Today’s Massive MIMO cellular operation is dominated by orthogonal frequency division multiplexing (OFDM) modulation. One of the advantages of OFDM is the flexibility to carve up the available spectrum into resource blocks (RBs) that can operate adjacent to one another. Massive MIMO adds spatial multiplexing layers on top of the RBs, enabling the simultaneous operation of dozens of UEs. Cyclic prefixed single carrier modulation (CP-SCM) is an alternative to OFDM that also benefits from massive MIMO and is useful as an OFDM alternative in specific scenarios. However, until recently, no resource allocation method has been proposed for CP-SCM. In this paper, we present a CP-SCM resource allocation scheme using virtual antennas in a massive MIMO time domain duplexed scenario. By creating several virtual antennas for each physical antenna, the benefits of massive MIMO are achieved with a smaller physical antenna count. Resources are quantized into data streams, and each user can be assigned a variable number of simultaneous streams. This paper presents a detailed development and analysis of multi-stream processing (MSP) for both uplink detection and downlink precoding. We also introduce heterogeneous MSP, where CP-SCM and OFDM signals can be processed in the same MSP framework.