Research on Power Control Algorithm of CDMA System Based on Matlab

CDMA mobile communication system has the advantages of strong anti-interference ability, good confidentiality, large capacity, etc., and has received widespread attention. CDMA uses the orthogonality and quasi-orthogonality of code sequences to distinguish different users. Under the conditions of the same frequency and time, each receiver separates the required signal according to the difference between the signal code types. Since the same frequency is reused in all cells in the CDMA system, the interference in CDMA is particularly serious. If there is no advanced power control technology to minimize the background interference of users, serious bit errors will occur. As the number of users increases, the signal-to-noise ratio of the signal drops sharply. When it is lower than a certain threshold, communication interruption may occur. Due to the problems of transmission attenuation, multiple access interference, and near-far effect in the CDMA system, the system capacity is limited by the mutual interference between users. Therefore, power must be controlled. This paper mainly studies the power control algorithm in the CDMA system.

1 Relationship between power and capacity

In a CDMA system, the capacity of a CDMA system is limited due to the restriction of transmission power or the interference of the system itself. On the reverse link, when the power of a mobile station is not enough to overcome the interference of other mobile stations, the system reaches the capacity limit. On the forward link, when there is no excess part of the total power of the base station to allocate to a new user, the system reaches the maximum capacity. That is, when the total power transmitted by a base station for the normal operation of all its users exceeds the rated power of the base station, the forward link reaches the power-limited capacity.

In order to access a call, the power of a CDMA mobile station must be large enough to overcome the interference generated by other CDMA mobile stations in the bandwidth, that is, a certain signal-to-interference ratio must be achieved. At any given moment, the transmission power required by the mobile station depends on the path loss from the mobile station to the base station and the total interference level of all reverse links. The latter depends on the number and location of other CDMA mobile stations.

Each time a new call is established by all mobile stations, the interference level is increased, and each mobile station must increase its transmit power accordingly to maintain the integrity of the call. This process is repeated as the number of mobile stations increases until a limit is reached. When this limit is reached, any new mobile station, no matter where it is located, cannot overcome it with sufficient power, and existing mobile stations do not have enough power to overcome the additional interference generated by the new call. All calls in the cell must have the same Eb/I0 requirement, which is manifested in the requirement that the signal strength received by the cell base station is equal to the same value. For any mobile station, the interference in the cell is (N-1)S, where N is the number of mobile stations in the cell. Co-channel interference from mobile stations outside the cell is a secondary interference source, and its size can be taken as a fraction of the value of the interference in the cell (β times). Due to the relatively low transmit strength of the surrounding mobile stations and the longer path loss distance, the resulting interference level can usually be characterized by β<1, which is less than the noise level of the cell base station. Unlike intra-cell interference, the interference from mobile stations outside the cell is not power controlled by the receiver of the base station in the cell, so the interference size is more difficult to determine. However, it is only necessary to know the overall impact of external mobile stations.

Since the co-channel interference level is relatively small, the same β value can be used for the surrounding fully loaded cells. For large N values, all interference can be reduced by the voice activation factor.

Where: Eb is the bit energy; I0 is the power spectral density of thermal noise plus interference; F is the base station noise index; Nth is the power spectral density of thermal noise; S is the received signal strength; R is the bit rate; α is the voice activation factor; β is the interference factor; N is the number of mobile stations in the cell; W is the system bandwidth; G=W/R is the processing gain. The product of thermal noise density Nth, CDMA bandwidth W and base station noise index F is called base station noise.

The range of Eb/I0 values ​​required by the cell site receiver is related to the mobile station speed and slow fading of multipath conditions. Different types of users have different Eb/I0 requirements to maintain a certain FER. The Eb/I0 of high-speed mobile users is also different from that of low-speed and stationary users.

