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We have developed an HTS SQUID system for both time and frequency domain measurements of magnetic signals from the Brownian relaxation of liquid-suspended magnetic nanoparticles (MNPs) coated with antibodies. A planar YBa2Cu3O7-x dc SQUID gradiometer with a baseline of 3 mm allows stable operation of the measurement system in an unshielded environment. Agglomeration of MNPs induced by prostate specific antigen-antibody binding complexes is characterized with our system and benchmarked with frequency domain measurements performed by Imego AB using an induction coil magnetometer. We estimate an upper bound for our immunoassay analyte sensitivity of 1.8 ng/radicHz.