# Mobile radio link adaptation by radio channel state prediction/Mobiliojo radijo rysio kanalo busenos prognozavimas.

IntroductionApplying the channel state prediction in 3G mobile communication networks [1, 2] allows securing a maximum spectral efficiency of the channel under the required error rate.

The paper deals with the selection analysis of the optimum sampling period of the radio channel signal envelope [3] and prediction interval adaptation using Kalman filter to achieve minimum channel state prediction error. Results of radio channel state prediction simulations performed in Matlabu are applicable in optimization of adaptation parameters of a real communication system [4].

Simulation of Kalman filter as radio channel state predictor

Kalman filter enables parameters prediction also for non-stationary signals [5, 6] using all information about the measured signal from the start of measurement or signal reception. The predictor applies a filter with a recursive structure. Kalman filter belongs to adaptive predictors because its coefficients are adapted in each step so as to provide optimal estimate of the signal. The predictor performs two repeatedly changing steps--prediction (time update) and correction (measurement update).

Algorithm for radio channel state prediction using Kalman filtering

Using the Kalman filter method, the following steps are performed in each simulation step:

* Based upon the specified sampling period of the radio signal envelope [f.sub.sampl], a set of input samples Z(n) is generated over the time T;

* Based on the input data Z (n), Kalman filter predicts the future state of the radio signal envelope [??](n+L), where L denotes the prediction range, i.e. the number of future samples for which the prediction is defined;

* The prediction error is evaluated using the formula [[epsilon].sub.(n+L)] = [[??].sub.(n+L)]--[Z.sub.(n+L)] , i.e. calculating the difference between the predicted value and the real one of the radio signal envelope level;

* Prediction error is evaluated after the time T (adaptation period) elapses, in our simulation T is the size of the UMTS time slot, i. e. 0.667 ms;

* Optimal setting of the prediction range [L.sub.scale,] i.e. the defined time of prediction, and radio channel envelope sampling frequency [f.sub.sampl] to guarantee the required prediction error level [[epsilon].sub.allow].

To be able to objectively evaluate obtained simulation results, the first simulations were carried out without adaptation of parameters of the prediction range [L.sub.scale] , with sampling frequency of the radio signal envelope [f.sub.sampl]. The parameters [L.sub.scale] and [f.sub.sampl] were constant during simulation. Two sampling frequencies of the radio signal envelope were chosen ([f.sub.sampl] = 12 kHz and 24 kHz), for which the best quality of prediction, i.e. the lowest value of the prediction error was achieved [7] (Fig. 1).

[FIGURE 1 OMITTED]

With regard to simultaneous utilization of predictors in the link adaptation loop it is important to know properties of the predictor with Kalman filter also for various prediction intervals, i.e. prediction range [L.sub.scale].

The received signal processing, generating of the related TPC link adaptation command and its transmission through the control channel takes certain time, hence the control station works with a relatively out-dated information about the radio channel state.

Elimination of the total delay [n.sub.total] is the main objective of implementation of prediction methods for radio channel state estimation into transmission power control algorithms. To simulate real system, for sampling frequency [f.sub.sampl] = 12 kHz, the UMTS time window period was chosen, i.e. [L.sub.scale] = 0.667ms (a sufficiently large prediction range). The prediction range for sampling frequency [f.sub.sampl] = 24 kHz was chosen as the period between two subsequent samples of the radio signal envelope, i.e. [L.sub.scale] = 0.041 ms (minimum prediction error). In this way, limits for the simulation without adaptation have been obtained, that can be further compared with results from simulation with prediction range adaptation (FSPRA and VSPRA algorithms).

From simulations results that the smaller is the sampling period of the radio signal envelope, the better prediction is achieved [8]. A drawback of a small radio signal envelope sampling period consists in hardware demands for computation unit and prediction possibility over a very small prediction interval; this lowers its applicability in the link adaptation loop. It is quite complicated to carry out real-time simulation using sampling frequency 24 kHz to guarantee the required QoS criterion in various types of communication environment and for various speeds of the mobile terminal. Similar results can be achieved using methods for optimal tuning of the prediction range [L.sub.scale] and the sampling frequency [f.sub.sampl] (algorithms FSPRA and VSPRA with adaptation).

