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Abstract— In recent years, software defined radio and digital

signal processing have been widely used in communication and

radar. As a result, the hardware and RF front-end for radar and

wireless communication tends to be similar. Thus, using the same

RF and hardware platform for joint radar-communication

becomes viable. Joint radar-communication would bring more

efficient plan and usage for the radio spectral resource.

Furthermore, it could enable new applications that require

information exchange and precise localization at the same time. In

this paper, cyclic prefixed single carrier (CP-SC) and its variations

are chosen as the waveforms for joint radar-communication. CP-

SC waveform and its variations are popular in wireless

communication and have been chosen by a few standards like

IEEE 802.11ad and LTE-advanced. Efficient algorithms are

proposed to use such waveforms for range and speed

detection/estimation of targets. The proposed algorithms are

derived from the maximum likelihood (ML) principle and have

low computational complexity. Simulations show that the

estimation performance of the proposed method is almost the same

as that of ML and is much better than that of the channel

estimation based method.

Index Terms— Radar; Communication; Localization; IOT; CP-

SC: SCCP; SC-FDE; PCP-SC; UW-SC; SC-OFDMA; OFDM

I. INTRODUCTION

Context-awareness is critical in many applications including

environmental monitoring, intelligent transportation,

healthcare, logistics, and smart home/building, etc. Internet of

Things (IoT) is an enabler to and beneficiary of context-aware

information [1-2], in which location/position information is of

particular importance. Radar is one of the most popular ways to

obtain location information. Traditionally, dedicated radio

frequencies are allocated for radar [3-4]. Radar waveforms are

also specially designed to optimize the range and speed

detection performances [3-4]. In addition, hardware and

software used for radar are different from those for wireless

communications [3-4]. In recent years, there have been

increased researches on using the same device and same radio

spectrum for joint radar-communication [5-13]. In fact, with the

increasing usage of software defined radio and digital signal

processing [5], the hardware and RF front-end for radar and

wireless communication tends to be similar. Thus, using the

This work is supported by the A*STAR Industrial Internet of Things

Research Program, under the RIE2020 IAF-PP Grant A1788a0023 and

A*STAR ETPL Gap-funded project “mmWave Radar-Camera Sensor Fusion

Module”.

same RF and hardware platform for joint radar-communication

becomes viable [5-7].

A. Advantages and challenges of joint radar-communication

Some advantages of joint radar-communication are listed as

follows:

• Save resources and reduce cost.

• Allow more efficient plan and usage for the radio spectral resource.

• Enable new applications that require information exchange and precise localization at the same time.

However, there are many special difficulties in joint radar-

communication by using standardized waveforms. Some major

challenges are as follows.

• Detection/estimation algorithms that can efficiently use the standardized waveforms. Unlike conventional radar operation where the waveform is optimized for range/speed detection/estimation performance [3-4], the standardized waveforms are optimized for communication performance. Thus conventional detection/estimation algorithm may not be suitable for joint radar-communications. New detection/estimation algorithms need to be designed.

• Full duplexing operation: communication transmission and radar receiving are at the same time, which induces strong self-interference to the radar receiver. Compared to dedicated radar system, communication system is more compact, which means that the self-interference is much more severe. Although the transmitted signal is known to the radar receiver, the channel between the transmitter and radar receiver is unknown, which makes the interference cancellation complicated.

• Reducing system complexity to share the same hardware and software for radar and communication as long as possible.

B. Overview of related works

Joint radar-communication in a relatively new research area.

There have been researches on this topic in recent years [5-13].

In [5-7], excellent reviews are presented on this topic with

emphasizes on the orthogonal frequency division multiplexing

(OFDM) or multi-tone waveforms. In [8-11], radar

The authors are with the Institute for Infocomm Research, A*STAR, 1

Fusionoplis. Way, #21-01 Connexis, Singapore 138632. Emails: {yhzeng,

mayg, sunsm}@i2r.a-star.edu.sg

Joint Radar-Communication with Cyclic

Prefixed Single Carrier Waveforms

Yonghong Zeng, Fellow, IEEE, Yugang Ma, Senior member, IEEE and Sumei Sun, Fellow, IEEE

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detection/estimation algorithms are proposed for cyclic

prefixed OFDM (CP-OFDM), which use channel estimation

and block processing based on the special structure of CP-

OFDM. In [12], auto-correlation based method is used for radar

detection by using the IEEE 802.11ad waveform, which relies

on the excellent auto-correlation property of the preamble

sequence in IEEE 802.11ad. In [13], methods are proposed to

achieve superior detection resolution for IEEE 802.11p

waveform. However, the method can only be applied for single

target scenario.

