Method for estimating condition of wireless channels

This invention relates to wireless communication and localization, and more particularly, to estimating and identifying conditions of wireless channels.

The conditions of channels are important to the performance of wireless networks. Wireless signals in a non-line-of-sight (NLOS) channel often suffer greater path loss, and therefore are less reliable for communication than a line-of-sight (LOS) channel of equal distance. If a wireless network is capable of detecting whether a path between two nodes is one of line-of-sight (LOS), partially blocked direct path NLOS (NLOS-DP), or no direct path NLOS (NLOS-NDP), then the network can route data to a different path to improve communication reliability.

Impact of Channel Condition in ToA Based Ranging

The distance between two nodes in wireless networks can be estimated using the received signal strength (RSS), or the time-of-arrival (ToA). ToA-based ranging is based on measuring a time t form when the signal is transmitted to when the signal is received. The distance is estimated as d=t*c, where c is the travel speed of the signal in the medium (for example, the electromagnetic wave travels in free space at ˜3×10 8 meters per second.

FIG. 1A shows two transceivers A 101 and B 102 separated by distance d 103 .

FIG. 1B shows that transceiver A transmits a wireless signal 111 at time instance t 0 , and the signal is received at transceiver B 102 , after a time τ 123 , at time t 1 =t 0 +τ. In ToA based ranging, time τ is the “flight” time used to estimate the distance d 103 . The travel distance of the signal is estimated as d=τ*c.

A wireless channel can include many paths as shown in FIG. 2 . The direct path 210 between transmitter and the receiver is referred to as the Line-of-Sight (LOS) path. Indirect paths that are reflective paths are referred to as the Non-Line-of-Sight (NLOS) paths.

The total travel distance of NLOS paths is greater than the LOS path. For instance, lengths 220 of two NLOS paths are d 1 +d 2 >d and d 3 +d 4 >d.

Generally the ToA is estimated based on the earliest arrival of the signal and the distance is

{circumflex over (d)} ij =d ij +z ij +ε ij ,

where d ij is the LOS distance, z ij is the NLOS bias with the value of zero in LOS channels and positive in NLOS channels, and ε ij is a measure error, with a zero-mean Gaussian distribution.

FIG. 3A shows the power-delay-profile (PDP) of a LOS channel. The direct path is the strongest component, and appears at the time 301 when the direct path is expected. The ToA estimation therefore contains very small error.

FIG. 3B shows the PDP of a NLOS channel in which the direct path is attenuated, but detectable (NLOS-DP channel). The direct path is not the strongest component and there are some energy appears at the time when the direct path is expected. As a results, the error of the time 302 of arrival estimation is larger than in a LOS channel.

FIG. 3C shows the PDP of a NLOS channel in which the direct path is attenuated and completed not detectable (NLOS-NDP channel). The direct path is not the strongest component and cannot be detected at the time when the direct path is expected. The earliest detectable signal is at time 303 , instead of time 301 or 302 . As a result, the ToA estimation can have significantly larger error compared to two other channel conditions. The major portion of the error is contributed by the NLOS bias because z ij >>τ ij .

Impact of Position Estimation in Wireless Networks

The localization of nodes in a wireless network can be performed using wireless signals. FIG. 4 shows an example network. Assuming a target node T 401 , whose location is to be estimated, is wirelessly connected to M nodes A 1 , A 2 , . . . A M 402 , with known locations. These nodes are referred to as anchor (A) nodes, and their locations are (x 1 , y 1 ), (x 2 , y 2 ), . . . (x M , y M ). Also, assuming the distance estimation between the node T and the anchor node A i , is available as {circumflex over (d)} i , then the location of the node T can be estimated as {circumflex over (θ)}=[{circumflex over (x)},ŷ], using a least square (LS) position estimator, which is

θ ^ = arg x , y ⁢ ⁢ min ( [ [ d - F ⁡ ( θ ^ ) ] [ d ^ - F ⁡ ( θ ^ ) ] T ) ,

where {circumflex over (d)}=[{circumflex over (d)} 1 . . . {circumflex over (d)} M ] is a range measurement vector, and F({circumflex over (θ)}) is the computed distance at the estimated location of the node T location, given as

The LS estimator treats each estimated distance, {circumflex over (d)} i equally. However, the distance {circumflex over (d)} 1 can be inaccurate because it a reflected by an object 410 . If the distance estimation is accurate, then the position solver returns the estimated position of node T, i.e., {circumflex over (θ)}=[x T ,y T ].

If errors in all of the distance estimations are equal or close, then the LS estimation using all available anchor nodes generally returns a more accurate estimation compared to an LS estimation using only a subset of the anchor nodes.

If one or more distance estimations contain error, which is significantly larger than others, the LS position estimator, or any other method that treats all distances equally, produces results with an increased error.

