Communication over channels with state is a classical problem extensively studied. Herein, the problem statement is extended to consider a multihop channel where the channel state information in hops, unavailable to neither the source, the destination, nor the relay(s), is to be estimated at the destination, along with reliable information transmission. Each relay in the multihop channel forwards the source's transmitted signal, estimates the preceding hops' channel states, and assists in the destination's reliable decoding of the transmitted message and reconstruction of the channel states. For a two-hop channel with independent states over the two hops, it is shown that a decode-(indirectly)-compress-and-forward strategy achieves the capacity-distortion function.

A scenario involving a source, a channel, and a destination, where the destination is interested in both reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel, is considered. The source knows the channel statistics but is oblivious to the actual channel state realization. Herein, it is established that a distortion constraint for channel state estimation can be reduced to an additional cost constraint on the source input distribution, in the limit of large coding block length. A newly defined capacity-distortion function thus characterizes the fundamental tradeoff between transmission rate and state estimation distortion. It is also shown that noncoherent communication coupled with channel state estimation conditioned on treating the decoded message as training symbols achieves the capacity-distortion function. Among the various examples considered, the capacity-distortion function for a memoryless Rayleigh fading channel is characterized to within 1.443 bits at high signal-to-noise ratio. The constrained channel coding approach is also extended to multiple access channels, leading to a coupled cost constraint on the input distributions for the transmitting sources.

The problem of time-varying channel estimation in multihop sensor networks is examined. Two relay processing methods are explored: amplify-and-forward and encode-and-forward. Bounds on the end-to-end distortion for all internode channel estimates are computed for these two relay processing schemes. Performance is analyzed via the asymptotic limit of the decay rate of the end-to-end distortion with respect to SNR at high SNR. It is also established that asymptotically in SNR, amplify-and-forward can outperform encode-and-forward and in fact can achieve the maximum possible distortion exponent (distortion decay rate) order of unity. Linear and many-to-one topologies are then examined and it is shown that orthogonal access in the many-to-one network is optimal.

A joint communication and channel state estimation problem is investigated, in which reliable information transmission over a noisy channel, and high-fidelity estimation of the channel state, are simultaneously sought. The tradeoff between the achievable information rate and the estimation distortion is quantified by formulating the problem as a constrained channel coding problem, and the resulting capacity-distortion function characterizes the fundamental limit of the joint communication and channel estimation problem. The analytical results are illustrated through case studies, and further issues such as multiple cost constraints, channel uncertainty, and capacity per unit distortion are also briefly discussed.

Algorithms for the estimation of a channel whose impulse response is characterized by a large number of zero tap coefficients are developed and compared. Estimation is conducted in a two-stage fashion where an estimate of the non-zero taps is followed by channel estimation. Tap detection is transformed into an equivalent on-off keying detection problem. Several tap detection algorithms are investigated which tradeoff between complexity and performance. The proposed methods are compared to an unstructured least squares channel estimate as well as a structured approach based on matching pursuit. Three schemes in particular are developed: a sphere decoder based scheme, a Viterbi algorithm based method and a simpler iterative approach. The latter offers a better tradeoff between estimation accuracy and computational cost. A joint estimation and zero tap detection scheme is also considered. All solutions exhibit a significant gain in terms of mean-squared error and bit error rate over conventional schemes which do not exploit the sparse nature of the channel, as well as the matching pursuit approach which does endeavor to exploit the sparsity

A new class of abstract sensor networks is introduced and analyzed. The object of the sensing is the inter-node channel. Examples of systems which seek to sense the channel include: underwater sonar, radar and optics based atmospheric sensor networks. In these networks, the sensing and communication tasks share the bandwidth resource in addition to the sharing of power resources as has been conventionally studied in the sensor network framework. Bounds on distortion tradeoffs are developed for various protocols, such as source coding analogues of decode-and-forward and amplify-and-forward and simple topologies such as two-hop networks (three node system).

A joint sensing/communication problem is considered for sensor networks. Herein, the channel(s) between a source and destination are the parameters to be sensed and communicated over the network. Lower bounds on the end-to-end distortion are developed for a multihop, linear network. Internode communication is assumed to be done via an encode-and-forward approach. For a many-to-one topology with two hops, data aggregation and time-division communication approaches are compared. Asymptotic in the SNR, it is shown that a time-division approach is superior

Algorithms for the estimation of a channel whose impulse response is characterized by a large number of negligible tap coefficients are developed and compared. Exploiting this sparsity, the estimation problem is transformed into an equivalent on-off keying detection problem, whose solution gives an indication on the position of the zero taps. The proposed schemes are compared to the standard least squares estimate via simulations in terms of mean square error and bit error rate. A scheme based on sphere decoding appears to give the best performance while maintaining moderate complexity.