There have been extensive researches on radar

detection/estimation without considering communication. Most

of such works are for dedicated waveforms optimized for radar.

Especially, super-resolution radar has been studied to identify

closely placed objects. The multiple signal classification

(MUSIC) or subspace method is one of the most popular

methods for super-resolution radar [28-31]. MUSIC can be used

for direction of arrival (DoA) estimation with multiple

antennas, speed estimation, or range estimation in some cases

[28-31]. However, MUSIC has high complexity (eigen-

decomposition and large number of matrix-vector

multiplications), and is sensitive to order estimation, especially

when the number of targets is large. Moreover, MUSIC usually

can only estimate a single parameter (DoA or speed or range)

at one time [28-31]. It does not offer a joint estimation for

multiple parameters, which leaves a difficult pairing problem

(for example, after separate range and speed estimation, it is

difficult to pair the estimated range with the estimated speed).

In recent years, compressive sensing (CS) has been used in

radar, especially for multiple input multiple output (MIMO)

radar [32-36]. CS can be used for different radar tasks. One

major application is to considerably reduce the sampling rate

(much lower than the Nyquist sampling rate) with sparse

sampling (reducing A/D conversion bandwidth) [32], which is

special helpful to ultra wideband radar. Another important

application is to achieve super-resolution, especially for DoA

estimation in MIMO radar [33-35]. The latest atomic norm

minimization method is a promising technique for this purpose

[35]. However, CS method in general has high complexity and

poor robustness in low signal-to-noise ratio (SNR).

Furthermore, its performance may degrade considerably in the

presence of basis mismatch [36].

In the joint radar-communication scenario, reducing the

sampling rate for radar receiver may not be that important, as

the same sampling device should also be used for

communication purpose.

C. Our contributions

Cyclic prefixed single carrier (CP-SC) is a popular modulation

scheme, which has lower peak to average power ratio (PAPR)

than OFDM while achieving similar performance [14-15]. CP-

SC is also called: single carrier with cyclic prefix (SCCP) or

single carrier with frequency domain equalization (SC-FDE)

[15]. CP-SC or its variations have been chosen by a few

standards like IEEE 802.11ad [27], LTE-advanced and C-V2X

(singe carrier frequency division multiple access (SC-FDMA)

is used) [23], and are also possible candidates for the 5G [24-

25].

In this paper, efficient algorithms are proposed to use CP-SC as

radar waveforms for joint range and speed detection/estimation

of targets. Although the method for OFDM radar based on

channel state information (CSI) can be extended for CP-SC

radar, the performances are degraded substantially due to the

difficulty of channel estimation in CP-SC. In fact, for OFDM,

there are simple and efficient channel estimation methods (for

example, the 1-tap least square channel estimation) that divide

the frequency domain signal by the transmitted signal [16-17].

However, the similar channel estimation method for CP-SC

needs to divide the discrete Fourier transform (DFT) of the

transmitted signal, which may have zero (or near zero)

coefficients. The zero (or near zero) coefficients make the

channel estimation unreliable. Although there are other channel

estimation methods with better accuracy [16-19] (for example,

the time domain channel estimation method), the complexity is

usually much higher. As the range and speed detections need to

have the channel estimation at every block, we cannot afford to

use high complexity channel estimation here. Thus, in this

paper, a new approach, referred to as “Fast Cyclic Correlation

Radar (FCCR)”, is proposed which does not require channel

estimation. The proposed FCCR method first uses a cyclic

correlation (circularly correlate the received signal with the

transmitted signal) at each block. Then it implements a DFT on

the processed signal along the blocks for each time index. After

these two steps, a two-dimensional (2D) range-Doppler matrix

(RDM) is produced. Based on the RDM, existing constant false

alarm (CFAR) algorithms can be used to detect the existence of

targets and estimate the range and speed of the targets. It is

verified that the algorithm is an approximation to the maximum

likelihood (ML) estimation. Simulations show that the

estimation performance of the FCCR is almost the same as that

of ML and is much better than that of the channel estimation

based method.

