RECEIVER-COORDINATED ZERO-FORCING DISTRIBUTED TRANSMIT NULLFORMING D. Richard Brown III ⋆ Patrick Bidigare † Soura Dasgupta ‡ Upamanyu Madhow ⋄ ⋆ Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, drb@wpi.edu † Raytheon BBN Technologies, 1300 17th Street Suite 400, Arlington, VA 22207, bidigare@ieee.org ‡ University of Iowa, Iowa City, IA 52242, dasgupta@engineering.uiowa.edu ⋄ University of California, Santa Barbara, CA 93106, madhow@ece.ucsb.edu ABSTRACT A coherent cooperative communication system is proposed in which a distributed array of transmit nodes forms a beam at a desired receiver while simultaneously steering nulls at several protected receivers. Coherent transmission is achieved through a receiver-coordinated protocol where the receivers in the system use state-space channel tracking and provide feedback to the transmit cluster to facilitate distributed transmission. Analytical estimates for the performance degradation in the nulls due to channel estimation errors are verified by simulations. Numerical results demonstrate that the technique is effective even with low channel measurement overhead, infrequent measurement intervals, and feedback latency. Index Terms— cooperative communication, distributed trans- mission, feedback systems, oscillator dynamics, tracking 1. INTRODUCTION Coherent cooperative transmission is a technique in which N ≥ 2 transmitters control the phase and amplitude of their transmissions to form a virtual (and typically sparse) antenna array. Distributed beamforming, see e.g. [1], is one example of this technique. In this paper, we develop and analyze a coherent cooperative transmis- sion system which simultaneously performs distributed beamform- ing to one intended receiver and distributed nullforming to M pro- tected receivers. Each receiver tracks, using a state space model, a time-varying state of “effective” channel phase and frequency offsets which include stochastic clock drift. Explicit state feedback from the M +1 total receivers is then used by each transmit node to predict the N × (M + 1) channel matrix and compute a “zero-forcing” transmit vector w for use during distributed transmission. This paper demonstrates the efficacy of this receiver-coordinated zero-forcing distributed transmit nullforming technique in the face of channel time variations caused by stochastic local oscillator drift. Unlike the prior work in [2, 3], we do not assume the transmit clus- ter is synchronized and the approach here is simplified in that the calculation of the transmit vector does not require knowledge of the state prediction error covariance. We also provide analytical per- formance estimates, verified using simulations, of the nullforming performance degradation due to channel estimation errors. 2. SYSTEM MODEL We consider a wireless communication system with N transmit nodes, M protected receivers, and one intended receiver. Each node in the system is assumed to possess a single antenna. We also assume the transmit nodes have some mechanism by which they can share a common baseband message to be transmitted to the intended receiver and also have some rough level of synchronization so that they can effectively participate in the receiver-coordinated protocol schedule described in Section 3. The coarse synchroniza- tion required here can be achieved with standard techniques such as global positioning system (GPS), network time protocol (NTP), or potentially through feedback messages from the receive nodes. Precise carrier synchronization as described in [4] is not assumed, but is implicitly achieved via channel tracking and feedback. The nominal transmit frequency in the forward link from the distributed transmit cluster to the receivers is at ωc. All forward link channels are modeled as narrowband, linear, and time invariant (LTI). Enu- merating the protected receivers as m =1,...,M and adopting the convention that the intended receiver is node 0, we denote the channel from transmit node n to receive node m at carrier frequency ωc as gn,m ∈ C for n =1,...,N and m =0,...,M. These LTI propagation channels, in contrast to the time-varying “effective” channels described below, do not include the effect of carrier phase offsets between transmit node n and receive node m. The receiver-coordinated protocol requires all of the receivers in the system to measure and track the channels from the transmit cluster and to provide feedback to the transmit cluster to facilitate distributed transmission. Figure 1 shows the effective narrowband channel model from transmit node n to receive node m which in- cludes the effects of propagation, transmit and receive gains, and carrier offset. Transmissions n → m are conveyed on a carrier nominally at ωc generated at transmit node n, incur a phase shift of ψ (n,m) = ∠gn,m over the wireless channel, and are then down- mixed by receive node m using its local carrier nominally at ωc. At time t, the effective narrowband channel from transmit node n to receive node m is modeled as h (n,m) (τ )= gn,me j  φ (n) t (τ )−φ (m) r (τ )  = |gn,m|e jφ (n,m) (τ ) (1) where φ (n) t (τ ) and φ (m) r (τ ) are the local carrier phase offsets at transmit node n and receive node m, respectively, at time τ with respect to an ideal carrier reference, and φ (n,m) (τ )= φ (n) t (τ ) - φ (m) t (τ )+ ψ (n,m) is the pairwise phase offset after propagation be- tween transmit node n and receive node m at time τ . local carrier LPF transmit node n local carrier receive node m h (n,m) (τ ) gn,m ∼ ωc ∼ ωc 1 Fig. 1. Effective narrowband channel model including the effects of propagation, transmit and receive gains, and carrier offset.