Zero-forcing Precoding - Mathematical Description

Mathematical Description

In a multiple antenna downlink system which comprises a transmit antenna access point (AP) and single receive antenna users, the received signal of user is described as

where is the vector of transmitted symbols, is the noise signal, is the channel vector and is the linear precoding vector. From the fact that each beam generated by ZF-precoding is orthogonal to all the other user channel vectors, one can rewrite the received signal as

For comparison purpose, we describe the received signal model for multiple antenna uplink systems. In the uplink system with a receiver antenna AP and K single transmit antenna user, the received signal at the AP is described as

where is the transmitted signal of user, is the noise vector, is the channel vector.

Read more about this topic:  Zero-forcing Precoding

Famous quotes containing the words mathematical and/or description:

    All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
    Roger Bacon (c. 1214–c. 1294)

    Do not require a description of the countries towards which you sail. The description does not describe them to you, and to- morrow you arrive there, and know them by inhabiting them.
    Ralph Waldo Emerson (1803–1882)