The proposed method can be directly used for similar

waveforms like pilot cyclic prefixed single carrier (PCP-SC)

[20, 21], unique-word based single carrier (UW-SC) [19], zero-

padded single carrier (ZP-SC) [22], and SC-FDMA [23].

The major contributions of this paper are summarized as

follows.

• First to propose fully using the CP-SC signal for joint

radar and communication. The CP-SC and its variations are

very popular waveforms in communications, but their usage for

radar is barely studied before. In [12], a correlation (matched

filtering) method is proposed for radar detection/estimation

based on IEEE 802.11ad standardized UW-SC (a variation of

CP-SC). The method only uses the preamble of the signal for

radar detection/estimation. We propose to use all the

transmitted signal (including the preamble and data) for radar

detection/estimation, which is more robust to noise and

interference. The algorithm can be directly applied to PCP-SC,

UW-SC, ZP-SC, and SC-FDMA radar.

• Proposed a near ML “Fast Cyclic Correlation Radar”

algorithm for joint range and speed detection/estimation based

on CP-SC and its variations. It is shown that the algorithm is an

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approximation to the ML estimation, hence substantially better

than the channel estimation based method.

• The proposed FCCR algorithm has low and affordable

complexity.

The remaining part of the paper is organized as follows. The

system model is given in Section II. In Section III, a channel

estimation based radar algorithm is briefly discussed. The

FCCR algorithm and the separate range-speed estimations are

proposed in Section IV. A simple CFAR detection is discussed

in Section V. Simulations are shown in Section VI. Finally,

conclusions and future researches are given in Section VII.

II. USE CASES AND SYSTEM MODEL

A. Use cases

There are many use cases for joint radar-communication.

Here we show two application scenarios in Fig. 1:

(1) Vehicle to vehicle (V2V) communication and

localization: Source vehicle sends information to the target

vehicle and at the same time use the reflected signal to localize

the target vehicle. This can be used for collision avoidance,

hence improve the driving safety.

(2) Video broadcasting and localization: the intelligent

server broadcasts video to the children and obtains the accurate

position and gesture of the children using the reflected signal.

The position and gesture information can then be used to timely

adjust the video content.

Fig. 1. Use case examples of joint radar-communication

Fig. 2. Overall structure for joint radar-communication

B. System model

The overall structure for joint radar-communication is shown

in Fig. 2. The communication transmitter (TX) generates a

signal based on a communication standard and sends it to

targets via a TX antenna. The receiver (RX) can be used for two

purposes: radar detection or conventional communication

(demodulation and decoding), but not at the same time. When

the radio signal reaches a target, it is bounced back to the

receiver antenna, which captures the reflected signal. Thus, the

receiver can use the reflected signal from the target to detect the

range and speed of the target. Unlike conventional radar, here

the transmitted signal contains useful information (modulated

data) for the targets (like the cars in front), and uses the

standardized communication waveform. The data transmission

and radar processing are at the same time. As seen in the figure,

the transmitter chain and most parts of the receiver chain are

shared by radar and communication.

The system model is described as follows. Let ���� be the

baseband transmitted signal. The passband analog signal is

���� � R�������� �������, ⑴

where �� is the carrier frequency, � is the initial phase, and R��∙� means the real part. The signal reflected from targets is

received at the receiver. Assume that there are � reflectors

(targets). The received passband signal is:

����� � � ��R���� � ���� ����!"���#$"����%"�&

�'(, ⑵

where �� is the attenuation coefficient of reflector *, � is the

round-trip delay of reflector *, +� is a phase error, and ,� is the

Doppler frequency shift induced by the moving of reflector *. The Doppler shift can be expressed as

,� � �-"� �� , ⑶

where .� is the relative speed of the reflector (target) and / is

the speed of light. Down-converting the signal into baseband

and sampling it, we get the baseband discrete signal as

��012� � � ℎ���012 � ��&

�'(�� 4!"56 . ⑷

where ℎ� � ��#�� ����!"�$"���%" is the complex channel gain

of reflector * (random phase error is absorbed into this term as

well), and 12 is the sampling period. Radar receiver is to find

the delay � (corresponding to range) and Doppler shift ,� (corresponding to the relative speed).

