Interplanetary Cubesats would enable low-cost missions for high-quality scientific and exploration programs. In particular cubeSats in formation have been proposed to operate in the vicinity of the Lunar Lagrangian L1 to collect lunar scientific data and to perform surface observation. In this paper we present a low complexity CDMA system for CubeSats (M small spacecraft) for communications between the Lunar L1 and Earth station. It is well known that the complexity of a CDMA transmitter is much lower than the complexity of the CDMA receiver. Moreover, the complexity of a channel encoder is always much lower than the complexity of the channel decoder. So for downlink communications it makes sense to use encoders for modern codes such as Turbo and LDPC followed by a spread spectrum transmitter for CDMA systems for CubeSats. Here we used an LDPC coded CDMA with BPSK modulation with rectangular and half-sine pulse shaping. Except for the PN generator seed numbers, the communication structure of all CubeSats would be identical and operating at one single RF frequency. For the uplink we may choose an uncoded CDMA system since the uplink transmit power is expected to be high enough to support the use of uncoded CDMA system. In addition since there would be no multipath for the uplink (broadcast channel) the use of orthogonal spreading codes such as Walsh codes is appropriate. The choice of orthogonal codes would reduce the multiuser interference. However due to some limitation (bandwidth, data rates, and M) we may be forced to use nonorthogonal PN codes. In addition, one of the spreading codes will not carry any data, which acts as an unmodulated pilot to reduce the complexity of synchronization. The proposed uncoded CDMA yields receivers for CubeSats that have low complexity implementation. Each component of CubeSats could easily extract its own received data with almost no interference from other users in case of orthogonal spreading codes. For the downlink, depending on the available bandwidth, and the data rates, a large processing gain could be obtained if the N is not large. Thus the multiuser interference degradation due to the other CubeSats could be made small at the Earth station. If N is large, and the bandwidth and data rates do not allow large processing gains then the multiuser interference could be high. In such cases we could use a simple parallel interference cancellation method with two stages that dramatically improves the system performance for the downlink. In this paper we accurately analyzed and simulated the proposed CDMA system for a concept Constellation of 20 CubeSats (M=20). All system simulations are done using Simulink platform.