Use of orthonormal transformation for improving performance of digital transmission under heavily faded channels with doppler effects

An error correction method for use in a wireless network, comprising:

• converting incoming information into N discrete samples, wherein said N range from 2-5;
• transforming each of the discrete samples into N coefficient samples having finite set of real values in coefficient samples using
• ⁢
• C
• ij
• =
• M
• *
• b
• T
• ⁢
• [
• c
• i
• ⁢
• ⁢
• 1
• c
• i
• ⁢
• ⁢
• 2
• c
• i
• ⁢
• ⁢
• 3
• c
• i
• ⁢
• ⁢
• 4
• ]
• =
• ⁡
• [
• 1
• 2
• 1
• 2
• 0
• 0
• 0
• 0
• 1
• 2
• 1
• 2
• 1
• 2
• 1
• 2
• 0
• 0
• 0
• 0
• 1
• 2
• 1
• 2
• ]
• ·
• [
• b
• i
• ⁢
• ⁢
• 1
• b
• i
• ⁢
• ⁢
• 2
• b
• i
• ⁢
• ⁢
• 3
• b
• i
• ⁢
• ⁢
• 4
• ]
• T
• ;
• interleaving the N coefficient samples;
• encoding each said finite set of real value as a discrete constellation and transmitting the encoded information over the wireless network;
• receiving the encoded information at the receiver;
• providing phase and amplitude compensation, demodulation and de-interleaving for the encoded information at a receive side of the wireless network;
• decoding the encoded information and error correcting the decoded information;
• and
• mapping the decoded information to provide output information that matches the incoming information.

An error correction method for use in a digital communications system comprising:

• grouping incoming message bits from a message source into a plurality of groups;
• creating discrete analog samples from each group;
• transforming each of the analog samples into coefficient samples with a real 4-square ortho-normal matrix to create ortho-normal samples;
• generating additional coefficient samples using d1=C1−C2+C3−C4 and d2=C1+C2−C3−C4 and transmitting the ortho-normal samples and the additional coefficient samples over the digital communications system;
• receiving the ortho-normal samples and the additional coefficient samples at the receiver;
• applying the ortho-normal samples and the additional coefficient samples to an invertible ortho-normal transform to correct an error in any of the ortho-normal samples;
• producing estimated discrete samples by transforming the corrected ortho-normal samples;
• and
• decoding the estimated discrete samples to provide received message bits which match the incoming message bits.