Optimization of cyclic prefix transceivers - Signal Processing and Optimization for Transceiver Systems - page 538

q ( n )

permutation matrix

s ( n ) s ( n )

W
M

W
M

P T

H

P T

Λ g P

Σ f

P

normalized IDFT circulant

channel

normalized DFT

Λ p

Σ p

(a)

precoder equalizer

q ( n )

s ( n ) s ( n )

W
M

W
M

P T

Λ g

H Σ f

P

(b)

circulant
channel

normalized IDFT normalized DFT

precoder equalizer

Figure 17.6 . (a) Structure of the MMSE cyclic-prefix transceiver in Fig. 17.5, redrawn
using a permutation matrix P . (b) A variation with identical transmitted power and
MSE.

Here

⎧
⎨

D
|

1

C [ k ] | −

0 ≤ k ≤ K − 1

|

C [ k ] | 2

q kk = (17 . 29)

⎩

0 otherwise,

with D defined as

K− 1

p σ q 1

| C [ k ]

+

| 2

k =0

D = (17 . 30)

K− 1

1
| C [ k ] |

k =0

and K is the largest integer ≤ M, which yields q kk ≥ 0 for all k in Eq. (17.29).

The diagonal matrix Λ g is given by