We are currently working on the following topics:

- Source coding and joint source-channel coding
- MIMO/OFDM channel estimation
- Cognitive radio
- Scheduling and resource allocation
- Distributed detection and estimation
- Compressive sensing
- Interference management

Abstracts of some of our recent projects (in an arbitrary order) can be found below:

Spectrum sensing for cognitive radio.We considered the case where the primary transmitter’s signal occupies a large bandwidth, but with a high power narrowband component. Such a signal opens up two possibilities for detection: one could either try to detect the entire wideband signal, or one could filter out only the narrowband component and detect its presence or absence. The fact that the signal propagation characteristics of narrowband and wideband signals are quite different leads to an interesting tradeoff between the two options. We analytically characterized this tradeoff, and determined which of the two options offers better detection performance.

Joint work with Sanjeev Gurugopinath.

Achievable rates and outer bounds for the interference channel with cooperation and privacy constraints.In this line of research, we first developed algorithms for interference alignment in a multiuser MIMO interference constant channel setup. Next, we analyzed the generalized degrees of freedom of the K-user MIMO interference channel. Finally, we considered the 2-user interference channel with rate-limited cooperation between the transmitters and secrecy constraints at the receivers. We were able to derive achievable schemes and outer bounds on the rate pairs first for the so-called deterministic approximation of the interference channel, and then extended the results to the Gaussian interference channel.

Joint work with Parthajit Mohapatra.

Algorithms for sparse signal recovery.We developed algorithms for wideband channel estimation exploiting the sparsity of the channel in the time-domain. Starting from algorithms for channel estimation in the single-antenna case, we extended our algorithms to track time-variations in the channel, to exploit “cluster sparsity”, where the signals arrive in clusters of closely separated delays, and to multiple antenna systems where the signals between different pairs of transmit and receive antennas have a common sparsity structure (support). This latter work won the best paper award in the National Communications Conference 2014, which was held at IIT Kanpur.

Joint work with Ranjitha Prasad.

Finding healthy individuals from a large population.Here, one considers the scenario where a large population contains a small number of “defective” items. A commonly encountered goal is that of identifying the defective items, for example, to isolate them from the population. In the classical non-adaptive group testing approach, one groups the items into subsets, or pools, and runs tests on each pool. Tests come out positive if the pool contains at least one defective item, and come out negative if all items in the pool are non-defective. Using the outcomes of the tests, a fundamental goal of group testing is to reliably identify the complete set of defective items with as few tests as possible. We studied a variant of this problem: one of non-defective subset identification, where the primary goal is to identify a “subset” of “non-defective” items given the test outcomes. This is useful when one wants to quickly identify a batch of non-defective items, for example, when it is required to send out a shipment of items on high priority. We have developed fundamental limits on the number of tests required for non-defective subset recovery, as well as computationally efficient algorithms for recovering the non-defective items that approach the bounds.

Joint work with Abhay Sharma.

Performance Comparison of Energy, Matched-Filter and Cyclostationarity-Based Spectrum Sensing:This work addressesspectrum sensing, i.e., the problem of detecting the presence or absence of a primary signal by a cognitive radio. Three popular choices are comprehensively contrasted: energy detection, matched-filter detection and cyclostationarity-based detection. For the cyclostationarity-based detection, two options for signal detection are investigated: using the Spectral Correlation Density (SCD) function, and using the Magnitude Squared Coherence (MSC) function. Analytical expressions for the probability of detection and false alarm performance of the cyclostationary feature detectors as well as the ED and MFD, as a function of the SNR and sensing duration are derived. It is shown that the cyclostationarity-based detectors are naturally insensitive to uncertainty in the noise variance, as the decision statistic is based on the noise rejection property of the cyclostationary spectrum. Monte-Carlo simulations of the receiver operating characteristics corroborate the theoretical results, and illustrate the significant performance improvement offered by the MSC relative to the ED in a noise uncertain environment. The MFD, on the other hand, serves as an important performance benchmark.

Work of: Deepa B.

Receiver-only optimized semi-hard decision VQ For noisy channels:This work proposes a new receiver optimized semi-hard-decision vector quantization (SHDVQ) for noisy channels, as a technique to alleviate the drastic increase in distortion incurred when the output of the classical source optimized vector quantizer (SOVQ) is sent over a noisy channel. The advantages of the proposed method are that it is computationally simple, requires minimal extra storage, and can be implemented solely at the receiver; thus allowing the encoder to be independent of channel conditions. Another advantage is that it can be used in conjunction with an index assignment to obtain the beneﬁts of index assignment (IA). The decoder considers errors and erasures based on thresholding the log-likelihood ratio (LLR) of the bits comprising the transmitted index. Then, the proposed decoder computes the output as a linear combination of the codebook vectors based on the erasure bit locations and the IA. A novel performance analysis is presented, where the overall distortion is expressed as a convex combination of the distortion with anidealIA and the distortion withrandomIA. The analysis is used to ﬁnd the erasure threshold that minimizes the overall distortion. ~Monte-Carlo simulation results are used to corroborate the derived theoretical expressions.

