Recent results in MIMO Research at Canterbury University

Mansoor ShafiMay 2007

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Contents

Research team at Canterbury University

Prior work

Broadcast MIMO results

Eigen channel characteristics

Impact of Interference

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MIMO Research Team at Canterbury University

Faculty

Desmond Taylor- Professor

Peter J Smith- Associate Professor

Dr Lee Garth- Senior Lecturer

Mansoor Shafi- Adjunct Professor

PhD students

Tim King (focus area: BC channels)

Ping- Heng Kuo (focus area: Eigen channel Characteristics)

ME student

Min Zhang (completed)

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Prior Work

Key results over the last 10 years are:

MIMO capacity for a single iid channel is Guassian- ( Smith/Shafi). The Gaussian assumption holds true for various WF algorithms (AusCTW)

MIMO capacity is also Gaussian for a semi correlated Channel ( one end of the channel is correlated) (Smith/Roy/Shafi)

Asymptotic capacity behaviour for Ricean channels also determined (Lebrun et al)

Exact expressions for capacity level crossing rate and average fade duration can be found (Chiani /Andrea)

Exact expressions for BER and outage using SVD receivers have been derived (Garth et al)

Channel models for polarised channels and 3D impulse responses.

Current focus is on multi user MIMO

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BC capacity : Student Tim KingMotivation

There is increasing interest to study the MIMO capacity for multi user .

Computing the capacity of MIMO MAC and MIMO BC has attracted much interest. The MAC capacity is easy to find than the BC. The capacity of the BC remains an unsolved problem.

A duality technique published by Vishwanath et al ( Trans IT Oct 2003) and Jindal ( trans IT April 2005) enables the following statement via a duality technique:

The MAC capacity region is found via Iterative Water filling

Vishwanath does not consider SNR variations that arise due to shadow fading and distance dependent loss

The ITWF is an optimal approach to find the BC capacity but there are other sub optimal and simpler approaches

Therefore we :

compare the sum capacity various algorithms with ITWF during shadow fading

examine the fairness of the different algorithms

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System Model for Multi user MIMO

Diagrams care of [1]: “Sum Power Iterative Water-Filling for Multi-Antenna Gaussian Broadcast Channels” Nihar Jindal, Wonjong Rhee, Sriram Vishwanath, Syed Ali Jafar and Andrea Goldsmith, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 51, NO. 4, APRIL 2005 pp. 1570-1580

Tx has MantennasThere are KUsers. User ias ri antennas.Hi is iid and is an ri X M complex Channel matrix

The BC Channel The MAC Channel

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Channel Model

Our channel model included both distance and shadowing effects:

Where: U is an iid. Complex Gaussian matrix with elements with mean 0 and variance 1.

L is a log-normal shadow fading variable with 8dB standard deviation.

is the path loss exponent (3 in our simulations)

d is the distance (uniformly chosen from a field of radius 100m with a 10m exclusion zone in the centre)

is a normalization constant to ensure a constant average power across the field

ULdH

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Iterative Waterfilling with Sum Power Constraint

Iterative Waterfilling (ITWF) is an algorithm we use to maximise the sum capacity of a system. It is based on maximizing the following equation (for a MAC system).

ITWF can be done on an individual power constraint basis or on a sum power constraint basis. We used the sum power constraint basis to mirror a broadcast system with fixed power at the transmitter.

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Simpler Algorithms

Equal Power Independent Uncorrelated Transmission ( EPUIT)

This is the simplest approach. Here in the case of the MIMO-MAC

Row Selection

S1 – We choose the best x rows from all possible rows in the system. We allocate 1/x of the total power to each of the chosen rows.

S2 – We choose the best row from each of the K users in the system and allocate 1/K of the total power to each of the chosen rows. A row corresponds to a chosen antenna on which transmission is made. The rows are ordered on the basis of their norms.

