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Moreover, orthogonal pilot allocations are considered in channel estimation, i.e., each antenna transmits neutral subcarrier in pilot subcarriers of the other antennas.

Besides, to omit the interference of other antenna's pilots on each other, we consider to utilize the orthogonal pilot allocation, i.e., not only N p subcarriers are allocated to pilot subcarriers, but also pilot subcarriers assigned to other (N_{mathbb {S}} ~-~ 1) transmit antennas are reserved to be zero [19].

In the first scenario the pilot allocation is performed randomly, while in the second scenario the pilot is allocated using the proposed PCE-based algorithm.

Thus, utilizing PCE-based pilot allocation will confirm two critical aspects of pilot allocation algorithms.

The BER performance is compared using random pilot allocation and optimized PCE-based pilot allocation.

Specifically, Sequential Cross-Entropy (SCE -based pilot allocation, Extended ESCE -basedof Distribution ApilotimallocationA)-basExtended allocation, and ParallEstimatingntrofy (PCE)-baseDistributioncApproximationEEDA -basedt pilot allocation approachEEDA -basedve been pilotsed in this pallocation

Fig. 4 Performance comparison for different pilot allocation algorithms.

The pilot allocation is optimized using proposed SCE-based sequence determination algorithm and extended to MIMO pilot allocation.

a BER performance using random pilot allocation and b BER performance using optimized PCE-based pilot allocation.

In order to increase the speed of convergence of SCE-based pilot allocation, a special case is used called EEDA-based pilot allocation.

To achieve a symmetric pilot allocation in this network, the pilot reuse factor can be β∈{1,3,4,7}.