Performance analysis of time diversity combining with frequency offset for cellular IoT

In the growing context of Machine Type Communications (MTC), synthesized by the concept of Internet of Things (IoT), the need of an increased coverage pushes the industrial companies to develop efficient transmission techniques. Especially, the 3rd Generation Partnership Project (3GPP) already standardized evolutions of the 2G and 4G networks to include IoT features. These new standards share the common trait of using blind repetitions to improve the legacy coverage of the system, renewing interest for diversity combining. The present paper focuses on the IQ combiner approach which works on complex baseband samples without any previous phase synchronization. Our study evaluates the impact of the frequency offset, resulting of an imperfect frequency synchronization, on the average Signal to Noise Ratio (SNR) of IQ-combined frames. We derive new closed-forms: a first one for the statistical distribution of the residual phase angle between two consecutive symbols after imperfect frequency demodulation, a second one for the average SNR of the combined frame. These derivations allow us to highlight and quantify the negative impact of an inaccurate frequency synchronization in the context of IQ combining strategies.