Recent results in MIMO Research at Canterbury University

1. Recent results in MIMO Research at Canterbury University Mansoor Shafi May 2007

2. Contents • Research team at Canterbury University • Prior work • Broadcast MIMO results • Eigen channel characteristics • Impact of Interference

3. 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)

4. 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

5. 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

6. System Model for Multi user MIMO The BC Channel The MAC Channel Tx has M antennas There are K Users. User i as ri antennas. Hi is iid and is an ri X M complex Channel matrix 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

7. 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. • g 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) • m is a normalization constant to ensure a constant average power across the field

8. 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.

9. 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.

10. 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

11. Results – No Shadowing SNRav = 10dB

12. Results –Shadowing SNRav = 10dB

13. Results- Shadowing SNR av = 0 dB

14. 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

15. 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.

16. users Channels users (shadowing) Channels (shadowing) Results – Fairness of ITWF

17. 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

18. Eigen Structure Analysis : Student- Ping Heng KuoSVD and Eigenmode Transmission • By using singular value decomposition (SVD), we can re-write the MIMO channel matrix as follows: HRxT = U∑V* • For the general flat-fading channel, the relationship between input symbol x, and output symbol y, is: • where n represents Gaussian noise. Unitary matrices If we further Define

19. SVD and Eigenmode Transmission By pre-processing the input symbols and post-processing the received symbols, we can obtain an equivalent form of the MIMO channel: TX V H U* RX σ1 TX RX σ2 …. σmin(M,N) σ1≥ σ2≥ σ3≥… ≥ σmin(M,N) These parallel channels are called eigen-channels (a.k.a. eigenmodes). Also, the squared singular values σi2 = λi are the power gains of the channel.

20. 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 H U* RX Channel Estimation Feedback Link

21. 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.

22. 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).

23. Derivation of 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.

24. 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.

25. Instantaneous BER Performance (2,2)

26. Instantaneous BER Performance (4,4) BER with feedback delay Without delay

27. 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

28. 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 Link A Cell A Cell B Link B

29. Spectral Efficiency of Various Existing Systems 6 Shannon bound Shannon bound with 3dB margin 5 HSDPA EV-DO 802.16 4 achievable rate (bps/Hz) 3 2 Typical value of Mean SINR= 5dB 1 0 -15 -10 -5 0 5 10 15 20 required SINR (dB) 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

30. Modelling of Other Cell Interference

31. Fundamental Limits in Per Sector Throughput • Sector 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 dB for universal and 1/3 reuse and 30% of the users are within approx 10dB of the min SINR for universal re use Ref: Smith, Shafi, Aus CTW 06 Huang : PIMRC 06

32. 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 Adaptive Antennas : Cancelling Interference Cancelling 4 dominant interferers has an effect that is almost the same as frequency re use of 1/3

33. No interferer removed 4 interferers removed Mean capacities when Interferers are removed Removing 4 dominant interferers has a > 100% improvement for 4,4 antennas

34. 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