Because of the size of the moon, bandwidths of lunar relay communication links have been below 10 kc. This study describes and analyses an approach to the problem of increasing lunar relay bandwidth. An adaptive receiving array is described which makes possible the use of exceptionally large apertures capable of being focused on a small spot on the lunar surface. However, an analysis shows that side-lobe effects considerably reduce expected bandwidth gains. A bandwidth of 40 kc is calculated for a 1000-ft square X-band array which employs a "maximum energy!! taper. Between 256 and 1024 array elements are required.