Figure 2 can show the conventional LFMCW radar's system structure from which the signal model is analyzed in previous chapters. The power of the signal source is limited by the apparatus in the THz wave band. The single frequency source has difficulty transmitting and mixing at the same time. If two independent frequency sources are employed in a radar system, it may lead to the issue of phase out of sync.

The ‘non-coherent dual-source implementing coherence’ way is applied in the THz LFMCW radar system. The coherent system structure can be shown in Figure 3. Mixing twice needs to be done in order to realize the coherent system. The intermediate frequency receiver is designed after the first mixing of the received THz band frequency signal. The second mixing, I/Q demodulation, signal correction, and some other processing are involved in the intermediate frequency receiver.

Signal sources *S*_{1} and *S*_{2}, two low-frequency linear frequency modulation signals, are used to produce the transmitting signal and the local oscillator (LO) signal, respectively. They can be respectively represented as

\begin{array}{l}{S}_{1}\left(t\right)={A}_{1}exp\left\{2\pi {f}_{C1}t+\pi {K}_{S1}{t}^{2}+{\varphi}_{1}\right\}\\ {S}_{2}\left(t\right)={A}_{2}exp\left\{2\pi {f}_{C2}t+\pi {K}_{S2}{t}^{2}+{\varphi}_{2}\right\}\end{array}

(6)

where *f*_{c 1} and *f*_{c 2} are the carrier frequency, *t* is the time variable, *K*_{s 1} and *K*_{s 2} are the frequency modulation slope, and *ϕ*_{1} and *ϕ*_{2} are the initial phase.

The transmitting signal can be generated from the source *S*_{1} by means of × 12 frequency multiplication (×2 twice and × 3 once), band-pass filtering, and amplification. Then, it can be represented as

{S}_{T}\left(t\right)={A}_{T}exp\left\{2\pi \xb712{f}_{C1}t+\pi \xb712{K}_{0}{t}^{2}+12{\varphi}_{1}\right\}

(7)

where *A*_{
T
} is the signal amplitude. It is supposed that *R*(*t*) is the range of target and *τ*(*t*) = 2*R*(*t*)/*c* is the echo signal time delay. The received echo signal can be expressed as

\begin{array}{ll}{S}_{R}\left(t\right)=& K{A}_{T}exp\{2\pi \xb712{f}_{C1}\left(t-\tau \left(t\right)\right)\\ +\pi \xb712{K}_{0}{\left(t-\tau \left(t\right)\right)}^{2}+12{\varphi}_{1}\}\end{array}

(8)

The LO signal in the THz band can come from the source *S*_{2} by the same procedure as the transmitting signal. It can be expressed as

{S}_{\mathrm{LO}1}\left(t\right)={A}_{\mathrm{LO}1}exp\left\{2\pi \xb712{f}_{C2}t+\pi \xb712{K}_{0}{t}^{2}+12{\varphi}_{2}\right\}

(9)

where *A*_{LO1} is the amplitude of the LO signal. The first mixing is realized between the received echo signal (*S*_{
R
}(*t*)) and the LO signal (*S*_{LO1}(*t*)). So the obtained intermediate signal is

\begin{array}{ll}{S}_{\mathrm{IF}}\left(t\right)=& {A}_{\mathrm{IF}}exp\left\{2\pi \right[12\left({f}_{C2}-{f}_{C1}\right)t+12{f}_{C1}\tau \left(t\right)\\ +\mathit{\mu \tau t}\left(t\right)-\mathit{\mu \tau}{\left(t\right)}^{2}/2]+12\mathit{\Delta \varphi}\end{array}

(10)

where *A*_{IF} is the amplitude of the intermediate frequency signal, *μ* = 12 *K*_{0} is the frequency modulation slope, and *Δϕ* = *ϕ*_{2} - *ϕ*_{1} is the difference of initial phases.

The other LO signal is acquired through the following procedure: mixing *S*_{1} and *S*_{2}, ×12 frequency multiplication, amplifying, and filtering. It can be represented as

{S}_{\mathrm{LO}}\left(t\right)={A}_{\mathrm{LO}}exp\left\{2\pi \xb712\left({f}_{C2}-{f}_{C1}\right)t+12\mathrm{\Delta}\mathit{\varphi}\right\}

(11)

In the end, the result of mixing intermediate frequency signal *S*_{IF}(*t*) and LO signal *S*_{LO}(*t*) is

\begin{array}{ll}{S}_{B}\left(t\right)& ={S}_{\mathrm{IF}}\left(t\right)\times {S}_{\mathrm{LO}}^{\ast}\left(t\right)\\ ={A}_{B}exp\left[2\pi \left(\mathit{\mu \tau}\left(t\right)t+12{f}_{C1}\tau \left(t\right)-\mathit{\mu \tau}{\left(t\right)}^{2}/2\right)\right]\end{array}

(12)

The results show that the initial phase difference is offset through taking advantage of the dual-source system structure. The results are consistent with the traditional single-source LFMCW radar system structure. Thereby, the problem about the dual-source's non-sync can be solved effectively.