On the Error Probability of Spatial Modulation over Keyhole MIMO Channels

The keyhole effect causes a dramatic performance degradation to Multiple-Input Multiple-Output (MIMO) systems. The main contribution of this letter is the analytical performance evaluation of Spatial Modulation MIMO (SM-MIMO) systems over the keyhole channel. The closed-form Pairwise Error Probability (PEP) is derived with accuracy verified by simulations. Based on the PEP, the achievable diversity gain is extracted and shown to be no more than 1 under any configuration. In addition, a tight Average Bit Error Probability (ABEP) upper bound is given. Numerical results demonstrate that compared to independent fading scenarios, the keyhole channel causes a significant performance degradation to the SM-MIMO system. It is shown that SM-MIMO schemes outperforms Space-Time Block Code (STBC) and V-BLAST schemes over the keyhole channel. Therefore, among multiple antenna transmission schemes, SM-MIMO schemes are better choices for systems that may experience the keyhole effect. However, owing to the inherent unfitness of the keyhole channel for multiple antenna transmission, SM-MIMO schemes are still inferior to SISO/SIMO schemes.