In MCP enabled networks each group of collaborating BSs forms a distributed antenna array. Therefore all the typical multiuser MIMO precoding techniques can be applied in order for the ICI to be mitigated. In this paper linear precoding is considered for MCP transmission as it provides a good trade-off between performance and complexity, and it is more robust to imperfect CSI compared to nonlinear schemes . Furthermore linear precoding together with the more practical quantized feedback can be optimal under certain circumstances . In addition to this, linear precoding scales optimally when a large number of MSs is available and opportunistic scheduling is employed .
Thus if single-antenna BSs jointly perform linear precoding on the downlink, the BS antennas combine and serve at most single-antenna mobile stations simultaneously. The complete channel matrix of the system is
where is the channel vector of the th MS. Let be the set of MSs scheduled to be served in a specific time slot, where . Therefore is the channel matrix related to these MSs. The vector of transmit symbols with power , where , is mapped to the transmit antennas as follows:
is the precoding matrix of size which is a function of the received CSI of the scheduled users, and is the beamforming vector corresponding to MS . Therefore with linear precoding, the th MS, where , receives
The term represents the detrimental ICI. In matrix notation the scheduled users receive
where is the received signal vector and is a vector of independent complex circularly symmetric additive Gaussian noise components. The SINR of the th MS is
The term corresponds to the intercell interference power.
Per-antenna power constraints are considered due to the fact that cooperating antennas are spatially distributed, and they cannot share their power. It is assumed that each antenna has an average power constraint, thus for . For equal power allocation , where is a column vector of 1s with dimension , the elements of the power allocation vector must meet the following constraint :
Therefore the power allocation vector is
As a result, the SINR of the th MS is
With equal power allocation and an equal power constraint per BS, for , the expression for the power allocation vector (10) reduces to .
The entity of the network responsible for user scheduling and precoder design receives an imperfect version of the matrix H, due to quantization error (limited digital feedback) and to errors introduced by the feedback channel. The chosen precoding scheme is zero-forcing, where the precoding matrix inverts the imperfect channel matrix describing the received CSI. Hence the precoding matrix is
where is a diagonal matrix that normalizes the columns of to unit norm. Note that other choices of linear precoding apart from zero-forcing (e.g., MMSE) can be considered . The evaluation metric we are interested in is the ergodic achievable rate per cell:
3.1. Quantized Limited Feedback
In the case of quantized limited feedback, for each user there is a quantization codebook consisting of vectors of unit norm, where is the number of feedback bits. This codebook is known both by the user and by the scheduling entity. Each MS after obtaining an estimate of its channel vector (in this paper we assume a perfect estimate) quantizes its direction to the vector from the codebook that best approaches it, which is the one leading to the smallest angle separation [19–21]. Therefore
where results from the inner product rule. The quantity determining the efficiency of quantization is the quantization error defined as . The codebook should be user specific in order to avoid multiple users quantizing their channel direction to the same vector.
After quantization, MS i feeds back to the system the index k in binary form which corresponds to the quantization vector that best describes its channel direction. Therefore this piece of information is defined as Channel Direction Information (CDI). The more the feedback bits are, the larger the quantization codebook is, which leads to a better approximation of the MS's channel direction. Apart from CDI, the scheduling entity needs some information regarding the channel quality of each user in order to be able to make user selection decisions; this is defined as Channel Quality Information (CQI). In this paper we consider the unquantized channel norm as the fed back CQI which does not capture the interuser interference. This is because we are interested in investigating the precoding performance and not the efficiency of scheduling; therefore the consideration of more complex CQI metrics is unnecessary.
A random codebook has been considered as optimization of the codebook design is beyond the scope of this paper. Thus the codebook is comprised of unit norm complex Gaussian random vectors, and .
Hence the concatenated quantized channel matrix of the system is . The binary indices corresponding to the CSI vectors (lines of ) are fed back to the scheduling entity through one or several radio channels, depending on the MCP framework, that introduce errors. Therefore the concatenated channel possessed by the scheduling entity is , where is a function of the errors introduced by the feedback channel.
3.2. Feedback Error Model
When quantized feedback is employed, each MS feeds back a sequence of bits, , . These bits are the index of the vector in the employed codebook that best describes the CDI of a user in binary form. It is assumed that each transmitted bit is received in error with probability . Therefore
The probability of bit errors is considered to be identical and independent across different radio links. The received feedback can be protected from errors by the use of appropriate error correction techniques requiring the addition of a number of bits in the fed back sequence. However such consideration is beyond the scope of this paper which aims at examining the impact of feedback errors in the worst case scenario, when no error detection or correction schemes are employed.