Work of: Ganesan T.

Three-user cognitive channels with unidirectional message sharing: an achievable rate region:In this work, an achievable rate region for the three-user discrete memoryless interference channel with asymmetric transmitter cooperation is derived. The three-user channel facilitates different ways of message sharing between the transmitters. Here, two manners of non-causal unidirectional message-sharing, which are termedcumulative message sharingandprimary-only message sharing, are introduced. Receivers with various (predetermined) decoding capabilities are considered, and used to define a cognitive interference channel. An achievable rate region for these channels are then derived by employing a coding scheme which is a combination of superposition and Gel'fand-Pinsker coding techniques.

Work of: Nagananda K. G.

Reverse channel training for reciprocal MIMO systems with spatial multiplexing:This work investigates the problem of designing reverse channel training sequences for a ~TDD-MIMO spatial-multiplexing system. Assuming perfect channel state information at the receiver and spatial multiplexing at the transmitter with equal power allocation to the 'm' dominant modes of the estimated channel, the pilot is designed to ensure an estimate of the channel which improves the forward link capacity. Using perturbation techniques, a lower bound on the forward link capacity is derived with respect to which the training sequence is optimized. Thus, the reverse channel training sequence makes use of the channel knowledge at the receiver. The performance of orthogonal training sequence with MMSE estimation at the transmitter and the proposed training sequence are compared. Simulation results show a significant improvement in performance.

Work of: Bharath B. N.

Trellis coded block codes and applications:Trellis coded modulation (TCM) is used widely in wireline and wireless modems in order to improve BER performance without extra bandwidth or energy requirements. Ungerboeck’s introduction of TCM in 1976 and 1982, stimulated a search for good TCM codes and performance gains, typically with a small increase in complexity. In this work, a similar trellis coded modulation, but using linear block codes (LBC) referred to as Trellis Coded Block (TCB) codes, is presented. Unlike conventional TCM, these TCB codes can be used for both discrete as well as continuous channels. This has been made possible by utilizing an algebraic structure inherent in any block code, that allows one to partition any it into subcodes with constant distance between the code words. This code-set partitioning is used to maximize the minimum distance between code words. Another feature of TCB is that implementations are possible both with as well as without bandwidth expansion. The encoder/decoder without bandwidth expansion uses the multilevel coding and is more complex compared to the pair with bandwidth expansion.

Work of: Ganesan T.

Robust semi-blind estimation for beamforming based MIMO wireless communication:In this work, robust semi-blind (SB) algorithms for the estimation of beamforming vectors for multiple-input multiple-output wireless communication are presented. The transmitted symbol block is assumed to comprise of a known sequence of training (pilot) symbols followed by information bearing blind (unknown) data symbols. Analytical expressions are derived for the robust SB estimators of the MIMO receive and transmit beamforming vectors. These robust SB estimators employ a preliminary estimate obtained from the pilot symbol sequence and leverage the second-order statistical information from the blind data symbols. Employing the theory of Lagrangian duality, the robust estimate of the receive beamforming vector is derived by maximizing an inner product, while constraining the channel estimate to lie in a confidence sphere centered at the initial pilot estimate. Two different schemes are then proposed for computing the robust estimate of the MIMO transmit beamforming vector. Monte Carlo simulations illustrate the benefits offered by the proposed schemes.

Joint work with: Aditya Jagannatham, Bhaskar Rao.

Receiver-only optimized vector quantization for noisy channels :This work considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess ~Mean-Squared Error (MSE) distortion caused due to channel errors. It is assumed that the source encoder is channel-agnostic, i.e., that a Vector Quantization (VQ) based compression designed for a noiseless channel is employed. The index output by the source encoder is sent over a noisy memoryless discrete symmetric channel, and the possibly incorrect received index is decoded by the corresponding VQ decoder. The output of the VQ decoder is processed by a receive filter to obtain an estimate of the source instantiation. Given this scenario, the optimum linear receive filter structure to minimize the overall MSE is derived, and shown to have a minimum-mean squared error receiver type structure. Further, expressions are derived for the resulting high-rate MSE performance. The performance is compared with the MSE obtained using source-optimized VQ as well as the channel-optimized VQ, and it is shown that under some situations, the receiver-only optimized VQ can perform comparably to the channel-optimized VQ.

Work of: Chandra Murthy

Power management and data rate maximization in wireless energy harvesting sensors:In this work, the problem of power management and throughput maximization for energy neutral operation when using Energy harvesting Sensors (EHS) to send data over wireless links is considered. Assuming that the EHS are designed to transmit data at a constant rate and are power-controlled, a framework under which the system designer can optimize the performance of EHS is developed. For example, the highest average data rate that can be supported over a Rayleigh fading channel given the energy harvesting capability, the battery efficiency and the maximum allowed transmit energy per slot is derived. Furthermore, the optimum transmission scheme that guarantees a particular data throughput is also derived.

Work of: Chandra Murthy

Performance of quantized equal gain transmission with noisy feedback channels:In this work, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the Equal Gain Transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received SNR relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming.

Joint work with: Bhaskar Rao