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Simpler algorithms (contd): Beam forming

In the MIMO MAC BF consists of user i transmitting ni symbols along the

principal eigenvectors of

User i selects the top ni<= min( ri,M) eigenchannels which have eigenvalues

Then beamforming results if we use

We consider two kinds of beamforming:

BF1 – We find the best x eigenvalues from all possible eigenvalues of all users. We then beamform with power 1/x down these channels.

BF2 – We find the maximum eigenvalue from each user and beamform along its eigenvector with 1/Kof the total power

Eigen vectors

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Results – No Shadowing SNRav = 10dB

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Results –Shadowing SNRav = 10dB

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Results- Shadowing SNR av = 0 dB

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Comments

In the absence of shadowing we observe the well known approximately Gaussian cdf shapes.

With shadowing, averaging over the SNR changes the shape of the sum capacity cdf

ITWF is the best in all cases

In the no shadowing results, the EPIUT and BF approaches are very close to ITWF. This is to be expected as WF advantages over equal power are well known especially for low SNR

In the shadowing case S1 and BF1 perform almost as well as ITWF. During the presence of shadowing skewing the channel in favour of some users, concentrating the array gain in certain directions or using a subset of antennas yields excellent results

It would also seem relevant to consider S1 as a kind of lower bound on ITWF when shadowing is present

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Fairness

A system can be described as fair if every user in it is achieving a suitable non-zero rate.

However the definition of a suitable rate can be up to the user.

Various metrics can be used to measure fairness. We have used number of users with non-zero rates as a raw measure of fairness.

Other indicators can be minimum rates, power in the dominant user as well as number of spatial channels open.

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Results – Fairness of ITWF

Channels

users

users (shadowing)

Channels (shadowing)

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Comments on Fairness

At high SNRav ITWF is essentially fair with each user getting a portion of available power

For low SNR ITWF is inherently un fair. It causes one or more users to shut out. Note we had 3 users, so the percentage of users is lower bounded by 33%. In the shadowed case one user is frequently experiencing communication

Fairness results for the spatial channels are very similar to the users- ie under shadowing, a lot of the spatial channels are shut out

S1 and BF1 communicate with70% of the users even at low SNR

S2 and BF2 communicate by definition to all 3 users

Eigen Structure Analysis : Student- Ping Heng KuoSVD and Eigenmode Transmission

HRxT = U∑V*

If we further Define

• For the general flat-fading channel, the relationship between input symbol x, and output symbol y, is:

where n represents Gaussian noise.

• By using singular value decomposition (SVD), we can re-write the MIMO channel matrix as follows:

Unitary matrices

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TX V

….

U* RX

σ1

σ2

σmin(M,N)

σ1≥ σ2≥ σ3≥… ≥ σmin(M,N)

H

TX RX

By pre-processing the input symbols and post-processing the received symbols, we can obtain an equivalent form of the MIMO channel:

These parallel channels are called eigen-channels (a.k.a. eigenmodes). Also, the squared singular values σi

2 = λi are the power gains of the channel.

SVD and Eigenmode Transmission

SVD and Eigenmode Transmission

• In order to obtain matrices U and V, channel state information (CSI) is required at both transmitter and receiver. So a feedback link is needed for this architecture. Note that the columns of U and V are the eigenvectors of channel correlation matrices HH* and H*H respectively.

• The performance of the system is strongly related to the accuracy of CSI.

• Two main impairments on CSI quality: channel estimation error and feedback time delay.

TX V U* RXH

Feedback Link ChannelEstimation

SVD with Feedback Delay

• Due to the feedback delay, V is outdated.

• With such imperfect CSI, the channel matrix cannot be perfectly diagonalized.

• The input-output relationship of the system becomes:

• Two main effects of mismatch between steering matrices: Loss of signal power and introduction of interference in the eigenmode transmissions.

• The effects of channel estimation errors are neglected in this paper.

Objectives

We are interested in the resultant signal and interference power in eigenmode transmission with the presence of feedback delay. In particular, we will derive an analytical expression for the instantaneous Signal to Interference Noise Ratio (SINR).