If a given distance measurement {circumflex over (d)} i has a large error, then a position estimation method, which discriminates the distance measurements during the position estimation, can be used to achieve position error performance improvement. One of such methods uses a weighted-least-square (WLS)

θ ^ = arg x , y ⁢ min ( [ [ d ^ - F ⁡ ( θ ^ ) ] ⁢ W [ d ^ - F ⁡ ( θ ^ ) ] T ) ,

where W=[W 1 W 2 . . . W M ] is a weight vector, W i is the weight assigned to the i th distance measurement. A larger weight is assigned to a distance measurement with a greater confidence score. Conversely, if a distance measurement has a large error and low confidence, a small weight is assigned.

For the WLS method to have good performance, the correct weight assignment is critical.

Prior Art Channel Classification

Several channel condition classification methods are known.

“Channel statistics” (such as RMS delay spread) can be used to identify NLOS channels. That method is computationally complex, and energy inefficient, because multiple range measurements are needed per channel to determine channel statistics.

“Frequency diversity” can also be used to identify the direct-path blockage. Based on channel measurements in a typical indoor environment, the variation of ToA estimation across frequency sub-bands has a positive correlation with the channel condition. That approach requires a frequency hopping capable radio frequency (RF) front end, and therefore the transceivers have higher cost, complexity, and power consumption. It is also difficult to isolate the frequency dependency of the antennas from the channel, which directly impacts the effectiveness of that approach.

“Running variance” is another method for channel condition identification. It computes the variance of subsequent range estimates, and compares the variances with a predetermined threshold to decide between LOS and NLOS. That method has high computation complexity, and is energy inefficient.

“Change of SNR” method detects sudden change of SNR to determine whether the channel is moving from LOS to NLOS, or vise versa.

The embodiments of invention provide a method for estimating wireless channel condition based on measured Time-of-Arrival (ToA) and Received-Signal-Strength (RSS).

The method provides reliable estimation. The method has low complexity and can be implemented with at a low cost because that RSS is readily available at the receiver.

FIG. 1A is a block diagram of two nodes in a wireless network with a distance of d;

FIG. 1B is a schematic of the time of transmitted and received messages;

FIG. 2 is a schematic of a multipath wireless channels;

FIGS. 3A-3C are graphs of channel power-delay-profiles (PDPs);

FIG. 4 is a schematic of a simple wireless localization network;

FIG. 5 are graphs comparing measured and calculated path-loss over distance;

FIG. 6 are distributions of received signal strength for different channels at a given distance;

FIG. 7 is a histogram of distributions of NLOS-NP and NLOS-NDP channel conditions over distance;

FIG. 8 is a flow diagram of a method for estimating channel conditions according to embodiments of the invention; and

FIG. 9 is a graph comparing a position error for a localization method using least square (LS) and a weighted-least-square (WLS) using the channel condition estimation and soft weight assignment method according to embodiments of the invention.

According to embodiments of our invention, C 0 , C 1 and C 2 denote three channel conditions: line of sight LOS, partially blocked direct path NLOS (NLOS-DP) and no direct path NLOS (NLOS-NDP), respectively.

The objective of our invention is to estimate the likelihood if a channel is in one of the three channel conditions, C i , i={0, 1, 2}, based on the ToA-based distance estimate {circumflex over (d)}, and RSS measurement {circumflex over (r)} RSS . The likelihood can be expressed by a conditional probability, p(C i |{circumflex over (d)},{circumflex over (r)} RSS ).

The conditional probability p(C i |{circumflex over (d)},{circumflex over (r)} RSS ) can be computed using Bayes' equation given by

p ( C i , ❘ d ^ , r ^ rss ) = f ( r ^ rss ⁢  C i , d ^ ) ⁢ p ( C i  ⁢ d ^ ) ∑ k = 0 2 ⁢ f ( r ^ rss ⁢  C i , d ^ ) ⁢ p ( C k  ⁢ d ^ ) , ( 1 )

where f({circumflex over (r)} RSS |C i ,{circumflex over (d)}) is the distribution of the signal power for a given channel condition C k at a ToA estimated distance {circumflex over (d)}. p(C i |{circumflex over (d)}) is the probability of the channel condition given the ToA estimated distance.

A priori information f({circumflex over (r)} RSS |C i ,{circumflex over (d)}) can be obtained through channel measurements and modeling of the path-loss PL=P t −r rss , which defines the distance-power relationship. The mean of f({circumflex over (r)} RSS |C i ,{circumflex over (d)}) is the average path-loss in wireless channels, PL. The relationship of the average path-loss and antenna separation normally can be expressed using a simple model given by

PL= P 0 +10 n log( d )+χ,  (2)

where P 0 is the path-loss at a fixed distance, typically at 1 meter, n is the path loss exponent and χ is the shadow fading component, generally modeled as a lognormal distribution. This model is valid for LOS channels.

