In this project, I implemented a minimum mean squared error (MMSE) channel estimation of low complexity using techniques from the field of machine learning. The covariance matrices of these channels vectors depend on random parameters. For example, the random parameter in this project is the angles of propagation paths. If the covariance matrix exhibits certain Toeplitz and shift-invariance structures, the complexity of the MMSE channel estimator is in the order of 훩(푀 푙표푔푀) (푀 is the channel dimension or, in this project, the number of antennas at the base station) floating point operations, otherwise 훩(푀3). In this case, an efficient suboptimal estimator with low complexity is obtained by using the MMSE estimator of the structured model as a blueprint for the architecture of a neural network. This network learns the MMSE estimator for the unstructured model, but only within the given class of estimators, that contains the MMSE estimator for the structured model.
14. MMSE channel estimation
Learning Fast MMSE Estimator using a Convolutional Neural Network:
𝑦𝑡
𝜎2Know noise variance,
Received signal,
ℎ = 𝐹 𝐻 𝑾 𝑪𝑵𝑵 𝐹𝑦
Estimated channel
ℎ 𝑡Generated channel,
Conv ReLU Conv
Bias Bias
𝑾 𝑪𝑵𝑵
𝑦𝑡Generated channel,
Parameter Value
Epochs 10 000
Training batch size 600
Testing batch size 100
Learning rate (64/M)*1e-4
Convolutional layer 2
Hierarchical Training
1. Train CNN for M antennas
2. Interpolate kernel from length M to 2M
3. Use interpolated values of kernel from previous step
for initializing CNN when training for M antennas.
15. MMSE channel estimation
Learning Fast MMSE Estimator using a Convolutional Neural Network:
ℎ 𝑡Generated channel,
Conv ReLU Conv
Bias Bias
𝑾 𝑪𝑵𝑵
𝑦𝑡Generated channel,
16. MSE per antenna at an SNR of 0 dB for estimation from a single snapshot (T=1). Channel model with
one propagation path with uniformly distributed angle.
17. MSE per antenna at an SNR of 0 dB for estimation from a single snapshot (T=1). Channel model with
three propagation paths.
18. MSE per antenna for M = 64 antennas and for estimation from a single snapshot (T = 1). Channel
model with three propagation paths.