Where: d is the required Eb/Ib. When using a 13 Kb/s vocoder, it is approximately 24 for one sector. Rewriting expression (1) yields the average signal power required by each user as:

As can be seen from Figure 1, the signal-to-noise ratio of the cell base station required by each user increases nonlinearly with the increase in cell load. The greater the load, the steeper the slope, and the average power cost paid by the cell is much greater. Therefore, for each additional mobile user, a highly loaded cell pays a greater price than a lightly loaded cell. In addition, a heavily loaded cell will not be able to respond to the statistical fluctuations of its user voice activation. Equation (1) is further adjusted to reflect the total received interference Prec = α (1 + β) NS. The ratio of Prec to the base station noise can be fully expressed by the cell load u = N / Nmax. From Figure 2, it can be seen that the interference increases nonlinearly with the cell load.

The relationship between power and load can be expressed as the ratio of total power (received signal plus base station noise) to base station noise:

It can be seen from Figure 3 that each time the capacity is increased by half, the ratio of total power to base station noise doubles. For example, when the load increases from 0 dB to 0.5 dB, the ratio of total power to base station noise increases from 0 dB to 3 dB; when the load increases from 0.5 dB to 0.75 dB, this ratio increases from 3 dB to 6 dB.

2 Power Control Channel Simulation Model

In order to achieve real-time power control, not only the slow fading caused by shadowing and path loss but also the fast fading caused by multipath propagation should be considered in the channel. The statistical law of slow fading can be expressed as:

Where: r is the distance between the base station and the mobile station; α is the path loss exponent; ξ is a Gaussian random variable with a mean of 0 and a standard deviation of σ. The typical values ​​of σ and α are 8 dB and 4 dB, as shown in Figure 4.

As shown in Figure 4, slow fading is a function based on distance. In a very short period of time (such as a few ms), the distance between the user and the base station does not change much. Therefore, for the convenience of system simulation, it can be regarded as unchanged. For fast fading, this simulation adopts the Jakes model proposed by Jakes to simulate the fading technology of mobile communications. The frequency change of the receiving level caused by the relative motion of the mobile station and the base station is called the Doppler frequency shift. The maximum frequency shift fm=υm／λ, where υm is the maximum vehicle speed, λ is the carrier wavelength, and ωm=2πfm. The Rayleigh fading process can be approximated by superimposing N complex sinusoids. The frequency and phase of this set of sinusoids are given by specific formulas. Define N0=(1／2)(N／2-1), then the channel function T(t) of the fading channel can be expressed as:

Where: ωn=ωmcos(2πn／N), n=1, 2, …, N0; φN is the initial phase of the maximum Doppler frequency sinusoid, φn=the initial phase of the nth Doppler frequency shift sinusoid. The speed of the mobile station is 50 km／h (13.9 m／s), and the Doppler frequency shift fm=41.6 Hz. N0=8, φN=0. Matlab is used for simulation, as shown in Figure 5.

As can be seen from Figure 5, the fixed step power control algorithm has a strong "overshoot" phenomenon in the case of no diversity reception. This is because the system determines the power adjustment direction of the next moment based on the power strength of the received signal at the previous moment, and each power control cannot be compensated immediately when the system experiences deep fading, and when the control error is very small, it will cause a large fluctuation. The statistical diagram of the power of the received signal is shown in Figure 6.

As can be seen from Figure 6, the actual received signal fluctuates around the expected value, and the two sides of the distribution are asymmetric. Comparing Figure 6 with a step size of 1 dB and Figure 7 with a step size of 0.5 dB, it can be found that under the same fading conditions, the algorithm with a step size of 1 dB is more suitable. It can also be seen from here that the determination of the step size is related to the specific environment (such as the degree of fading and background interference), which is also the disadvantage of fixed step size power control.

3 Conclusion

This power control algorithm allows the base station to send power control commands. Users can adjust the transmission power in fixed steps through the control commands. The power change process is like a "ping-pong" control. This control method has poor system stability and has a large overshoot and stabilization time. From the perspective of power control alone, there are two ways to improve control accuracy. One is to increase the power measurement speed and correspondingly increase the frequency of power control, thereby increasing the correlation between two adjacent sample points to achieve the purpose of improving control accuracy; the other method is to increase the fine adjustment of the control amount, and each control command is represented by multiple bits to improve control accuracy.