Data-like interference mitigation in wireless communications systems, and in mobile cellular networks in particular, has always been a challenging problem which is becoming even more so for 5G networks and beyond including the Internet of things (IoT), to support a massive number of low data rate devices for given spectral resources. A promising solution to this problem consists in using one dimensional signaling(i.e., real-valued modulations) jointly with widely linear (WL) processing at the receiver, which has the capability to process up to 2N−1data-like interference from Nantenna receivers, and to fulfill, for N=1, single antenna interference cancellation (SAIC) of a one-dimensional interference in particular. However, when the signal of interest (SOI) and observations are jointly non-Gaussian, which is the case for most of digital radiocommunications systems, WL receivers become sub-optimal and optimal receivers become non-linear. It is then of interest to propose new non-linear receivers to improve performance of WL receivers. In this context, the paper aims at introducing, for small-scale systems, third-order complex Volterra (CV) minimum mean square error (MMSE) receivers, for the reception of a digital linearly modulated SOI whose waveform is known, corrupted by potentially non-Gaussian and non-circular interference, omnipresent in practical situations. Properties, performance and adaptive implementation of these receivers in the presence of non-Gaussian and potentially non-circular interference up to the 6th-order are analyzed in this paper. In particular, some of these receivers are shown to enhance WL receiver performance for SAIC of one rectilinear interference such as binary phase-shift keying (BPSK) interference. Whereas some other receivers allow us to fulfill SAIC of 4th-order non-circular interference such as quadrature phase-shift keying (QPSK) interference, which is not possible using WL receivers. These new receivers open new perspectives for cancellation of non-Gaussian and potentially non-circular interference up to 6th-order in radiocommunication networks.