Presentation on theme: "The Impact of Channel Estimation Errors on Space-Time Block Codes Presentation for Virginia Tech Symposium on Wireless Personal Communications M. C. Valenti."— Presentation transcript:
The Impact of Channel Estimation Errors on Space-Time Block Codes Presentation for Virginia Tech Symposium on Wireless Personal Communications M. C. Valenti D. A. Baker Wireless Communications Research Lab West Virginia University
Benefits of Space-Time Block Codes Space-time block coding utilizes multiple transmit antennas to create spatial diversity. This allows a system to have better performance in a fading environment. Benefits: Good performance with minimal decoding complexity. Can achieve maximum diversity gain equivalent to space-time trellis codes. Receivers that use only linear processing.
Diagram of Block STC Transmission X1X1 X2X2 0 T2T X1X1 -X 2 * X2X2 X1*X1* 0 T2T Ant 1 Ant 2 Data STC encoder Data STC encoder Fading i AWGN n STC decoder x r Modulation Encoder matrix:
Wireless Channel Model: Rayleigh Fading The channel between the i th transmit antenna and the receive antenna undergoes flat-fading: We assume quasi-static fading: Quasi-static means that the path gains from one transmit antenna to the receive antenna is constant over a frame. Rayleigh UniformGaussian
Block STC decoder Each symbol in a block is decoded separately by minimizing the metric The decoder outputs the hard-decisions on the data. The more TXs and RXs the system has, the better performance the system can achieve.
Decoding Block STC Since |x 1 |=|x 2 | (PSK), we can get: The received signals are: In order to minimize it is equivalent to minimize By using: we have: and
Simulation of STBC Channel fading coefficients were modeled as samples of Gaussian random variables with variance 0.5 per dimension. The channel was assumed to be static over the length of a frame, and varies from frame to frame. Noise was modeled as Gaussian with zero mean and variance n/(2*SNR). Where n is the number of transmit antennas.
STBC With Channel Estimation Errors The fading coefficient between the i th transmit antenna and the receive antenna is given as A channel estimate with phase error is of the form A channel estimate with gain error is of the form
Simulation Results: Phase Errors @ Low SNR The SNR at the receiver is fixed at 10 dB. This shows a rapid decline in BER performance for small errors in the phase of either channel estimate.
Simulation Results: Phase Errors @ Medium SNR The signal to noise ratio (SNR) at the receiver is fixed at 20dB Even with the increased SNR a rapid decline in bit error rate performance still occurs.
Simulation Results: Phase Errors @ High SNR The signal to noise ratio (SNR) at the receiver is now fixed at 25dB Increasing SNR only results in a steeper curve as the performance is quickly degraded.
Simulation Results: Average Phase Error Per Channel 0 10 1 Received SNR BER avg. phase error/channel = 0.2 rad avg. phase error/channel = 0.4 rad avg. phase error/channel = 0.6 rad avg. phase error/channel = 0.8 rad As the average phase error in each channel approaches 0.5 radians, the performance is completely degraded even with increasing values of SNR at the receiver.
Simulation Results: Gain Errors The SNR is fixed at 10dB. The curve has a valley- like shape. This shows that if the error in both channel estimates is roughly equal, then only a small performance penalty is incurred. However, if the errors in each estimate are very different, performance can suffer.
Normalized Gain Error Since the performance of the system is not adversely affected by errors in the gain of the estimates if the estimates are the same in each channel, the concept of normalized gain error is introduced.
Simulation Results: Normalized Gain Error SNR fixed at 10dB. SNR fixed at 20dB.
Simulation Results: Normalized Gain Error The performance loss is negligible when the normalized gain error is unity. When the difference between the gain errors in the two channels is nearly double the loss approaches 7dB at a BER of 10 -3.
Simulation Results: Combined Gain and Phase Errors The shape of the curves remain similar to the curves generated when only considering the errors in the gain. However, the curves get flattened as the average phase error in each channel is increased. The phase errors are obviously the primary source of performance loss.
Pilot Sequence Estimation A pilot sequence is a series of symbols that are known to the receiver in advance. By comparing what was transmitted with what was received, the receiver can estimate the effects of the channel. However, since the AWGN noise samples at the receiver are not known, the channel estimates will be imperfect, or noisy.
STBC Estimation Scheme: How It Works If we have only one receive antenna then the received signal at time t can be expressed as follows:
STBC Estimation Scheme: How It Works The received signal can also be expressed using a matrix of transmitted signals instead of a matrix of channel gains as shown in the following:
STBC Estimation Scheme: How It Works If the receiver knows the signals that were transmitted then an estimate of the channel fades can be derived from the received signal.
STBC Estimation Scheme: How It Works The channel estimate can now be shown.
QPSK Using Pilot Sequence Estimation 10 0 QPSK with running average estimation Received SNR BER The equation from the previous slides was used to implement a pilot symbol estimation scheme. The frame size for each example was 60 bits. The channel was assumed to be quasi-static, or constant fading over a frame. r=1/2 r=2/3 r=3/4 r=4/5 perfect CSI
Results of Pilot Estimation Simulations The rate 1/2 and rate 2/3 schemes perform at a loss of only 2dB as compared to the case of perfect CSI. The rate 3/4 and rate 4/5 schemes perform at a loss of approximately 3 dB as compared to the case of perfect CSI.
Conclusions and Future Work Conclusions: Block space time codes are sensitive to channel estimation errors. The impact of phase and amplitude errors were studied separately and jointly. Pilot symbol techniques can be used to assist estimation. Future Work: Other modulation types, such as QAM, FSK, and DPSK, will be tested. Correlated fading between transmit and receive pairs and variable fading rates should be taken into account. Turbo principles can be used to facilitate the implementation of iterative channel estimation and decoding techniques.