Abstract
The current global bandwidth shortage in orthogonal frequency division multiplexing (OFDM)-based systems motivates the use of more spectrally efficient techniques. Superimposed training (ST) is a candidate in this regard because it exhibits no information rate loss. Additionally, it is very flexible to deploy and it requires low computational cost. However, data symbols sent together with training sequences cause an intrinsic interference. Previous studies, based on an oversimplified channel (a quasi-static channel model) have solved this interference by averaging the received signal over the coherence time. In this paper, the mean square error (MSE) of the channel estimation is minimized in a realistic time-variant scenario. The optimization problem is stated and theoretical derivations are presented to attain the optimum amount of OFDM symbols to be averaged. The derived optimal value for averaging is dependent on the signal-to-noise ratio (SNR) and it provides a better MSE, of up to two orders of magnitude, than the amount given by the coherence time. Moreover, in most cases, the optimal number of OFDM symbols for averaging is much shorter, about 90% reduction of the coherence time, thus it provides a decrease of the system delay. Therefore, these results match the goal of improving performance in terms of channel estimation error while getting even better energy efficiency, and reducing delays.
Highlights
Wireless communications have become more demanding and complex with each generation, and the fifth generation (5G) expects to improve on the capabilities of the preceding ones by several orders of magnitude, either in data traffic, lower latencies or multi-connectivity
The mean square error (MSE) is studied in scenarios with different speeds and the signal-to-noise ratio (SNR) dependence on the optimum number of averages is exposed
All the presented results are focused on the MSE of the channel estimation because under the same power allocation factor β and symbol modulation scheme, the bit error rate (BER) performance of the superimposed symbols will improve as long as the MSE is enhanced [11]–[13]
Summary
Wireless communications have become more demanding and complex with each generation, and the fifth generation (5G) expects to improve on the capabilities of the preceding ones by several orders of magnitude, either in data traffic, lower latencies or multi-connectivity. In terms of channel modeling, most studies define the channel to behave under quasi-static constraints, which mean that for a specific number of time symbols, whose duration is given by the coherence time, the channel coefficients remain completely constant This simplification is usually employed for two reasons: firstly, the averaging of the received signal over these specific symbols guarantees a better estimation because the channel has not changed, VOLUME 9, 2021 and secondly, the simpler model allows closed-form MSE expressions or their respective optimization solutions to be obtained. Other approaches implemented the time-varying models of [28] which expressed the channel with discrete prolate spheroidal basis, with Slepian sequences as the basis functions, [29] Even though, both studies were more realistic than previous works that considered quasi-static constraints, they did not optimize the averaging since the expressions of the channel became too complex. Notation: For simplicity, the analysis is element-kind and non-vectorial notation is required, except in the Appendices, which are self-contained; (·)∗ denotes complex conjugate, · and · represent the nearest and the integer value operation, respectively, E{·} is the expectation, Em{·} is the mean over m and Var {·} refers to the variance
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