The context of this paper is adaptive waveform design for estimating parameters of an unknown channel under average energy constraints. This paper focuses on the simpler problem of adaptive waveform-amplitude design for which we obtain interesting analytical results. We treat an TV-step design problem where a fixed waveform can be transmitted into the channel N times with amplitudes that can be chosen as a function of past channel outputs. For N = 2 and a linear Gaussian channel model, we derive the optimal amplitude to transmit at the second step as a function of the first measurement. This adaptive 2-step energy allocation strategy yields a mean-squared error (MSE) improvement of at least 1.7 dB relative to the optimal non-adaptive strategy. Motivated by the optimal two-step strategy we propose a suboptimal adaptive TV-step strategy that can achieve an MSE improvement of more than 5 dB for N = 50. Applications of our results to MIMO and inverse scattering channel models are discussed.
['Raghuram Rangarajan', 'Raviv Raich', 'Alfred O. Hero']
Sequential Energy Allocation Strategies for Channel Estimation