The values of n and P 0 are normally channel condition dependent. For NLOS channels, the path-loss can be modeled as a two-piece model.

PL = { P 0 + 10 ⁢ n 1 ⁢ log ⁡ ( d ) + χ 1 ⁢ PL ⁡ ( d break ) + 10 ⁢ n 2 ⁢ log ⁡ ( d / d break ) + χ 2 ⁢ ⁢ d ≤ d break d > d break , ( 3 )

where n 1 , n 2 , χ 1 and χ 2 are path-loss exponent and the shadow fading before and after the break distance d break . These values vary in different channel conditions due to the different degrees of shadowing.

FIG. 5 shows such relationships for channels C 0 , C 1 and C 2 . The measurement results are also shown in FIG. 5 .

Here, f({circumflex over (r)} RSS |C i ,{circumflex over (d)}) is a distribution with the mean computed based on Equations (2) and (3).

FIG. 6 shows the distributions of {circumflex over (r)} RSS for all three channel conditions at given distance {circumflex over (d)}.

p(C i |{circumflex over (d)}) can be obtained using the Bayes' equation given by

p ⁡ ( C i , ❘ d ^ ) = f ( d ^ ❘ C i ) ⁢ p ⁡ ( C i ) ∑ k = 0 2 ⁢ f ( d ^ ❘ C k ) ⁢ p ⁡ ( C k ) , ( 4 )

where f({circumflex over (d)}|C i ) is the distribution of the ToA estimated distances given the channel condition and p(C i ) is the probability of channel being under condition C i .

f({circumflex over (d)}|C i ) is the distribution of the ToA estimated distances, given the channel condition. Generally, f({circumflex over (d)}|C 0 ) is distance independent within the range. f({circumflex over (d)}|C 1 ) and f({circumflex over (d)}|C 2 ) are distance dependent. Intuitively, f({circumflex over (d)}|C 2 ) is monotonically increasing, and f({circumflex over (d)}|C 1 ) is monotonically decreasing within the communication range d c . Equation (5), (6) and (7) are distributions satisfy these requirements.

FIG. 7 shows f({circumflex over (d)}|C 1 ) and f({circumflex over (d)}|C 2 ) based on actual measurements. It also shows the distribution given by Equations (6) and (7).

Weight Assignment Scheme

After the channel condition probabilities are computed using the above equations, we can then generate a weight for the channel. A hard weight or a soft weight can be generated.

Hard Weight

We select the channel that satisfies the following condition

C k = arg ⁢ ⁢ max Ck ⁢ P ( C k ❘ d ^ , r ^ rss ) , ( 8 )

where arg max returns the argument which maximize the probability, p(C k |{circumflex over (d)},{circumflex over (r)} RSS ), i.e., the channel condition with highest probability. Then, we assign a weight to the channel based on the selected channel, i.e., w=w(C k ).

Soft Weight

The weight of a given channel is computed by

w = ∑ k = 0 2 ⁢ G k ⁢ p ( C k , ❘ d ^ , r ^ rss ) ∑ k = 0 2 ⁢ p ( C k , ❘ d ^ , r ^ rss ) , ( 9 )

where k is index for different channel conditions, G k is the corresponding weight for channel condition C k .

The weight of the channels can then be used by a positioning method, e.g., the WLS positioning method.

General Method

FIG. 8 shows the method for estimating a channel condition according to embodiments of the invention. A distance d is estimated 810 based on the time of arrival (ToA) of the ranging signal. A path loss is estimated 820 based on a received signal strength (RSS) of the ranging signal.

A conditional probability of the channel condition, p(C i |{circumflex over (d)},{circumflex over (r)} RSS ), is determined 830 according to the embodiment. The process can then either output p(C i |{circumflex over (d)},{circumflex over (r)} RSS ) directly 842 , or assign 841 a weight w first, and then output the weight 843 .

FIG. 9 shows the cumulative-distribution-function (CDF) of the root-mean-square-error (RMSE) of the location estimation. Without the weight information, the LS algorithm performance is plotted as curve 910 . Using the weight generated using the invented method, the CDF of the location RMSE is curve 920 . We can see on average an over 40% improvement.

Compared with conventional methods, the invention has the following advantages.

The invention reliably estimates the LOS/NLOS condition of wireless channels.

The invented method produces probabilities of three channel conditions. The probabilities can be used to generate hard or soft weight for each wireless channel.

The weight can be subsequently used by the localization method to improve the accuracy. The estimated channel condition probability can be used by other applications to improve communication reliability.

Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.