Let 8� � �/12 , :� � ,�12. Note that 8� � �/12 may not be an

integer. If so, we choose 8� as the nearest integer to �/12 . To

simplify notations, in the following we denote ��012� by ��0�,

and ��012� by ��0�. Note that noise is not included in the

equations above. With the noise (denoted by ;�0�) included

and simplified notations, we have

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��0� � � ℎ���0 � 8��&

�'(�� 4<" + ;�0�, 0 � 0,1, … . ⑸

The above model is applicable to any waveform. Here and after,

we assume that the transmitted time domain signal has a “block

structure” and each block has a CP. The signal ��0� is

composed of A blocks with each block having a length of BC � B + B�, where B is the length of data block and B� is the

length of CP. Note that ��0� can be precoded like that in SC-

FDMA [23]. In each block, the first B� symbols (the CP) are

the repetition of the last B� symbols. OFDM and CP-SC are the

two most popular waveforms with this structure. To cater for

this structure, we divide the received discrete signal ��0� into

blocks of length BC. In each block, the first B� elements

(corresponding to the CP of that block) are discarded. The block D (after discarding the CP) is denoted as �E�0�, 0 �0,1, … , B � 1, D � 0,1, … , A � 1. Assume that the normalized

delay is always smaller than the CP length:

8� ≤ B�. ⑹

Then the received signal can be expressed as

�E�0� � � ℎ��E�⟨0 � 8�⟩I�&

�'(�� EIJ�IK�4�<" + ;E�0�

� � ℎL��E�⟨0 � 8�⟩I��� 4<"&

�'(�� EIJ<" + ;E�0� ⑺

where ℎL� � ℎ��� IK<". Here and in the following, we use ⟨0⟩M

to denote the remainder of 0 modulo N:

⟨0⟩M � 0 mod N. ⑻

Note that the structure of PCP-SC [20, 21] or UW-SC [19,

27] is slightly different from that of CP-SC, where the CP is

replaced by a fixed sequence called PCP or UW. For PCP-SC

or UW-SC, equation (7) should be revised as

�E�0� � � ℎL��E⟨0 � 8�⟩IJ��� 4<"&

�'(�� EIJ<" + ;E�0�,

0 � 0,1, … , BC � 1, D � 0,1, … , A � 1. ⑼

III. CHANNEL ESTIMATION BASED RADAR

ALGORITHM

Here we consider equation (7) based on CP-SC waveform

(extension to PCP-SC or UW-SC is direct based on equation

(9)). Let RE�S� be the DFT of �E�0�, and TE�S� be the DFT of �E�0�. In OFDM system, TE�S� is simply the input frequency

domain signal at block D and subcarrier S. In CP-SC, an

additional FFT is required to transform the time domain signal

into frequency domain signal. After simple mathematical

derivation, we have

RE�S� � � �� EIJ<" � U��V�ℎL�I#(

�'WTE�⟨S � V⟩I�&

�'(

∙ #�� �X#��Y"I +ZE�S� ⑽

where ZE�S� is the DFT of ;E�0�, and

U��S� � � �� 4�X#<"�II#(

4'W� 1 � �� �X#<"�

1 � �� �X#<"�I , ℎL� � ℎ��� IK<"

⑾

Equation (10) can be rewritten as

RE�S� � � ℎL�#�� XY"I �� EIJ<"&

�'([E,��S� + ZE�S� ⑿

where

[E,��S� � � U��V�I#(

�'W�� �Y"I TE�⟨S � V⟩I�.

Note that :� is the normalized Doppler shift: :� � �-"56��� . It is

usually a very small value. If it is small enough: :� ≈ 0, we

have U��S� ≈ 0, for 1 ≤ S ≤ B � 1, and U��0� ≈ B. Thus [E,��S� ≈ BTE�S�. Hence, we have the approximation for

small Doppler shift case as

RE�S� � BTE�S� � ℎL�#�� XY"I �� EIJ<" + ZE�S�. ⒀&

�'(

This simplified model is also used in [8-11]. However, we

should keep in mind that it is only an approximation.

Note that ∑ ℎL�#�^_`a"b �� EIJ<"&�'( is the frequency domain

channel (the round-trip channel) at block D and subcarrier S. TE�S� is the DFT of the transmitted signal at block D, which is

known at the receiver. As shown in [8-11], the range and speed

information are included in the frequency domain channel and

can be extracted with very efficient algorithms. If we can obtain

the channel, the methods in [8-11] can be directly used here to

find the range and speed.

