What is Constructive Interference?
Let us assume a two-user transmission as shown in the figure above. Define the desired symbol as x1 and the interfering symbol as x2. Without loss of generality we assume that these are taken from a Binary Phase Shift Keying (BPSK) constellation and that x1 = 1; x2 = -1. For the purposes of the illustrative example, we assume a unitary channel from the intended transmitter to the intended receiver and an interfering channel represented by the coefficient ρ. The received signal at the intended receiver y1, given by the expression in the figure contains the desired symbol x1 and the interference x2·ρ. In the right hand side of the figure two distinct cases are shown, depicting the transmitted (x) and received (o) symbols for user 1 on the BPSK constellation diagram. In case i) with ρ = 0.5 it can be seen that y1 = 0.5. In this case, the destructive interference from user 2 has caused the received symbol of user 1 to fall closer to the decision threshold (dashed line) in the BPSK constellation. Therefore, due to destructive interference the received power of user 1 has been reduced and its detection is prone to noise with reduced power. In case ii) however, for ρ = -0.5 it can be seen that y1 = 1.5, in which case the interference from user 2 is constructive. The received signal power of user 1 has been augmented due to the interference from user 2 and now its detection is tolerant to higher noise power (nconstr compared to north). It should be stressed that in both cases the transmit power for each user is equal to one.
Modulation-Dependent Interference Classification
Interference is constructive when it shifts the received symbols away from the decision thresholds of the transmit symbol constellation. Mathematical criteria for the classification of interference into constructive - destructive are available for the most practical PSK and QAM constellations in the relevant literature.
Transmission schemes to exploit constructive interference
In single cell downlink transmission the Base Station shapes the transmit signal by means of precoding, so that the interference received at the Mobile Units is optimized. To accommodate for constructive interference the precoding can be designed such that the signal received at the MUs allows for the existence of interference when this is constructive.
There exist such techniques in the literature in the form of linear precoding, namely Selective Channel Inversion and Correlation Rotation Precoding, or techniques based on optimization such as Constructive Beamforming Optimization. Recent work presents some low-complexity closed form precoders based on optimization.
Schemes based on non-linear Tomlinson Harashima precoding (THP) that optimize interference in a similar way can be found in the form of Interference Optimized THP and precoders based on Vector Perturbation that allow for constructive interference are in the form of Constructive Vector Perturbation.
There exist such techniques in the literature in the form of linear precoding, namely Selective Channel Inversion and Correlation Rotation Precoding, or techniques based on optimization such as Constructive Beamforming Optimization. Recent work presents some low-complexity closed form precoders based on optimization.
Schemes based on non-linear Tomlinson Harashima precoding (THP) that optimize interference in a similar way can be found in the form of Interference Optimized THP and precoders based on Vector Perturbation that allow for constructive interference are in the form of Constructive Vector Perturbation.
In multi cell downlink transmission the adaptation of the above concepts is still an open research problem. Simple adaptations of these in the context of Cognitive Radio (CR) have been studied in the Overlay CR transmission and the Relay Assisted CR scenario, based on the linear Correlation Rotation precoding above. Optimization based multi-cell precoders for CoMP scenarios, robust to CSI errors, have recently been studied.
Future work will involve the adaptation of the non-linear transmission schemes as above into the multi-cell, HetNet and Cognitive Radio transmission.
Future work will involve the adaptation of the non-linear transmission schemes as above into the multi-cell, HetNet and Cognitive Radio transmission.
Proof-of-Concept
Proof of concept experiments have verified the usefulness of these approaches and the theory of constructive interference in over-the-air experiments. They employ low-complexity closed-form precoders and are based on software defined radio platform. The experiments have been reported in this INFOCOM paper. The following figures show the experiment setup and the received QPSK constellations, for transmission (a) without precoding, (b) with zero forcing precoding, (c) with constructive interference precoding.