II. CONCEPTS AND FORMULATIONS

A) Concept

In this paper, we focus on TDOA estimation because of its high precision in wireless indoor applications and the fact that the synchronization of reference devices (RDs) and mobile device (MD) is not required in this positioning method. TDOA estimation is classically computed using correlation techniques. In addition, direct-sequence spread spectrum (DSSS) signals can be used to extract the TDOA [Reference Liu, Darabi, Banerjee and Liu7, Reference Li, Pahlavan, Latva-aho and Ylianttila8]. As presented in Fig. 1, multiple RDs receive signal from one transmitter (MD) and the relative position of MD is determined by measuring the difference in time-arrival at each RD. By extracting the TDOA, the locus of points with constant range differences between two RD's, a hyperbola, is obtained.

Fig. 1. Classical TDOA positioning method.

A two-dimensional (2D) target location can be estimated from the intersections of two or more hyperbolas, as shown in Fig. 1. Two hyperbolas are formed from TDOA measurements at three fixed RD's to provide an intersection point, which locates the MD.

As presented in Fig. 1, in classical TDOA-based one-dimensional (1D) localization, two RDs are needed. In the proposed method, as shown in Fig. 2, only one RD with two antennas is used. The two antennas transmit the same signal provided by a unique source. The spectrum of the received signal should be observed, and thanks to interferometry techniques in the frequency domain [Reference Bocquet, Loyez and Benlarbi-Delai9], the TDOA can be extracted as explained in the following section. In this approach, the baseline B (the distance between the two RD antennas) is relatively small, and, therefore, a wide-band signal should be used in order to extract small TDOA.

Fig. 2. New proposed TDOA extraction method.

B) Formulation

To implement this technique, a multi-input single-output (MISO) structure is used. To do so, an RD with two antennas A ₁ and A ₂ and a MD are placed in an indoor environment. The distance between MD and A ₁ is d ₁ and between MD and A ₂ is d ₂. In the case of line of sight (LOS) between RD and MD, the delays of propagation are τ₁ = d ₁/c and τ₂ = d ₂/c, with c the speed of light. A ₁ and A ₂ transmit the same OFDM 60 GHz signals with a sample rate frequency F _s, N sub-carriers and M data sub-carriers, but with a delay of τ_p. τ_p is applied as suggested in [Reference Panta and Armstrong10], in order to vary the delay of the signal in a predetermined manner. If we call, x(t), the baseband complex envelope (CE) signal and, x _RF(t), the RF representation of the transmitted signal, following equations are obtained:

(1)$$x\lpar t\rpar =\sum\limits_{k=- N/2}^{N/2 - 1} c_k e^{i2\pi kF_s t/N}=\sum\limits_{k=- M/2}^{M/2 - 1} c_k e^{i2\pi kF_s t/N}$$

and

(2)$$x_{RF} \lpar t\rpar ={\bf \Re}\left({x\lpar t\rpar e^{i2\pi F_{RF} t} } \right)\comma \;$$

where ℜ is the real part operator, c _k are the complex coefficients, with k the carrier index, and F _RF the RF frequency. Calling channel gains between A ₁ and MD, and A ₂ and MD, h ₁ and h ₂, respectively, the time-invariant channel impulse responses in the CE domain for the two different delays of propagation, τ₁ and τ₂, are:

(3)$$h_1 \lpar t\rpar =h_1 e^{ - i2\pi F_{RF} \tau _1 } \delta \lpar t - \tau _1 \rpar$$

and

(4)$$h_2 \lpar t\rpar =h_2 e^{ - i2\pi F_{RF} \lpar \tau _2+\tau _p \rpar } \delta \lpar t - \tau _2 - \tau _p \rpar \comma \;$$

where δ is the Dirac function. Then, the received signal at MD, y(t) = x(t) ⊗ h(t) in the CE domain is equal to:

(5)$$\eqalign{y\lpar t\rpar &=h_1 x\lpar t - \tau _1 \rpar e^{ - i2\pi F_{RF} \tau _1 }\cr & \quad + h_2 x\lpar t - \tau _2 - \tau _p \rpar e^{ - i2\pi F_{RF} \lpar \tau _2+\tau _p \rpar } .}$$

The two antennas at RD being relatively close to each other, we can assume in an LOS scenario, that h ₂ = h ₁. Assuming that τ = τ_p + τ₂ − τ₁, the received signal in the frequency domain can be presented as follows:

(6)$$\eqalign{Y\lpar f\rpar & =h_1 \sum\limits_{k=- M/2}^{M/2} {c_k } \delta \lpar f - kF_s /N\rpar e^{ - i2\pi \lpar kF_s /N+F_{RF} \rpar \lpar \tau _2+\tau _p - \tau \rpar } \cr & \quad \times \left[{1+e^{ - i2\pi \lpar kF_s /N+F_{RF} \rpar \tau } } \right].}$$

From equation (6), it can be shown that in the received spectrum, carriers k are cancelled for values of τ given by:

(7)$$\tau=\displaystyle{{\lpar 2n+1\rpar } \over {2\left({\displaystyle{{kF_s } \over N}+F_{RF} } \right)}}n=0\comma \; 1\comma \; 2\comma \; \ldots .$$

Equation (7) can also be presented as follows:

(8)$$\displaystyle{{kF_s } \over N}=\displaystyle{{\lpar 2n+1\rpar } \over {2\tau }} - F_{RF}\comma \; \quad n=0\comma \; 1\comma \; 2\comma \; \ldots\comma \; $$

where kF _s/N is the kth sub-carrier. The frequency difference between two consecutive null sub-carriers (or minimum power sub-carriers in practice), F _n = (k _nF _s/N) + F _RF and F _n+1 = (k _n+1F _s/N) + F _RF, is written as:

