The key bottleneck for secondary spectrum usage is the aggregate interference to the primary system receivers due to simultaneous secondary transmissions. Existing power allocation algorithms for multiple secondary transmitters in the TV white space either fail to protect the TV service in all cases or they allocate extremely low power levels to some of the transmitters. In this paper, we propose a power allocation algorithm that favors equally the secondary transmitters and it is able to protect the TV service in all cases. When the number of secondary transmitters is high, the computational complexity of the proposed algorithm becomes high too. We show how the algorithm could be modified to reduce its computational complexity at the cost of negligible performance loss. The modified algorithm could permit a spectrum allocation database to allocate near optimal transmit power levels to tens of thousands of secondary transmitters in real time. In addition, we describe how the modified algorithm could be applied to allow decentralized power allocation for mobile secondary transmitters. In that case, the proposed algorithm outperforms the existing algorithms because it allows reducing the communication signalling overhead between mobile secondary transmitters and the spectrum allocation database.

The main requirement for secondary spectrum usage is interference control. For single secondary transmitter, the power level maximizing the secondary transmission rate under primary system protection constraints has been derived in [

The SE43 working group in the Electronic Communications Committee (ECC) in Europe announced a power allocation rule for secondary operation in the TV white space (TVWS), hereafter referred to as the SE43 rule [

Power allocation algorithms that satisfy the TV protection constraints have been proposed by the academic research community [

A proportional fair (PF) power allocation rule would favor equally the secondary transmitters by equalizing their resource consumption. The available resource is the maximum permitted generated interference at the TV system. Note that the SE43 rule resembles a PF power allocation scheme in the limiting scenario with 2–4 transmitters. Unlike the SE43 rule, the scheme proposed in this paper is able to protect the TV service in all cases. When the number of secondary transmitters is high, the complexity of the proposed scheme may prohibit a real-time implementation in a spectrum allocation database. Because of that, a suboptimal method with low complexity is also introduced. The suboptimal method not only allows protecting the TV service but also enables power allocation to mobile users in a decentralized manner.

The ECC report [

The remainder of this paper is organized as follows. In Section

In TV network planning the location probability describes the percentage of locations within a square area of

The probability constraint (

Expressing (

By using the concept of interference margin one essentially turns the chance type of constraint (

By using the concept of interference margin the probability constraint (

Allocating the transmit power levels can be viewed as a resource sharing problem. In order to equalize the resource consumption we propose a PF power allocation scheme. For PF power allocation the sum of secondary transmission power levels in the log-domain should be maximized [

The optimization function and the constraints are continuously differentiable functions of

The solution has the form

One can show that the Hessian matrix of the objective function is negative definite and thus the optimization function is concave. Since the constraints are linear functions of transmit power levels, the optimization problem (

We propose associateing each transmitter with the TV test point where its generated interference is maximized. In this way, we end up with a subset

We denote by

The generated interference at the

Since each transmitter

With the parameter

In Figure

Comparison of simplified PF and PF power allocation schemes.

Simplified proportional fair power allocation

Proportional fair power allocation

The two schemes are characterized by different implementation complexity. The complexity to identify the set of dominating test points in the simplified scheme is

The power allocation scheme proposed in Section

Following the ECC approach, we discretize the secondary deployment area into pixels. We assume that the UE inside each pixel is distributed according to a Poisson point process (PPP). The density of the process in the

Similar to the power allocation rule described in Section

The parameter

The transmission power level

Allowing UE mobility within a group

The flexibility introduced with (

Thus far, the transmission power levels for BS and UE have been calculated assuming that the full interference margin is available to BS and UE, respectively. When the BS and the UE are simultaneously active, the power allocation algorithm may have the following steps:

allocate some fraction

compute the parameter

compute the BS transmission power levels

by using the identified BS transmission power levels compute the remaining interference margin

group the secondary pixels and identify the transmission power level for UE in each pixel by using (

For testing the proposed power allocation rule we select a study area in Jyväskylä in Finland where the Vihtavuori TV transmitter operates at

In order to identify the TV coverage area we cover the full study area with square pixels with side equal to

For testing power allocation for mobile UE, the population density map of the area is utilized; see Figure

Secondary UE density map in the study area.

First, we compare the allocated transmit power levels of secondary BS by using PF and simplified PF power allocation rules. For PF rule the power levels are obtained by solving (

TV protection area (blue-shaded area), secondary BS (red triangles), and dominating TV test points (yellow stars).

Distribution of transmission power levels by using PF and simplified PF schemes for different protection distances. The locations of secondary transmitters are fixed and known.

Next, we compare the proposed power allocation method with other existing methods. If we are to use equal transmit power for all secondary transmitters [

Next, we compare our method with the existing SE43 proposal. The transmission power level for each BS by using the SE43 rule is [

Instead of using protection margins one can scale the transmission power of each BS with the total number

The TV SINR distribution at the test point experiencing the highest interference level is depicted in Figure

TV SINR distribution at the dominating test point experiencing the highest secondary interference level by using different power allocation rules and protection distance

The proposed rule can also be used to allocate the transmission power levels to the UE (

Distribution of UE transmission power levels by using the simplified PF power allocation rule for different protection distances. The power allocation scheme (

Finally, we consider simultaneous BS and UE transmissions and the power allocation algorithm described in Section

Distribution of UE transmission power levels for different fractions

In this paper we proposed a power allocation algorithm for multiple secondary transmitters in the TVWS that protects the TV service in the cochannel. The proposed rule can incorporate secondary transmitters with different antenna heights, for instance, base stations and mobile UE. The impact of terrain morphology can be considered by using different slow fading standard deviations for transmitters located at different pixels. The proposed rule allows reducing the communication signaling overhead between the UE and the spectrum allocation database with the reason being that the database groups secondary pixels and controls the aggregate interference from each group instead of doing it on a per pixel basis. The proposed rule outperforms the existing SE43 rule because it protects the TV service in all cases and results in smaller communication signalling overhead. However, it does not consider the scenario where some of the secondary transmitters fall inside the coverage area of an adjacent TV channel. The SE43 rule takes into account the protection of adjacent channel TV service by using reference coexisting geometries. The reference geometry rule is conservative particularly at low user densities [

This work was partially supported by the TEKES-funded project IMANET+ and by the Academy-of-Finland-funded project SMACIW under Grant no. 265040.