Friday, March 20, 2009

How Much Feedback Is Enough for MIMO? VI Rank Deficiency

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? V Feedback Reliabilities]
[3GPP2 TSG-C WG3 C30-20090511-030]
[3GPP2 TSG-C WG3 C30-20090511-032]

The adoption of multi-antenna techniques is believed to be able to provide additional antenna gain, diversity gain, multiplexing gain and interference cancellation gain. They can help improve link quality and increase link throughput. Multi-antenna techniques are believed to be critical in meeting the demand of high data rate and high link quality and can be employed for both forward link and reverse link transmission. However, there are many issues which should be carefully considered when multi-antenna techniques are implemented. These issues include the rank deficiency of actual MIMO channels, the limitations of mobile terminal's RF design and the impact of multi-antenna techniques on other services in bandwidth-limited situations.

In theory, the achievable capacity of a MIMO channel grows linearly with the minimum of transmit and receive antenna sizes. In reality, the achievable spatial multiplexing gain depends on both channel scattering of underlying and antenna configurations of both sides instead of the geometric limitation, min{ Ntx, Nrx }. The scattering statistics of a MIMO channel is usually quantified with angular intervals. The antenna array configuration is characterized by the area or size limitation in the unit of wavelength λ and the shape. Without considering AT size, the achievable spatial multiplexing gain is limited by spatial scattering. For example, in the case of a typical 4x4 MIMO mobile communication scenario and without the limitation of access terminal's size, it is observed that less than 1% of the users are able to use rank 4 and around 90% users have either rank 1 or 2. However, it is non-trivial to “squeeze” multiple antennas and RF circuits into a mobile phone in actual commercial mobile terminal design, especially when you need additional planning on the power consumption, mechanical limitation, antenna spacing and supported frequency bands of the mobile terminal. Currently, there are many radio interfaces already enabled in most mobile phones, such as GPS, bluetooth, WiFi, etc. However, from a RF engineering perspective, there is an antenna spacing requirement that the separation between antenna elements should be larger than 0.5λ in order to maximize spatial diversity gain. This can be translated into about 7.5 cm or 3.0 inches for a 2GHz operating band, as an example. Therefore, there usually is a tradeoff between the physical size and achievable performance in each mobile terminal design. For an AT with the physical size of a few times of wavelength, e.g., about 0.5~3λ, the achievable spatial multiplexing gain is limited by the angle spread, AT size and C/I ratio. This means for practical multi-antenna mobile devices, the expected spatial multiplexing gain mostly is less than 3.


Expected Spatial Degree of Freedom. 6 spatial cluser, angle spread = 35o, dual-polarized antenna array, f = 2GHz

Sunday, March 8, 2009

How Much Feedback Is Enough for MIMO? V Feedback Reliabilities

[How Much Feedback Is Enough for MIMO? I Introduction]
[How Much Feedback Is Enough for MIMO? II Channel Estimation]
[How Much Feedback Is Enough for MIMO? III Codebook Design]
[How Much Feedback Is Enough for MIMO? IV Channel Quantization]
[How Much Feedback Is Enough for MIMO? VI Rank Deficiency]


Figure 1. A Noisy Feedback Channel Model
The reverselink channel model is a concatenation of a Gaussian channel and binary erasure channel, which are independent to each other. In generally, the reliability of reverselink is controlled by both channel fading and received SNR. When the erasure rate εr is high, it means the amount of fading of reverselink is very high. Higher erasure rate also means it takes the forwardlink transmitter longer time to accurately filter out a proper forwardlink precoding word and it usually yields higher MIMO precoding mismatch given a certain channel coherent time. Since the unreliable symbols are erased based on their received SNR, the left symbols are more reliable and their reliability is mostly decided by γRL. In this case, the well-known sphere-packing upper bound of Gaussian channel reliability function is

Figure 2. The rate-reliability region with γRL = 7dB