Since TE�S� is known, the channel can be found. As an

example, we can simply use the zero-forcing (ZF) (also called

least square (LS)) method to obtain the channel as:

c�S, D� ≜ RE�S�BTE�S� � � ℎL�#�� XY"I&

�'(�� EIJ<" + Ω�S, D� ⒁

S � 0,1, … , B � 1; D � 0,1, … , A � 1, where Ω�S, D� � ZE�S�/BTE�S� is the noise of the estimated

channel at block D and subcarrier S.

However, in general the accuracy of the channel estimation in

a data block for CP-SC is much worse than that for OFDM. In

fact, the accuracy of the channel estimation is largely dependent

on TE�S�: the DFT of the transmitted signal �E�0�. At a given

data block D, if the amplitudes of TE�S� for some S are very

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small, the channel estimation will be very bad at this block. On

the other hand, in OFDM, TE�S� is simply the input frequency

domain signal at block D and subcarrier S, whose amplitudes

do not vary much. Thus, in OFDM, the simple one-tap channel

estimation can have good performance.

Although there are other channel estimation methods with

better accuracy [18-19] (for example, the time domain channel

estimation method with the assumption of limited channel taps),

the complexity is usually much higher. We cannot afford to

high complexity channel estimation here as the channel

estimation must be done at every block.

IV. CHANNEL ESTIMATION-FREE ALGORITHMS

In this section, a channel estimation-free approach for range and

speed detection/estimation, referred to “Fast Cyclic Correlation

Radar (FCCR)”, is proposed.

A. Cyclic correlations

Let the cyclic correlation of the received signal and the

transmitted signal be

g�0, D� � � �E�V��E∗ �⟨V � 0⟩I�I#(

�'W, 0 � 0,1, … , B � 1. ⒂

After simple mathematical derivations, we have

g�0, D� � � ℎi�j�⟨0 � 8�⟩I , D��� EIJ<" + k�0, D�, ⒃&

�'(

where k�0, D� is the noise,

j�0, D� � � �E�V��E∗ �⟨V � 0⟩I��� �<" , ⒄

I#(

�'W

ℎi� � ℎL��� Y"<" , 0 � 0,1, … , B � 1. ⒅

Note that in general j�0, D� is also related to *. In practice, the

normalized Doppler shift :� is very small. Hence the term �� �<" can be ignored in the above equation. Thus we have

j�0, D� ≈ � �E�V��E∗ �⟨V � 0⟩I�I#(

�'W. ⒆

Obviously, for fixed D, the maximum value of |j�0, D�| appears at 0 � 0. Thus |g�0, D�| will have peaks at 0 � 8�, which indicate the ranges of the targets.

B. Joint estimation of range and speed

Assume that the noise samples have Gaussians distributions,

and the noises at different time and different block are

independent and identically distributed. Then it is easy to show

that the maximum likelihood (ML) estimation for the ranges

and speeds are

arg min�Y",<"� � � |g�0, D�r#(

E'W

I#(

4'W� � ℎi�j�⟨0 � 8�⟩I , D��� EIJ<"

&

�'(|� ⒇

To simplify the problem, firstly we consider the case of one

target, that is � � 1. The ML estimation is simplified as

�8(, :(� � arg min�Y,<� 1ℎi, 8, :�, �21�

where

1ℎi, 8, :� � � � |g�0, D�r#(

E'W

I#(

4'W� ℎij�⟨0 � 8⟩I, D��� EIJt|�. �22�

This term can be expanded as

1ℎi, 8, :� � � � |g�0, D�r#(

E'W|�

I#(

4'W

+|ℎi|� � � |j�⟨0 � 8⟩I, D�r#(

E'W|�

I#(

4'W

�2R� uℎi∗ � � g�0, D�j∗�⟨0 � 8⟩I , D�r#(

E'W

I#(

4'W#�� EIJ<v. �23�

Obviously the first term is not related to the �8, :� at all. Thus,

it can be ignored. The second term can be turned to

|ℎi|� � � |j�0, D�r#(

E'W|�

I#(

4'W. �24�

It is also not related to �8, :� and can be ignored. Hence, the ML

estimation is simplified to the maximization of the third term.

