Robin Rajamäki

Ids van der Werf, Robin Rajamäki, Geert Leus

This paper characterizes the performance limits of optimal array designs using orthogonal and coherent waveforms for both linear and planar arrays. For orthogonal waveforms, we show that the single-target Cramér-Rao Bound (CRB) depends on the sum of the so-called spatial variances of the transmit (Tx) and receive (Rx) arrays, or equivalently, the spatial variance of the sum co-array weighted by the multiplicities of the virtual sensors. This reveals that CRB-optimal geometries are inherently redundant, highlighting a fundamental trade-off between mean squared error (MSE) and identifiability in parameter estimation. Moreover, we derive optimal Tx-Rx sensor allocations given a total sensor budget and show that unequal allocation (favoring the Rx) is optimal even for nonredundant arrays, questioning conventional designs. We extend our results to planar arrays, providing a new general condition that the spatial covariances of the Tx and Rx arrays should satisfy for the optimal waveforms to direct power in the target direction. Additionally, we establish a connection between Diophantine equations and array geometries with equal CRB, along with a constructive method for designing such arrays. Our work provides new guidelines for and insights into optimal array and waveform design with relevance in emerging active sensing multiple-input multiple-output systems.

Parthasarathi Khirwadkar, Robin Rajamäki, Piya Pal

This paper provides novel insights into channel and subspace codes in nonadaptive channel sensing with a single RF chain. Observing that this problem naturally maps to a noncoherent decoding problem, we show that the sensing performance of the maximum likelihood (ML) angle estimator, which does not require knowledge of the typically unknown channel coefficient, is governed by two key terms: the minimum subspace distance and beam gain of the used beamformers. We derive an exact expression for the subspace distance of binary linear channel codes mapped to BPSK, which illuminates the relationship between subspace and Hamming distance, used to design subspace and channel codes, respectively. Our result also reveals why good Hamming distance alone is insufficient for sensing, and shows that well-known families of channel codes such as Reed-Muller codes, yield zero subspace distance and thereby poor sensing performance when used naively without proper codebook pruning. Finally, we introduce so-called beamspace subspace codes based on sparse antenna selection patterns (Golomb rulers), which we show provide near-optimal subspace distance. We demonstrate that this property of judiciously designed sparse arrays can be leveraged together with beamforming gain via convolutional beamspaces, enabling hardware- and sample-efficient channel sensing with theoretical guarantees in large-scale multiantenna communications.