Acknowledgements

variance (σ<sup>2</sup>

Figure 6.

Multiplexing

as shown by Eq. (21).

Ld <sup>¼</sup> 1024, at a BER of 10�4.

Eq. (59)) and Scilab limitations.

5. Conclusions

62

<sup>w</sup>) decreases with increasing Lp, Ld, for a given average SNR per bit,

2. There is only 0.5 dB improvement in performance for Ld ¼ 8192 over

Bit error rate results for an 8 � 8 MIMO system. (a) Ld ¼ 1024 and Lp ¼ 512. (b) Ld ¼ 8192 and Lp ¼ 4096.

3. There is a significant improvement in performance between Nrt ¼ 2 and Nrt ¼ 4, for both Ld ¼ 1024 and Ld ¼ 8192. On the other hand, there is no significant difference in the BER for Nrt ¼ 2 and Nrt ¼ 4 in [34]. The reason is because in this work, the channel <sup>H</sup><sup>~</sup> k,i,nr,nt in Eq. (18) is highly correlated over the subcarrier index i, since it is obtained by taking an Ld-point FFT of an Lhtap channel (see Eq. (37) of [36]). On the other hand, the channel <sup>H</sup><sup>~</sup> k,i,j in [34] is independent over all the indices k, i, and j, where k is the retransmission index, i denotes the receive antenna index, and j denotes the transmit antenna

4.There is not much BER performance difference between the 4 � 4 and 8 � 8 MIMO systems. A 4 � 4 MIMO is computationally less complex than 8 � 8; however the 4 � 4 requires twice the number of carrier frequencies to achieve the same spectral efficiency as 8 � 8, for the same number of retransmissions.

5. The BER performance of the 8 � 8 MIMO system with Nrt ¼ 4 and Ld ¼ 8192 could not be simulated due to the large amount of memory involved (see

This work describes the discrete-time algorithms for the implementation of a massive MIMO system. Due to the implementation complexity considerations, more than one carrier frequency is required to obtain a truly single-user massive MIMO system. Each carrier frequency needs to be associated with an 8 � 8 or 4 � 4 MIMO subsystem. The average SNR per bit has been used as a performance measure, which has not been done earlier in the literature. Perhaps the channel can also be estimated using Eq. (27), instead of using Eq. (35). This needs investigation.

index. See also the discussion leading to Eq. (82) in [21].

The authors would like to thank the high-performance computing (HPC) facility at IIT Kanpur for running the computer simulations.