Note that, in the third term, there is a parameter ℎi, which is the

unknown complex channel gain and not related to �8, :�.

Following the derivation in [8, 26], we can obtain the ML

estimation for �8(, :(� without the parameter ℎi as follows:

�8(, :(� � arg max�Y,<� Φ� 8, :�, (25)

where

Φ� 8, :� � {� � g�0, D�j∗�⟨0 � 8⟩I , D�r#(

E'W

I#(

4'W#�� EIJ<{ . �26�

Although it is simplified considerably, the maximization above

still needs two-dimensional (2D) search. Especially the solution

for the speed requires exhaustive search in non-integer points.

We can simplify the maximization further as follows. Firstly,

note that j�0, D� is the auto-correlation of the random input

sequence at block D. Thus, the cross terms j�0, D� �0 ≠ 0� are

generally small. For simplicity, we set

j�0, D� � V, 0 � 0; j�0, D� � 0, 0 ≠ 0. (27)

That is, j�0, D� � Vδ�0�, where δ�∙� is the Dirac delta

function. By this approximation, we have

�8(, :(� � arg max�Y,<� Ψ� 8, :� (28)

where

Ψ� 8, :� � {� � g�0, D�r#(

E'W

I#(

4'W��⟨0 � 8⟩I�#�� EIJ<{. �29�

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This eliminates the necessity to compute the auto-correlations j�0, D� completely. However, 2D exhaustive search is still

required. To reduce the search complexity, we can constrain the

search points for the speed to: : � Xr�IJ, S � 0,1, … , A( � 1,

where A( � �A with � being a positive integer number. Let the

discrete Fourier transform of g�0, D� on the second dimension

be

��0, S� � � g�0, D��#� EXr�r#(

E'W. �30�

Then

Ψ � 8, SA(BC� � {� ��⟨0 � 8⟩I���0, S�I#(

4'W{ � |��8, S�|. �31�

Finally, the ML is approximated by the maximization �0(, S(� � arg max�4,X�|��0, S�|. (32)

The normalized range and speed are then obtained as: 8( � 0(,

and :( � S(/�A(BC�.

The method can be directly used for the general cases with

multiple targets as well, where the largest � points are found as

the estimations to the normalized ranges and speeds of the �

targets. The validation of the method can be seen from another

angle. In fact, in the general case of � targets, we have

��0, S� � � ℎi�&

�'(� j�⟨0 � 8�⟩I , D��#� E�X#r�IJ<"�r�r#(

E'W. �33�

Similar to the definitions in [37], we call ��0, S� in (30) the

range-Doppler matrix (RDM), though here the RDM is

different. Based on the RDM, we can use existing CFAR

algorithms to detect the existence of target and estimate the

range/speed of target [37-38]. Obviously, the peaks of |��0, S�| are at following points:

�0�, S�� � �8� , A(BC:��, * � 1, … , �, (34)

if A(BC:� and 8� are positive integer numbers. Please note that

the speed can be negative. For negative :� , the peak point

appears at �8�, A( + A(BC:��. To guarantee that both positive

and negative speed can be resolved, we must constrain

A(BC:� < A(/2, or BC:� < (� . (35)

If they are not integer numbers, approximations of �8� , :�� are

found from the peak points of |��0, S�|. From the estimated normalized values, finally we get the

estimations for the delays and speeds as follows:

� � 0�12 , * � 1, … . �, (36)

.� � S�//�2A(BC��12�, if S� < A(/2, (37)

.� � �S� � A(�//�2A(BC��12�, if S� ≥ A(/2. (38)

The cyclic correlation can be computed by FFT. In fact, let RE�S� be the DFT of �E�0�, TE�S� be the DFT of �E�0� and [�S, D� be the DFT of g�0, D�. Based on the cyclic

convolution theorem, we have

[�S, D� � RE�S�TE∗ �S�. (39)

Then g�0, D� is the inverse DFT of [�S, D�:

g�0, D� � 1B � RE�S�TE∗ �S��� 4XII#(

X'W. �40�

The method is called Fast Cyclic Correlation Radar (FCCR),

which is summarized as follows.

• Compute the cyclic correlations g�0, D� by FFTs as described in (39) and (40).

• Compute the FFTs of g�0, D� to get the RDM ��0, S� as described in (30).

