Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work, we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.

In this work, we consider a two-hop multiuser amplify-and-forward relay network with multi-antenna nodes. The results are three-fold. First, for any relay amplification matrix D in the multiple-access channel (MAC), we show that duality holds when ¿D¿is employed in the broadcast channel (BC), and vice versa, where re is obtained from switching the total source and relay power constraints. Second, under a total network power constraint, we show that MAC-BC duality holds when D and D¿are the relaying matrices in the MAC and BC respectively. Third, for any D in the MAC and cD¿in the BC where c is any positive real scalar, MAC-BC duality under total network power constraint holds only for the above two cases.

In wireless relay networks, noise at the relays can be correlated possibly due to common interference or noise propagation from preceding hops. A parallel relay network with noise correlation is considered in this network. For the relay strategy of amplify and forward (AF), the optimal rate maximizing relay gains when correlation knowledge is available at the relays are determined. Interestingly, it is shown that, on average, noise correlation is beneficial regardless of whether the relays know the noise covariance matrix. However, the knowledge of correlation can greatly improve the performance. Typically, the performance improvement from correlation knowledge increases with the relay power and the number of relays. With perfect correlation knowledge the system is capable of canceling interference if the number of interferers is less than the number of relays. For a two-hop multiple-access parallel network, closed-form expressions for the maximum sum rate and the optimal relay strategy are determined. Relay optimization for networks with three hops is also considered. Based on the result of two-hop network with noise correlation, an iterative algorithm is proposed for solving the relay optimization problem for three-hop networks.

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.

In wireless relay networks, noise at the relays can be correlated possibly due to common interference or noise propagation from preceding hops. In this work we consider a parallel relay network with noise correlation. For the relay strategy of amplify-and-forward (AF), we determine the optimal rate maximizing relay gains when correlation knowledge is available at the relays. The effect of correlation on the performance of the relay networks is analyzed for the cases where full knowledge of correlation is available at the relays and when there is no knowledge about the correlation structure. Interestingly we find that, on the average, noise correlation is beneficial regardless of whether the relays know the noise covariance matrix or not. However, the knowledge of correlation can greatly improve the performance. Typically, the performance improvement from correlation knowledge increases with the relay power and the number of relays. With perfect correlation knowledge the system is capable of canceling interference if the number of interferers is less than the number of relays.

We consider multi-hop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting capacity regions. We find that the parallel AF relay MAC with total transmit power of the two users P1+P2=P and total relay power PRis the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is PRand the total transmit power of the AF relays is P.

We explore the SNR-optimal relay functionality in a mernoryless relay network, i.e. a network where, during each channel use, the signal transmitted by a relay depends only on the last received symbol at that relay. We develop a generalized notion of SNR for the class of memoryless relay functions. The solution to the generalized SNR optimization problem leads to the novel concept of minimum mean squared uncorrelated error (MMSUE) estimation. For the elemental case of a single relay, we show that MMSUE estimate is a scaled version of the MMSE estimate. This scheme, that we call estimate and forward (EF), performs better than the best of amplify and forward (AF) and demodulate and forward (DF) in both parallel and serial relay networks. We determine that AF is near-optimal at low transmit power in a parallel network, while DF is near-optimal at high transmit power in a serial network. For hybrid networks that contain both serial and parallel elements, the advantage of EF over the best of AF and DF is found to be significant. Error probabilities are provided to substantiate the performance gain obtained through SNR optimality. We also show that, for Gaussian inputs, AF, DF and EF are identical

We investigate the performance degradation of basic modulation schemes in a rapidly time-varying channel using a first-order autoregressive channel model. Various performance metrics are used to indicate the relative advantages of each modulation scheme. We find that noncoherent frequency-shift keying (FSK) is suitable for operating at very high mobility and high signal-to-noise ratio, ideal for some military applications. We then propose a partially coherent detector for FSK and differential phase-shift keying that exploits partial channel knowledge to enable the receiver to operate effectively in both fast and slow fading. The maximum-likelihood rule obtained for the partially coherent FSK turns out to be a linear combination of coherent and noncoherent detection rules. Results demonstrate that significant performance improvement can be achieved over the best of coherent and noncoherent FSK detection. The detector is robust to estimation errors present in the channel statistics. We also propose a few adaptive schemes that employ various combinations of modulation schemes to increase the robustness of the system in fast fading

In this paper, we consider multihop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two-hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions. We find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair (R1, R2) that maximizes mu1R1+mu2R2as the solution of a pair of simultaneous equations. We find that the parallel AF relay MAC with total transmit power of the two users P1+P2=P and total relay power PRis the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is PRand the total transmit power of the AF relays is P. The duality means that the rate region of the AF relay MAC with a sum power constraint P on the transmitters is the same as that of the dual BC. The duality relationship is found to be useful in characterizing the rate region of the AF relay BC as the union of MAC rate regions. The duality is established for distributed multiple antenna AF relay nodes and multiple (more than 2) hops as well.

In a relay network, the signal processing at the relay significantly affects the capacity benefits of cooperation. In this work, we explore the optimal relay functionality for capacity maximization in a memoryless relay network, i.e. a network where, during each channel use, the signal transmitted by a relay depends only on the last received symbol at that relay. By relating some of the existing memoryless forwarding strategies to the fundamental signal processing operations of estimation and detection, we develop a new scheme that forwards the unconstrained minimum mean square error (MMSE) estimate obtained at the relay to the destination. For a single relay system, we derive the characterization of the optimal relay function and show that the relay function of EF (estimate and forward) satisfies the optimality condition. For the multiple relay case, we consider both parallel and serial relay networks and show that EF performs better than both AF (amplify and forward) and DF (demodulate and forward). For hybrid networks that contain both serial and parallel elements, and when robust performance is desired at all SNR, the advantage of EF over the best of AF and DF is found to be significant.

We investigate the performance degradation due to rapidly time varying channels in a repetition based coherent cooperative system. We demonstrate that mobility of source affects the performance much more than the mobility of destination, for both amplify and forward (AF) and demodulate and forward (DF) relays, despite the symmetry of the network. Exploiting the property of FSK modulation that allow us to detect either coherently or noncoherently or even semi-coherently, we develop ML detection rules for a variety of mobile scenarios. The detection rules that take into account the mobility of the nodes, are mostly hybrids of partially coherent detectors and noncoherent detectors. The performance of these detectors is better than the best of coherent and noncoherent detectors in fast fading and a gain of about 2 dB is obtained over a wide range of SNR and a gain of almost 3 dB is achieved at the crossing of coherent and noncoherent curves. As energy efficiency is one of the main objectives for pursuing cooperation and relaying, these hybrid detectors assume significance in fast fading scenarios

We investigate the performance degradation of basic modulation schemes in a rapidly time varying channel using a first order auto regressive channel model. We propose a partially coherent detector for both noncoherent frequency shift keying (FSK) and differential phase shift keying (PSK) that exploits partial channel knowledge to enable the receiver to operate effectively in both fast and slow fading. The maximum likelihood rule (ML) obtained for the partially coherent FSK turns out to be a linear combination of coherent and noncoherent detection rule. Results demonstrate that significant performance improvement can be achieved over the best of coherent and noncoherent FSK detection in fast fading. We also propose a few adaptive schemes that vary the modulation scheme in response to degrading quality of the channel estimate between successive training symbols