Fixed step prediction range adaptation

Realization of the Fix Step Prediction Range Adaptation (FSPRA) algorithm consists in guaranteeing minimum value of the adaptation criterion [[epsilon].sub.error] by changing the prediction range parameter [L.sub.scale].

The FSPRA algorithm is based upon evaluation of the current value of prediction error [[epsilon].sub.error and consecutive increasing/decreasing of the prediction range [L.sub.scale] by a fix adaptation step [L.sub.step] . In our case, the prediction range step corresponds to time between two subsequent samples of the radio signal envelope, which corresponds to the sampling period of the radio signal fading envelope.

To objectively compare simulation results, the mobile station moved in heterogeneous environment. Because the environment parameters depend on the time-varying mobile station velocity, the system has to periodically update the adaptation process with the period of the UMTS time window, i.e. every 0.667 ms. Simulation was performed for two sampling frequencies of the radio signal envelope [f.sub.sampl] = 12 kHz and 24 kHz. The required prediction error value was [[epsilon].sub.allow] = 1 dB.

Variable step prediction range adaptation

The Variable Step Prediction Range Adaptation algorithm (VSPRA) is the second method for optimal changing of the prediction range parameter [L.sub.scale] in order to minimize the adaptation criterion value [[epsilon].sub.error]. The main principle of the prediction range adaptation block with variable step is based upon evaluation of the current value of the prediction error [[epsilon].sub.error] for the given prediction range, as well. Two parameters were introduced, affecting the prediction range change [DELTA][L.sub.scale] based on the evaluation of the current value of the prediction error [[epsilon].sub.error].

The qualitative parameter [[phi].sub.trend] (n + L) characterizes the prediction error change trend and can achieve three distinct values [[phi].sub.trend] (n + L) = <-1,0,1> describing the trends of the prediction range [DELTA][L.sub.scale], namely decrease, without change and of growth.

Another qualitative parameter is the change weight [[PHI].sub.[DELTA]](n + L) with values from the interval <0,1> where [[PHI].sub.[DELTA]](n + L) = 0 indicates that the new prediction range equals the previous one [L.sub.scale](n + L) = [L.sub.scale](n + L -1), i.e. the prediction range change [DELTA][L.sub.scale] = 0 , and vice versa, the value 1 indicates the highest possible slope of the prediction range change. The change weight [[PHI].sub.[DELTA]](n + L) is directly proportional to the current prediction error [[epsilon].sub.error]. The resulting prediction range value [L.sub.scale] is defined as follows

[L.sub.scale](n+L) = [L.sub.scale](n+L-1) + ([[theta].sub.[DELTA]](n+L) * [L.sub.step] * [[phi].sub.trend](n+L). (1)

The objective evaluation of simulations requires securing equal conditions, hence also in these simulations the mobile station moved in a heterogeneous environment. The adaptation process was periodically updated with the period of UMTS frame time window (0.667 ms). Simulation was carried out for two sampling frequencies of the radio signal envelope [f.sub.sampl] = 12 kHz and [f.sub.sampl] = 24 kHz. Required value of the prediction error was again [[epsilon].sub.allow] = 1 dB.

Evaluation of simulation results

Results of the radio channel state prediction simulation without prediction range adaptation, with fix step adaptation (FSPRA algorithm) and with variable step adaptation (VSPRA algorithm) are compared in Fig. 2 using cumulative distribution function CDF.