• Based on |��0, S�|, determine which points are targets. This can be done by using a CFAR detection [37-38], which will be discussed further in Section V.

• Estimate the range and speed of each detected target as described in (36) to (38).

For fixed D, the computation of g�0, D� needs 2 FFTs and one

inverse FFT (IFFT). Thus the total computational complexity

for g�0, D� (0 � 0,1, … , B � 1; D � 0,1, … , A � 1� is O�ABlog��B��. The computation of ��0, S� needs B FFTs of

length A(. The computational complexity is O�A(Blog��A(��.

The 2D search of maximum points on |��0, S�| needs O�A(B�

operations. Thus the overall complexity is O�A(B�log��A(� +ABlog��B��.

C. Separate estimation of range and speed

Although the joint estimation offers nearly optimal

performance, the complexity and memory requirement are high.

To reduce memory and complexity, we can estimate the two

parameters separately. This is especially useful when only the

range or speed information is needed. The method is briefly

discussed as follows. As shown in equation (16), g�0, D� can

be used for separate range estimation at any D. As the speed is

unknown, we cannot coherently combine g�0, D� for different D. Thus, here we use a non-coherent power combine. Similarly,

as shown in equation (33), ��0, D� can be used for separate

speed estimation at any 0. Let

��0� � 1A � g�0, D�g∗�0, D�, �41�r#(

E'W

��D� � 1B � ��0, D�I#(

4'W�∗�0, D�. �42�

Then the round-trip ranges are found from the peak points of ��0�, and the relative speeds are found from the peak points of ��D�. The computation of g�0, D� and ��0, D� are the same

as above. The method only needs 1D search, which reduces

searching complexity. Furthermore, we do not need to save ��0, D� as we only need ��D�. Thus, it reduces the memory

considerably. In fact, the required memory is only O�AB�. The

comparison of complexity and memory for separated, FCCR

and ML are shown in TABLE I.

7

TABLE I. COMPARISON OF COMPLEXITY AND MEMORY

Method Complexity Memory

Separated

estimation

O�A(B�log��A(� + ABlog��B�� O�AB�

FCCR O�A(B�log��A(� + ABlog��B�� O�A(B�

ML O�A(B�A� O�A(B�

Separate range-speed estimation has a common problem: how

to pair the range and speed? From equation (16) and (33), we

can see that the peak points of |��0�|� and |��D�|� are

proportional to |ℎi�|� (reflected signal strength of the target *).

That means, the higher power peak in |�(0)|� should be paired

with the higher power peak in |�(D)|�. Thus we can use a

simple pairing method as follows. Let 0X and DX be the

detected range index and speed index in (41) and (42),

respectively. Reorder |�(0X)|� and |�(DX)|� respectively in

desending order. Then the range index in the reordered

|�(0X)|� is paired with the speed index in the reordered

|�(DX)|�. However, if the reflected signal strengths of different

targets are the same, the paring could lead to wrong range-speed

match.

D. Error bounds

As the algorithms are based on the sampled signal and the

delay/speed are estimated after sampling, the estimation

accuracies are inevitably limited by the sampling rate and the

FFT size. Let �� be the sampling rate. The sampling period is

12 = 1/��. As the detected time delay must be integer multiples

of the sampling periods, thus the absolute error of detected

round-trip delay is bounded by 12/2 at noise-free case. Hence,

the absolute error of range detection at noise-free case is evenly

distributed in [0,�56

�) , where / is the speed of light. The average

absolute error of range detection is �56

� at noise-free case. Due

to the similar reason, the absolute error of speed detection at

noise-free case is evenly distributed in[0,�

��5), where � is the

wavelength, � is the over-sampling factor for speed (see

definition above the equation (30)), and 1 is the total time

duration of the transmitted signal. Thus, the average absolute

error of speed detection is �

��5 at noise-free case. The error

values are summarized in Table II.

TABLE II. ERRORS FOR RANGE AND SPEED ESTIMATIONS (AT NOISE-FREE CASE)

Absolute error interval Average absolute error

Range

estimation [0,/12

4)

/12

8

Speed

estimation [0,�

4�1)

�

8�1

E. Practical considerations

To keep the signal within the given bandwidth with required

out-of-band (OOB) emission, usually we need to filter the

transmitting signal. The filtering will induce delay and inter

symbol interference (ISI). Thus, the effective channel is the

convolution of the actual propagation channel and the filter.

