Praise for Fundamentals of WiMAX

5.5 Spatial Multiplexing 179Antenna IndexAntenna IndexInterference123 4NulledWasted11111 234222212343333Wasted123 44444CancelledDetection OrderTimeTime(a)Figure 5.13 (a) D-BLAST detection of the layer 2 of four. (b) V-BLAST encoding. Detection isdone dynamically; the layer (symbol stream) with the highest SNR is detected first and thencanceled.where w r,i is the ith row of the zero-forcing or MMSE receiver G of Equation (5.57) andEquation (5.60), respectively.Since this SNR is held hostage by the lower channel eigenvalues, the essence of V-BLASTis to combine a linear receiver with ordered successive interference cancellation. Instead ofdetecting all N tstreams in parallel, they are detected iteratively. First, the strongest symbolstream is detected, using a ZF or MMSE receiver, as before. After these symbols are detected,they can be subtracted out from the composite received signal. Then, the second-strongest signalis detected, which now sees effectively N t− 2 interfering streams. In general, the ith detectedstream experiences interference from only N of the transmit antennas, so by the time thet− iweakest symbol stream is detected, the vast majority of spatial interference has been removed.Using the ordered successive interference cancellation lowers the block error rate by about a factorof ten relative to a purely linear receiver, or equivalently, decreases the required SNR byabout 4 dB [28]. Despite its apparent simplicity, V-BLAST prototypes have shown spectral efficienciesabove 20 bps/Hz.Despite demonstrating satisfactory performance in controlled laboratory environments, theBLAST techniques have not proved useful in cellular systems. One challenge is their dependenceon high SNR for the joint decoding of the various streams, which is difficult to achieve ina multicell environment. In both BLAST schemes, these imperfections can quickly lead to catastrophicerror propagation when the layers are detected incorrectly.5.5.3 Closed-Loop MIMO: The Advantage of Channel KnowledgeThe potential gain from transmitter channel knowledge is quite significant in spatial-multiplexingsystems. First, we consider a simple theoretical example using singular-value decompositionthat shows the potential gain of closed-loop spatial-multiplexing methods. Then we turn ourattention to more practical linear-precoding techniques that could be considered in the near to(b)