# Introduction to Millimeter Wave Wireless Communications

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## 1.6 Symbols and Common Definitions

We use the notation in Table 1.2 and assign specific definitions to the variables in Table 1.3 throughout this text.

#### Table 1.2 Generic notation used in this text.

 ≜ by definition ⋆ convolution operator a bold lowercase is used to denote column vectors A bold uppercase is used to denote matrices α A non-bold letters are used to denote scalar values |α| magnitude of scalar α ∥a∥ vector 2-norm of a ∥A∥F Frobenius norm of A A calligraphic letters denote sets |A| cardinality of set A AT matrix transpose A* conjugate transpose Ac conjugate A1/2 matrix square root A-1 matrix inverse A† Moore-Penrose pseudo inverse ak kth entry of vector a [A]k,l scalar entry of A in kth row lth column [A]:,k kth column of matrix A [A]:,k:m column consisting of rows k, k + 1,..., m of matrix A (·) used to index a continuous signal a(t) continuous scalar signal and value at t a(t) continuous vector signal and value at t A(t) continuous matrix signal and value at t [·] used to index a discrete-time signal a[n] denotes discrete-time scalar signal and value at n a[n] discrete-time vector signal and value at n A[n] discrete-time matrix signal and value at n a[n] denotes discrete-time vector signal in frequency domain at subcarrier n A[n] discrete-time matrix signal in frequency domain at subcarrier n log denotes log2 unless otherwise mentioned

#### Table 1.3 Common definitions used in this text.

 Es signal energy No noise energy L channel order discrete-time ISI channel impulse response with (L + 1) taps frequency domain channel transfer function y[n] symbol sampled received signal x[n] symbol sampled transmitted signal s[n] symbol sampled transmitted signal before precoding IN N × N identity matrix 0N,M N × M all zeros matrix j imaginary number E expectation operator x ~ N(m, σ2) means that x is a Gaussian random variable with mean m and variance σ2 x ~ Nc(m, σ2) means that x is a circularly symmetric complex Gaussian random variable with complex mean m, total variance σ2, the real and imaginary parts of x are independent, and the variance of the real and imaginary parts are each σ2/2 Aeff effective aperture of an antenna (square meters) Amax maximum effective aperture of an antenna (square meters) d transmitter-receiver separation distance (meters) EIRP effective isotropic radiated power λ wavelength (meters) c speed of light in free space = 3 × 108 m/s