•SINR of the ith eigenmode is shown to be:

fD and τ are Doppler frequency and time displacement respectively.

This result is very interesting, because we can see that the extra interference is equal to the loss of signal power.

• We verify this expression by generate 1000 channel realizations from 1 fixed channel, and compare the average SINR from calculation and simulation.

Derivation of SINR

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A Novel Channel Metric

Assuming Doppler frequency and feedback delay time are constant, both the loss in signal power and the triggered interference power are proportional to the parameter Q:

Therefore, we can use Q to gauge the system performance sensitivity to channel time variation. That is, error probability due to feedback delay is higher with a larger value of Q.

Clearly, loss in signal power (and hence interference) is highest when the sum of multiple eigen-channel gains is large, and the eigen-channel gains are close in magnitude.

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Instantaneous BER Performance (2,2)

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Instantaneous BER Performance (4,4)

BER with feedback delay

Without delay

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Comments on Eigen Structures

The Q factor may be considered a metric to determine sensitivity to feedback delay. The worst scenario occurs when two eigen values are close to each other. They tend to repel and move away from each other. In this case the repelling eigen values may cause outdated eigen vectors and in turn outdated steering matrices.

Large peaks in BER are very well correlated with large peaks in Q.

Our simulations have shown that increasing system size ( say from 2,2 to 4,4 antennas, Q values increase and the gap between BER with and without delay increases. Large systems may provide higher capacity but are subject to increased interference

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Impact of Other Cell Interference

•Universal reuse maximizes spectral efficiency but OCI is a problem•Performance of wireless networks dominated by interference•Link performance is approximating fundamental limits•Difficult additional gains from smaller cells, increased spectrum and Interference cancellation

Cell A

Cell B

Link A

Link B

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The link capacity of current systems is quickly approaching the Shannon limit (within a factor of two in power).

Future improvements in spectral efficiency will focus on interference mitigation techniques.

Source: Simulations done by Lucent

-15 -10 -5 0 5 10 15 200

1

2

3

4

5

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required SINR (dB)

achi

evab

le r

ate

(bps

/Hz)

Shannon boundShannon bound with 3dB margin

EV-DO802.16

HSDPA

Spectral Efficiency of Various Existing Systems

Typical valueof Mean SINR= 5dB

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Modelling of Other Cell Interference

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Fundamental Limits in Per Sector ThroughputSector throughput is determined only by available bandwidth, SINR distribution, and   link spectral efficiency

Spectrum efficiencies  approaching fundamental limits to within 2-3 dB

Distribution of SINR throughout the sector is determined by reuse distance

Increasing frequency reuse distance increases SINR but reduces the per-sector bandwidth

Sector  throughput can only be increased significantly (>50%) by frequency re use (increasing bandwidth) Novel  ways of dealing with out- of -cell interference are needed to go beyond this fundamental limit

Mean SINR is about 4 -5dB and 14 dBfor universal and 1/3 reuse

and 30% of the usersare within approx 10dB of the min SINR

for universal re use

Ref: Smith, Shafi, Aus CTW 06Huang : PIMRC 06

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Adaptive Antennas : Cancelling Interference

Cancelling 4 dominant interferers has an effect that is almost the same as

frequency re use of 1/3

Rural Mean SINR with f=1/3

is about 6 dB

Suburban Mean SINR with f=1/3

is about 9 dB

Urban Mean SINR with f=1/3

is about 14 dB

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Mean capacities when Interferers are removed

No interferer removed

4 interferers removed

Removing 4 dominant interferershas a > 100% improvementfor 4,4 antennas

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Summary

MIMO single user is well researched and nearing saturation

MIMO multiuser is a new field and has potential for new research but the gains seem small relative to complexity

Interference is a key issue in MIMO and unless this is addressed the promise of MIMO will be heavily compromised. Some preliminary studies we have done show that under OCI, conventional diversity outperforms MIMO. Also if 3-4 dominant interferers can be cancelled we may be able to reclaim the lost gains