## 1 Introduction  
In a cellular network, the cell-edge user throughput is mainly limited owing to the path loss by the long distance from the serving base station and the inter-cell interference from neighboring base stations. Coordinated multi-point (CoMP) transmission technology can improve the signal quality and/or throughput at a cell-edge region and can also widen the coverage of high throughput via cooperative transmission and/or coordinated inter-cell interference control by multiple coordinated transmission points (CTPs) [1; 2]. CoMP has been included not only as a promising technology for fourth-generation (4G) mobile communication standards, but also it is expected to suit even better in fifth-generation networks, whose novel architectures will accommodate extremely larger amount of data traffic that can be currently circulated in 4G networks [1]. In particular, CoMP joint diversity transmission (JDT) can significantly improve the signal quality because two or more CTPs coordinately transmit signals so as to be meaningfully exploited at a user equipment (UE) receiver, at the expense of a radio-resource deficiency [2]. Many studies on CoMP transmission technology have been conducted [3; 4; 5; 6]. For CoMP transmission technology, expanded researches have been conducted recently such as the joint transmission techniques with adaptive modulation [3], spectrum resource allocation method for CoMP transmissions [4], as well as fundamental researches have been conducted steadily such as the coordinated beamforming techniques [5], the determination techniques of a CTP set [6]. In the context of wireless green communication [7], the total coordination point power (TCPP) over all CTPs in the cooperating set for a targeted UE could be constrained to a certain level [8; 9; 10]. Hence, the CTPs should share the TCPP by distributing it efficiently. However, in a CoMP configuration where all the CTPs in the cooperating set for the targeted UE share the TCPP, JDT may not be effective if the received signal level from one CTP is extremely lower or higher than those from the other CTPs. Therefore, a simple and efficient process to determine the number of CTPs participating in JDT and subsequently, the power levels to be allocated over the CTPs in the resulting JDT cooperating set should be developed. In [11], an optimum joint power allocation (JPA) scheme to maximize the instantaneous capacity in an orthogonal frequency division multiple access CoMP JDT network with individual CTP power constraints was introduced. However, this scheme may be used only in a slowly varying fading environment because the instantaneous channel state information may not be exchanged quickly enough among the CTPs. In [8], the authors dealt with the problem of JPA in a coordinated two-point (Co2P) JDT network with a unity TCPP constraint, aimed at maximizing the ergodic cooperative capacity (ECC) in Rayleigh fading channels. However, the approach in [8] cannot be used in a CoMP configuration when two CTPs in the cooperating set share a non-unity TCPP and/or in a CoMP configuration where more than two CTPs participate in JDT under a TCPP constraint. In this paper, we consider the problem of JPA in a CoMP JDT network with a TCPP constraint, to maximize the ECC in Rayleigh fading channels. We first extend the JDT power allocation problem in the Co2P JDT network with the unity TCPP constraint in [8] to the case of a non-unity TCPP constraint. Furthermore, we introduce more accurate log-quadratic approximated (LQA) and log-linear approximated (LLA) CTP power expressions with respect to the mean branch gain-to-noise ratios (GNRs). Next, we extend our study to a coordinated three-point (Co3P) JDT network with the relationship that yields the optimum three CTP powers as a function of the mean branch SNRs.