This paper introduces the CASINO (CAnopy backscatter estimation, Subsampling, and Inhibited Nonlinear Optimisation) algorithm for above-ground biomass (AGB) estimation in tropical forests using P-band (435 MHz) synthetic aperture radar (SAR) data. The algorithm has been implemented in a prototype processor for European Space Agency's (ESA's) 7th Earth Explorer Mission BIOMASS, scheduled for launch in 2023. CASINO employs an interferometric ground cancellation technique to estimate canopy backscatter (CB) intensity. A power law model (PLM) is then used to model the dependence of CB on AGB for a large number of systematically distributed SAR data samples and a small number of calibration areas with a known AGB. The PLM parameters and AGB for the samples are estimated simultaneously within pre-defined intervals using nonlinear minimisation of a cost function. The performance of CASINO is assessed over six tropical forest sites on two continents: two in French Guiana, South America and four in Gabon, Africa, using SAR data acquired during airborne ESA campaigns and processed to simulate BIOMASS acquisitions. Multiple tests with only two randomly selected calibration areas with AGB > 100 t/ha are conducted to assess AGB estimation performance given limited reference data. At 2.25 ha scale and using a single flight heading, the root-mean-square difference (RMSD) is <= 27% for at least 50% of all tests in each test site and using as reference AGB maps derived from airborne laser scanning data. An improvement is observed when two flight headings are used in combination. The most consistent AGB estimation (lowest RMSD variation across different calibration sets) is observed for test sites with a large AGB interval and average AGB around 200-250 t/ha. The most challenging conditions are in areas with AGB < 200 t/ha and large topographic variations. A comparison with 142 1 ha plots distributed across all six test sites and with AGB estimated from in situ measurements gives an RMSD of 20% (66 t/ha).