# Reverse link feedback power control in pilot symbol assisted systems

##### Saarinen, Ilkka (2000-09-18)

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https://urn.fi/URN:ISBN:9514257626

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Abstract

Reverse link feedback power control in subject to a feedback delay and in conjuction with diversity is considered over a frequency-nonselective slow Rayleigh fading channel. The transmission power of a mobile station is adjusted as a function of fed back estimated channel state information, so that the average error probability is minimized when the average transmission power is fixed. The channel state is estimated by using known, constant-power pilot symbols. In each frame, a time multiplexed pilot symbol is transmitted in addition to the antipodal data symbols. In the literature, feedback MMSE (minimum mean-square error) power control has been analyzed in the case of a random time-invariant channel. Therein the frame size was two, i.e. one data and one pilot symbol were transmitted in each frame. Also, the fading gain was estimated by a one-shot MMSE estimator. This author’s main contribution is that the aforementioned analysis has been extended to a more general system model in which the frame size is arbitrary, and in which the time-variant fading gain is estimated by an optimal MMSE estimator. For power control purposes, the estimator has to be a predictor since feedback requires causality. First, in order to avoid a delay in detection, the predictor is used in both power control and detection. In the case of a frame size of two, the performance of feedback MMSE power control employing the predictor is compared to that of a system using the one-shot estimator. Then, the performance of feedback MMSE power control with an optimal frame size is evaluated. Finally, the system performance is derived when a smoother is employed in detection, and the additional effects of a feedback delay and diversity on the performance are investigated.

The performance difference between optimal (channel states are assumed to be known) and MMSE power control using a one-shot estimator is found to be significant at large signal-to-noise ratios (SNR’s). This is in contradiction with the result presented earlier in the literature. The reason for the large performance difference is that the SNR of the channel estimate is small, since each estimate is computed using only one pilot symbol. The performance difference between optimal and MMSE power control with the predictor is smaller than said difference in the case of the one-shot estimator because the estimate is averaged over many pilot symbols. It is also observed that the lag error of the estimator considerably reduces the benefit of MMSE power control, even when the channel changes very slowly. To diminish the lag error, and to achieve good performance, a large number of estimator coefficients is required. It is well known that fixed-step adjustment closed loop power control attempts to compensate for all changes caused by the channel. In contrast, according to Monte Carlo simulations, MMSE power control did not attempt to compensate for the deepest fades. At other time instants, it strives to set the received SNR to an approximately constant level, which depends on the bit-error rate (BER) target. Increasing the frame size from the value of two not only improves the spectrum utilization, but was also shown to yield better performance for the pilot symbol system with MMSE power control over a slowly fading channel. Also, a clear performance improvement was achieved by using the smoother in detection. The performance loss resulting from a feedback delay of 10–20% from the channel coherence time was shown to be small with reasonable BER values. Estimation errors were shown to diminish the benefit of power control when the diversity order was two, compared to the case of no diversity.

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