Comparison of FSPRA and VSPRA adaptation algorithms shows reduction of the prediction error [[epsilon].sub.error] when using the variable step prediction range adaptation (VSPRA). The using of parameters [[phi].sub.trend](n + L) and [[PHI].sub.[DELTA]](n + L) contributed to the global reduction of the prediction error [[epsilon].sub.error] and to keeping the allowed prediction error [[epsilon].sub.allow]. The difference in prediction error of the VSPRA algorithm for the two sampling frequencies 12 kHz and 24 kHz was 0.35 dB. If this difference value is acceptable, a lower sampling frequency can be used ([f.sub.sampl] = 12 kHz) which considerably reduces the real computational load of the algorithm and thus also the time needed for selection of the prediction range for the transmission of a new UMTS window. In simulations, an ideal feedback channel for information transmission into the transmitter is supposed.

[FIGURE 2 OMITTED]

Prediction gain of the predictor depends on the prediction error [8-10]. Achieved results for adaptation algorithms FSPRA and VSPRA are compared on Fig. 3. The largest prediction gain [G.sub.(L)] was achieved using the VSPRA algorithm with sampling frequency [f.sub.sampl] = 24 kHz. The prediction range [L.sub.scale](n + L) is updated with the period of the UMTS time window 0.667 ms.

From the simulation results comparison (Fig. 3) concludes that algorithms in which a small prediction error is achieved (VSPRA with sampling frequencies 12 and 24 kHz), work with relatively small prediction ranges in time when the mobile station moves at the highest speed. According to the prediction range adaptation algorithm the prediction range is selected one sample ahead, to guarantee the required prediction error.

Comparison of simulation results with respect to their application in the radio channel to guarantee optimal prediction gain for a sufficiently large prediction range is in Fig. 4.

The algorithm that uses the sampling frequency [f.sub.sampl] = 24 kHz without prediction range adaptation achieves the best results in terms of the prediction gain G(L) and on the contrary, it allows predicting the radio channel envelope state for a very small time [L.sub.scale] = 0.041 ms, which corresponds to the time period between two subsequent samples of the radio signal envelope. Elimination of the time delay [n.sub.total] is minimal.

[FIGURE 3 OMITTED]

Another drawback of algorithms without prediction range adaptation lies in the fact that the prediction range is fixed during the whole simulation. This means that the algorithm uses a small prediction range even if the mobile station is moving at a small speed (the coherent time of the radio channel is large) and thus does not eliminate the time delay in processing information needed for power control.

[FIGURE 4 OMITTED]

Conclusions

Optimal setting of the predictor's prediction range [L.sub.scale] and sampling period of the fading signal envelope is solution to the problem of channel coherent time, when small value of the coherent time brings very frequent changes of the fading envelope values. If the mobile station moves at high speed, the prediction error grows and the adaptation module reduces the prediction range [L.sub.scale] thus improving the signal fade estimate. If the value of the coherent time channel grows, the mobile station moves at a smaller speed and the adaptation module increases the prediction range [L.sub.scale] so as to ensure the required prediction error [[epsilon].sub.allow].

Acknowledgments

This paper was supported by the Scientific Grant Agency VEGA in the project No. 1/0336/10.

References

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[6.] Kalman R. E. A New Approach to Linear Filtering and Prediction Problems // Journal of Basic Engineering.--1960. - No. 82.--P. 35-45.

[7.] Ziacik P., Wieser V. Optimum step for radiocommunication channel state prediction // 9th International Conference Research in Telecommunication Technology (RTT'2008). Vyhne, 2008.--P. 390-392.

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Received 2011 02 01

P. Ziacik

Microstep-HDO s.r.o., 821 01 Bratislava, e-mail: pziacik@microstep-hdo.sk

V. Wieser Department of Telecommunications and Multimedia, University of Zilina, Zilina, 01026, Slovak Republic, phone:+421 (41)5132260, e-mail: vladimir.wieser@fel.uniza.sk

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Title Annotation: | ELECTRONICS/ELEKTRONIKA |
---|---|

Author: | Ziacik, P.; Wieser, V. |

Publication: | Elektronika ir Elektrotechnika |

Article Type: | Report |

Geographic Code: | 4EXSV |

Date: | Aug 1, 2011 |

Words: | 2201 |

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