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Table 1 Most important variables

From: Optimal pilot symbol power allocation under time-variant channels

Variable

Dimension

Description

y ~ n r

C N sub × 1

Received symbol vector at antenna nr

H ~ n r , n t

C N sub × N sub

Channel matrix between antennas ntand nrin frequency domain

x n t

C N sub × 1

Transmit symbol vector at antenna nt

x p , n t

P N p × 1

Pilot symbols vector at antenna nt

x d , n t

C N d × 1

Transmit data vector at antenna nt

n ~ n r

C N sub × 1

Additive noise at antenna nr

y k

C N r × 1

Received symbol vector at subcarrier k

H k,l

C N r × N t

Channel matrix between subcarriers k and l

W k

C N t × N l

Precoding matrix at subcarrier k

G k,k

C N r × N l

Effective channel matrix Hk,kW k

s k

D N l × 1

Transmit data at subcarrier k

n k

C N r × 1

Additive noise at subcarrier k

E k

C N r × N t

Channel estimation error at subcarrier k

σ s 2

R

Transmit power of one layer

σ p 2

R

Transmit pilot symbol power

σ x 2

R

Transmit data power

σ ICI 2

R

ICI power

σ n 2

R

Noise power

σ e 2

R

Channel estimation error variance

d

R

Channel saturation coefficient

f c

R

Carrier frequency

v max

R

Maximal user velocity

f d

R

Maximal Doppler frequency

T s

R

OFDM symbol duration

N p

N

Number of pilot symbols

N d

N

Number of data symbols

N l

N

Number of layers

N t

N

Number of transmit antennas

N r

N

Number of receive antennas

N sub

N

Number of subcarriers

p off

R

Offset between power of pilot symbols and data symbols

γ l

R

Post-equalization SINR at layer l