(9)$$F_{n+1} - F_n=\displaystyle{{\Delta kF_s } \over N}=\displaystyle{1 \over \tau }\comma \; \quad n=0\comma \; 1\comma \; 2\comma \; \ldots\comma \; $$

where Δk = k _n+1 − k _n and we supposed τ ≥ 0. Equation (9) shows that τ can be obtained on the received signal spectrum by measuring the frequency difference between two minimum power points or the difference between indexes of two consecutive minimum sub-carriers. Therefore, the value of TDOA = τ₂ − τ₁ = τ − τ_p is also obtained. The limit values of τ that guarantee the cancellation of two sub-carriers are τ_min = 2N/MF _s and τ_max = 3N/MF _s. These values ensure the cancellation of at least two and at most three sub-carriers. Indeed, although the cancellation of more than two sub-carriers within the received spectrum does not affect the localization of an MD, it translates in a larger loss of the information carried by the OFDM symbols. Remembering that τ = τ_p + τ₂ − τ₁ = τ_p + TDOA, the value of τ_p can be chosen to measure τ₂ − τ₁ with the maximum of dynamic range. The value of τ_p, is consequently chosen as (τ_max + τ_min)/2.

III. SIMULATION AND SYSTEM DESCRIPTION

Knowing the range of TDOA values that can be measured with the OFDM signal used, a possible configuration is proposed to perform the localization of an MD in a room. In Fig. 2, this configuration is presented with B the baseline distance and θ the angle of MD from baseline center. A ₁ transmits the same signal as A ₂ with a delay of τ_p. The OFDM parameters are fixed according to the IEEE 802.15.3c standard. We thus consider F _s = 2,64 GHz, N = 512, and M = 354. Therefore, the value of τ_p is fixed at 1.37 ns. As an example, with a baseline B = 8 cm and an MD located at d = 2 m from RD with an angle ofθ = 60°, the theoretical value of τ = τ_p + TDOA is τ = 1.14 ns, considering an LOS propagation. Therefore, according to equation (9), Δk = 170 is expected. It should be noticed that the distance between RD antennas is chosen in such a way that the condition τ_min ≤ τ ≤ τ_max is satisfied. It should also be emphasized that if the delay τ_p was not considered (τ_p = 0), then the baseline should have been chosen equal to B = 40 cm in order to obtain the same value of τ = 1.14 ns. To demonstrate the feasibility of our approach, a 60-GHz communication system is simulated using SystemVue software. As shown in Fig. 3, two direct paths with different path losses are considered, a delay block is used to define τ and a noise block and gain blocks are added in a manner to obtain at the receiver, a signal-to-noise ratio (SNR) of about 30 dB.

Fig. 3. Scheme of the simulated bench.

Figures 4(a)–4(c) present respectively the constellation, the spectrum, and the error vector magnitude (EVM) of the received signal. As shown in Fig. 4(a), the constellation at the RX presents a high quality communication in the LOS case. However, as shown in Fig. 4(b), the spectrum of the signal is totally deformed and the positions of minimum power points lead us to extracting TDOA. A precise estimation of TDOA can be performed by looking at the EVM of received signal. As shown in Fig. 4(c), the average EVM of received signal is about 2.5% but at the minimum power sub-carriers the EVM is about 15%. Therefore, the position of minimum power sub-carriers can be easily distinguished among the other sub-carriers. Figure 4(c) confirms the value of 170 for Δk, as predicted by the theory. This technique is a promising one as the localization data are carried by the minimum power sub-carriers, and therefore readily available from base-band processing.

Fig. 4. Constellation, spectrum, and EVM of received signal in LOS scenario.

IV. MULTI-BAND APPROACH

As mentioned previously, the new proposed TDOA principle is based on the spectrum of the received interfered signal. Obviously, when a larger bandwidth is provided, a more precise TDOA can be achieved and hence a better localization. In the previous section, we considered an effective bandwidth of 2 GHz. Transmission of a wider bandwidth is not possible due to technology, standards, and components' limitations. Hence, a multi-band approach is proposed to encounter this problem. In this case, the localization and communication cannot be achieved at the same time. Nevertheless, by using a multi-band system and a signal post processing, the total available bandwidth when using 60 GHz bands, which is 7 GHz, can be used. To experimentally prove the multi-band approach, a wire-line communication and signals at the lower-frequency bandwidths are chosen. To introduce the delay, two coaxial cables with different lengths were connected to the two channels of arbitrary waveform generator (AWG), where the same OFDM signals were generated (τ_p = 0). As shown in Fig. 5, the two cables are then connected to a power combiner working in the 1–4 GHz band. The output signal is then connected to the vector signal analyzer (VSA) for detection and demodulation. For the multi-band approach, six OFDM signals with 500 MHz bandwidth each but with different center frequencies are generated in a manner that the whole 3 GHz bandwidth available between 1 and 4 GHz can be utilized. In each experiment, one of these six OFDM signals is transmitted. At the end, the saved results are concatenated to cover the whole spectrum as shown in Fig. 6. Depending on the different delays, the positions of minimum power points change in the spectrum as expected. Three different delays are studied by changing the relative lengths of the two coaxial cables.

Fig. 5. Multi-band experimental schematic.

Fig. 6. Concatenated multi-band received signals for three different TDOA values.

To extract the highest TDOA value, TDOA = 2.2 ns, only one window of 500 MHz is sufficient since two consecutive minimum power points can be visualized in this bandwidth. But for TDOA = 0.95 and 0.65 ns, respectively, three and four windows of 500 MHz are required. The frequency difference between two minimum power points is equal to 1/TDOA. To extract lower values of TDOA, wider bandwidths are required, thereby involving more windows.