Local multipoint distribution systems (LMDS), which are operating worldwide in the frequency range of 26 to 43 GHz, have large bandwidths of 0.1 up to 2 GHz, but a very limited area coverage due to line of sight constraints and large propagation losses. As suggested in the Cellular Radio Access for Broadband Services (CRABS) Report , a high spectral efficiency can be obtained for a regular network of squared cells with a dual frequency and polarization reuse scheme. However, this frequency and polarization reuse leads to cochannel and adjacent channel interference. In this paper, we report a systematic two-dimensional study of interference in such a regular LMDS network for the downlink and uplink in order to assess the impact of different geometric and propagation parameters. The paper reports simple formulas to estimate the areas of high interference levels within an LMDS cell as a function of the half-power beamwidth of the customer-site antennas for the downlink. The effect on the carrier-to-interference distribution over a LMDS cell is evaluated by varying the half-power beamwidth of the customer-site antennas, the time percentage of short term enhancement due to atmospheric multipath and focusing effects and the cell dimensions. We also introduce a simple technique by reorientation of the customer-site antennas for interference reduction. The results presented in this paper can be used to carry out system-level design for interference-limited LMDS cells.