Compared with the conventional amplitude phase modulation (APM), spatial modulation (SM) is a low- complexity, yet energy-efficient transmission technique, whereby transmit antenna (TA) indices are utilized to convey the information. However, the number of the required TAs grows exponentially with the number of transmitted bits, which leads to unacceptable pilot overhead for channel estimation in practical systems. To reduce the number of TAs whereas keep the data rate unchanged, virtual spatial modulation (VSM) is proposed in the first time. Specifically, by activating multiple TAs with their corresponding analog phase shifters (APSs), massive equivalent channel vectors could be constructed based on the combinations of original channel vectors from different TAs and their phase rotations. By way of mapping each equivalent channel vector to a virtual transmit antenna (VTA) index which might convey the information, the number of the required TAs could grow linearly with the number of transmitted bits. Furthermore, the selection of a VTA subset from all available VTAs is formulated as a combinatorial optimization problem to maximize the minimal Euclidean distance (ED) among the equivalent channel vectors. A spatial constellation optimizing (SCO) algorithm is proposed to obtain a near-optimal solution to this problem with low-complexity. Simulation results demonstrate that the proposed VSM is able to achieve lower bit error rate (BER) under the same transmit rate compared with the conventional SM and APM schemes.
['Xudong Zhu', 'Zhaocheng Wang', 'Qi Wang', 'Harald Haas']
Virtual Spatial Modulation for MIMO Systems