For transmit-sensor-selection ISAC, the identifiability-constrained codebook size is exactly C(Nt-2,Q-2) for a uniform linear array and 1 for a nonredundant array, with general upper and lower bounds between them.
First, we define the set of Q-sensor Tx subarrays whose sum sets equal that of a given physical Tx-Rx array pair (Dt,Dr): Cc(Q,Dt,Dr) ≜ {S ⊆ Dt : |S| = Q, S + Dr = Dt + Dr}
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Sparse Array Sensor Selection in ISAC with Identifiability Guarantees
For transmit-sensor-selection ISAC, the identifiability-constrained codebook size is exactly C(Nt-2,Q-2) for a uniform linear array and 1 for a nonredundant array, with general upper and lower bounds between them.