Abstract
This paper investigates the optimal training duration and the optimal power allocation for the training and the data transmission that maximize the ergodic sum rate in single-cell uplink massive MIMO with MMSE receivers. Our channel model assumes that each user experiences the same spatial channel correlation. The expression for the ergodic sum rate is obtained in the large system regime where the number of antennas ( $N$ ) at the base station and the number of users ( $K$ ) tend to infinity with a fixed ratio. Interestingly, we show that the optimal training duration is equal to $K$ and independent of the spatial correlation. We also derive the optimal power allocation that in facts depends on the spatial correlation, the channel coherence interval, and the uplink SNR. We show that more energy should be allocated for the training if the data transmission duration ( $t_{d}$ ) is less than $K$ , and vice versa. Moreover, equal power allocation is optimal when $t_{d}=K$ . We also obtain an approximation for the optimal power allocation that depends on the mean of the correlation matrix eigenvalues. Numerical simulations show that our results based on the large system approximation are accurate and applicable for finite-size systems. The simulations also show that (1) the resulting ergodic sum rates obtained by employing the optimal power allocation and its approximation are indistinguishable, and (2) the optimal power allocation obtained from the uncorrelated channel model can be applied to the cases involving the correlated channels with indiscernible penalties on the ergodic sum rates.
Highlights
Since its introduction in [1], research on massive multipleinput multiple-output (MIMO) has been flourishing
We propose an approximation for the optimal power allocation and show that it depends on the mean of the spatial correlation matrix eigenvalues
By applying the orthogonality property of the MMSE estimate [21], the channel gk can be modeled as gk = gk + gk where gk ∼ CN (0, Ce) with Ce = R − is defined as the channel estimation error
Summary
Since its introduction in [1], research on massive multipleinput multiple-output (MIMO) has been flourishing. This paper considers training optimization in spatially correlated fading channels of multi-user massive MIMO systems. We derive the optimal training duration and the optimal power allocation for the training and the uplink data transmission that maximize the uplink ergodic sum rate. Our analysis and numerical results provide the following contributions: 1) We show that Ï„ = K , where Ï„ is the optimal training length It is independent of the factors such as the channel spatial correlation matrix, the channel coherence interval (T ) and the uplink SNR. The simulations indicate that the optimal power allocation from the uncorrelated channel model can be used for the cases involving spatially correlated channels with negligible penalties on the ergodic sum rates.
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