The use of multiple antennas at a transmitter and/or a receiver of a node in a wireless communication system may significantly boost the capacity and coverage of the wireless communication system. Such Multiple Input Multiple Output (MIMO) systems exploit the spatial dimension of the communication channel to improve performance by for example transmitting several parallel information carrying signals, so-called spatial multiplexing. By adapting the transmission to the current channel conditions, significant additional gains may be achieved. One form of adaptation is to dynamically, from one Transmission Time Interval (TTI) to another, adjust the number of simultaneously transmitted information carrying signals to what the channel may support. This is commonly referred to as transmission rank adaptation. Precoding is another related form of adaptation where the phases and amplitudes of the aforementioned signals are adjusted to better fit the current channel properties. Classical beam-forming is a special case of precoding in which the phase of an information-carrying signal is adjusted on each transmit antenna so that all the transmitted signals add constructively at the receiver.
The signals form a vector-valued signal and the adjustment may be thought of as multiplication by a precoder matrix. The precoder matrix is chosen based on information about the channel properties. A common approach is to select the precoder matrix from a finite and countable set, a so-called codebook. Such codebook based precoding is an integral part of the Long Term Evolution LTE standard and will be supported in MIMO for High Speed Downlink Packet Access (HSDPA) in Wideband Code Division Multiple Access (WCDMA) as well. The receiver (e.g. User Equipment, UE) would then typically evaluate all the different precoder matrices in the codebook and signal to the transmitter (e.g. Node B) which element is preferred. The transmitter would then use the signalled information, when deciding which precoder matrix to apply. Since codebook indices need to be signalled and the receiver needs to select a suitable codebook element, it is important to keep the codebook size as small as possible. On the other hand, larger codebooks ensure that it is possible to find an entry that matches the current channel conditions more closely.
Codebook based precoding may be seen as a form of channel quantization. Alternatively, methods may be used that compute the precoder matrix without resorting to quantization.
The fundamental goal of precoder codebook design is to keep the codebook size small while still achieving as high performance as possible. Design of the elements in the codebook thus becomes crucial in order to achieve the intended performance.
Different antenna array configurations influence how the codebook elements should be designed. Many existing solutions are designed with spatially uncorrelated channel fading in mind and where each channel coefficient fades with the same average power. However, such a channel model is not sufficiently accurate when cross-polarized antenna arrays are used. Consequently, the existing designs are ill-suited for such a configuration—an antenna configuration which is deemed important in practice.
To understand why existing designs tailored for equal powered channel coefficients are not efficient for a cross-polarized antenna array setup, consider for simplicity a 2x2 MIMO system in which both the transmitter and the receiver use cross-polarized arrays and the two orthogonal polarizations are aligned on the transmit and receive side, e.g. a pair of vertically and horizontally polarized antennas on both sides of the link. The MIMO channel matrix will then be diagonally heavy, meaning that the on-diagonal elements on average have substantially more power than the off-diagonal ones, since the vertical and horizontal polarizations are on average fairly well-separated even after experiencing the radio channel and reaching the receiver. For such a channel, an appropriate codebook of minimal size contains the unit vectors and the identity matrix. This ensures that when one-stream transmission (rank-one transmission) is performed, all the transmit power may be allocated to the antenna with the strong channel and no power is wasted on the other antenna, which on average will not be able to convey significant power to the receiver. The reason for the latter is because of the cross-polarized setup in conjunction with the selection of rank-one transmission, which means the channel matrix will typically have only one element with a power substantially larger than zero and that element will lie on the diagonal.
All power should hence be allocated to the antenna which corresponds to the aforementioned non-zero diagonal element. For a design which targets a scenario with equal powered channel coefficients, this is however typically not the case. Existing codebook designs do however not address this issue for the case of more than two antennas and also do not consider the structure of the codebook for various transmission ranks.