝑁 where ¿

The used dimensions are called Primary Reserved Dimensions, while the remaining dimensions are named Secondary Transmit Opportunities (TO).

The IA strategy, allows the secondary user to exploit these receive dimensions left unused by the primary link, while avoiding to interfere with the receive dimensions used by the primary link.

𝑆=𝑁 1−𝑚1

2. Secondary Link Performance

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THE END

“Once you stop learning ,you start dying”

Albert Einstein