The channel gain at the n th receiving branch of the reader is given by h n = ∑ l = 1 L h l f h l, n b.
For the l th receiving branch of this SIMO system, the squared magnitude of the channel gain is | H l | 2 = ∑ n = 1 N α l β l, n, where α l is the channel power at the l th receiving branch.
where P ̌ el,rx = P ̌ ADC + P ̌ filter + P ̌ mixer + P ̌ LNA + P ̌ IFA represents the power consumption of analog-to-digital converter (ADC), filters, mixer, low-noise amplifier (LNA) and intermediate frequency amplifier (IFA) of each receiving branch.
From the channel matrix in Equation (5), the channel power at the n th receiving branch, also referred as the instantaneous signal-to-noise ratio (SNR) at the n th receiving antenna, can be given by γ n = γ ̄ | ∑ l = 1 L h l f h l, n b | 2, (7).
Here α l is the squared magnitude of the channel gain of the l th receiving branch, N and L are the index of the function G N, L , and we define γ ̄ ̄ = g γ ̄ sin 2 θ, where γ ̄ is the average SNR and g is a constant which is modulation dependent.
Since noise is wide-sense stationary (WSS) and the power is independent of sampling instance, we have E [ v m 2 ( l T s ) ] = σ v 2 = N 0. The signal from the m th receive branch is weighted by a complex weight w m r.
For the Rayleigh fading channel, the frequency response of the kth subchannel of the vth receive branch ({H_{k}^{v}} = sum limits _{l = 0}^{{L_{v}} - 1} {h_{_{l}}^{v}{e^{- j2pi frac {{kl}}{K}}}} ) is a complex Gaussian RV of mean zeros and variance one, thus (left |{H_{k}^{v}}right |^{2}) is χ 2 distributed with 2 degrees of freedom and (Eleft { {|{H_{k}^{v}}{|^{2}}} right } = 1).
Because | | H | | 2 = ∑ l = 1 L | H l | 2, for the SER analysis we can view the N × L RFID channel which uses OSTBC as a virtual SIMO system with L receiving branches in which MRC is applied at the receiver side.
In contrast, for both the Rayleigh channel with independent receiving branches and the double Rayleigh channel with independent receiving branches, the diversity order is NL.
It receives branches of the femoral, common peroneal and saphenous nerves.
