Notes on transform domain adaptation (LMS)

Transform domain adaptive filter (e.g. DFT-LMS, DCT-LMS)

• Performance of LMS is sensitive to the eigenvalue spread of the input covariance matrix.
• The smallest eigenvalue contribute to slower convergence and the largest eigenvalue limit the range of allowed step-sizes, thus limiting the learning abilities of the filter.

A DFT/DCT type transformation allows one to whiten the input sequence in the transform domain without the need to know the correlation matrix (e.g. using KLT) of the sequence which may not be stationary.

[Hodgkiss, 1979] has shown the conditions under which time domain and frequency domain processing is equivalent.  

[Beaufays, 1995] showed analytically the eigenvalue distributions of a markov-1 sequence to have asymptotic eigenvalue spread of  [interesting matrix theory]

$$\left( \frac{1+\rho}{1-\rho} \right)^2, \quad \text{before transformation}$$  

$$\left( \frac{1+\rho}{1-\rho} \right), \quad \text{after DFT and power normalization}$$  

$$(1+\rho), \quad \text{after DCT and power normalization}$$

Random sequence whitening

• Orthogonal decomposition (e.g. EVD) and triangular decomposition (e.g. LDU) decorrelate a signal sequence.
• LDU decomposition allows us to whiten a signal causally (since $\mathbf{B}=\mathbf{L}^{-1}$ is a causal linear transform).

Notes on Discrete Karhunen-Loeve Transform (DKLT) and DFT

• In general, the DKLT is obtained from eigenvalue decomposition.
• The correlation matrix of a stationary process is Toeplitz.
• If the autocorrelation sequence of a random process is periodic with fundamental period $M$, its correlation matrix becomes circulant.
• The DFT provides the DKLT of periodic random sequences.
• This can be easily seen because DFT defines the complete set of eigenvectors for all circulant matrices.

Notes on Globecom 2015

Monday 12/7/2015 

Morning session 

• Suppression of Analog Self-Interference Canceller Nonlinearities in MIMO Full Duplex 
• Use of nonlinear modeling to cancel nonlinear behavior of the RF chain
• Receive Spatial Modulation (Marco Di Renzo) 
• New ideas for MIMO Broadcast Channel 
• A 60GHz LOS MIMO Backhaul Design Combining Spatial Multiplexing and Beamforming for a 100Gbps Throughput (Gerhard Fettweis' group)
• Deterministic Spatial Multiplexing (Antenna spacing determined by the distance between TX and RX)

Noon session (mmWave)

• Adaptive One-bit Compressive Sensing with Application to Low-Precision Receivers at mmWave (joint work University of Vigo, Spain and Robert Heath)
• Compressive sensing for estimating channel of 1-bit receiver

Afternoon session (Massive MIMO)

• Exploiting the Tolerance of Massive MIMO to Incomplete CSI for Low-Complexity Transmission (UCL)
• Exploit antenna correlation by training a subset of antennas and interpolate missing information.  (Perhaps CS based schemes can be used?)
• Downlink Performance and User Scheduling of HetNet with Large-Scale Antenna Arrays (University of Victoria)
• Lower bound analysis on Hetnet.  (Useful technique)
• Large System Analysis of Base Station Cooperation in the Downlink (Luca Sanguinetti, Couillet and Debbah)
• New RMT results for DL BS cooperation with imperfect CSI 

Tuesday 12/8/2015 

Morning session (Massive MIMO)

• Polynomial-Expansion Multi-Cell Aware Detector for Uplink Massive MIMO Systems with Imperfect CSI (Germany)
• replacing matrix inverse with polynomial expansion
• Joint Use of H-inf Criterion in Channel Estimation and Precoding to Mitigate Pilot Contamination in Massive MIMO Systems (University of Northeastern, China)
• H-inf Criterion used to design CE and Precoding (minimax like criterion, minimize worst case penalty)
• Location-Aided Pilot Contamination Elimination for Massive MIMO Systems (Chalmers, Sweden)
• estimate AoA and AS to compute Covariance matrix.
• Data-Assisted Massive MIMO Uplink Transmission with Large Backhaul Cooperation Delay: Scheme Design and System-Level Analysis (Very good analysis)
• Successively use data to improve channel estimation.   
• Develop network model with fixed BS location using stochastic geometry
• Shifted Zadoff Chu sequence used (do not reuse pilots)

Noon session 

• Maximal Ratio Transmission in Wireless Poisson Networks under Spatially Correlated Fading Channels
• Stochastic geometry.  Correlated channel.  Spatial correlation is SINR dependent.
• Performance Analysis of Single-Carrier Modulation with Correlated Large-Scale Antennas (Geoffrey Li, Georgia Tech) 
• Propose SC over OFDM in massive MIMO.  No equalizer under the condition of i.i.d channel.

Afternoon session

• Multi-switch for antenna selection in massive MIMO
• binary switching in antenna selection (have small loss in capacity)
• A Multi-cell MMSE Precoder for Massive MIMO Systems and New Large System Analysis (Emil Bjornson)  Good analysis
• Multicell MMSE precoder for TDD massive MIMO using idea of Pilot reuse.  Exploit UL/DL duality to come up with precoder design that spans B directions only.  
• Harmonized Cellular and Distributed Massive MIMO: Load Balancing and Scheduling (DOCOMO)
• Distributed massive MIMO with Hetnet, scheduling using blanking etc.  
• research has industry knowledge 

Multi-cluster massive MIMO

Ideas 

• [12/3/2015] It might be worthwhile to look into the design of the transmit unitary matrix.

Challenges

• When interfering channel is present, any use of the interfering channel will add to the noise temperature of the environment.

Key Concepts

• Successive decoding achieves the capacity region of degraded broadcast channel.  
• Scalar broadcast channel is a degraded broadcast channel.

• MISO channel: With only covariance feedback, water filling along the eigenvectors of the channel covariance achieve capacity.  Specifically independent complex circular Gaussian inputs along the eigenvectors of $\Sigma$ is optimal.