This will affect the radar performance.

V. TARGET DETECTION

Before the target range and speed estimation, we need to

determine if a given point is a true target or not. In general, a

CFAR detection is used for this purpose [37-38]. There have

been a lot of researches for the CFAR detections [37-38]. As

long as the 2D RDM is given, existing CFAR detections can be

readily used [37-38]. As the focus of this paper is on the RDM

generation and range/speed estimation accuracy, here we use a

simple 2D cell average CFAR detection for evaluation purpose

[37]. The method is summarized in the following.

Let Ε(0, S) be the RDM of the received signal. Note that, for

the FCCR method, Ε(0, S) = �(0, S); for the channel

estimation based method, Ε(0, S) = Υ(0, S), the 2D FFT of

c(S, D) in (14) [8, 11]; and for the ML method, Ε(0, S) =Φ(0, S) in (26). Let Ω be a given 2D cell (a 2D region within

the area [0, B − 1] × [0, A( − 1]) centered at (0, S). Let Θ� be

average value of |Ε(0, S)|� in the 2D cell excluding (0, S),

which can be treated as the noise power estimation in the cell.

For the given point (0, S), the CFAR detection is

Η(: |�(4,X)|^

��> Γ¢; ΗW:

|�(4,X)|^

��≤ Γ¢

where Η( is the hypothesis for (0, S) being a true target, ΗW is

the hypothesis for (0, S) being a clutter or noise point, and Γ¢

is a threshold.

For a given probability of false alarm (Pfa), the threshold Γ¢ can

be found by theoretic closed-form expression or through

Monte-Carlo simulations (in general). To save space, we will

not discuss the theoretic threshold setting here. We set the

threshold through simulations. The Pfa is a constant value at

any noise levels for a given threshold Γ¢ [37].

VI. SIMULATUIONS

Two waveforms are considered in the simulations: (1)

Standardized IEEE 802.11ad single carrier [27], which is based

on UW-SC modulation; (2) A self-defined waveform, which is

based on CP-SC modulation. The waveform and algorithm

parameters are shown in TABLE III. To simulate fractional

time delay and filtering, we first use a sampling rate that is four

times the symbol rate. The insertion of time delay and filtering

are done at this higher sampling rate. After this, the signal is

down-sampled to the basic symbol rate and all the

detections/estimations are conducted at the symbol rate. For

both cases, lowpass filters (root raised cosine filter with roll-off

factor 0.2) at both transmitter side and receiver side are used to

keep the signal within the given bandwidth.

TABLE III. WAVEFORM AND ALGORITHM PARAMETERS

IEEE 802.11ad Self-defined

8

Carrier frequency 60.48 GHz 5.9 GHz

Bandwidth 1.825 GHz 50 MHz

Symbol rate 1.76 GHz 48 MHz

UW-SC/CP-SC

block length

512 256

UW/CP length B� 128 64

Data modulation QPSK QPSK

Used packet length 0.38 ms 3.5 ms

No. of targets 3 3

Target ranges uniformly

distributed in

[0, 10] m

uniformly

distributed in

[0, 175] m

Target speeds uniformly

distributed in

[-120, 120] m/s

uniformly

distributed in

[-110, 110] m/s

Relative powers [0, -10, -20] dB [0, -10, -20] dB

� 8 16

Based on the settings and the discussions in Section IV.D, we

calculate the average range estimation absolute error to be 0.02

m and 0.78 m, respectively for the IEEE 802.11ad and self-

defined waveform, at the noise-free case. The average speed

detection absolute error should be 0.20 m/s and 0.11 m/s,

respectively for the IEEE 802.11ad and self-defined waveform,

at the noise-free case.

In the following, we use the average absolute error and

cumulative distribution function (CDF) for the strongest target

to evaluate the estimation performances of all methods. We will

see that the proposed methods achieve the theoretical

estimation performances shown above at much lower SNR

levels than the channel estimation based method. Performances

and comparisons with ML and channel estimation based

method will be discussed in detail in the following subsections.

A. Target detection performance

As an example to evaluate the CFAR detection (Section V)

performance based on different RDMs, here we consider

detecting the existence of target in the whole cell [0, B − 1] ×

[0, A( − 1]. We will compare the performances of the FCCR

and the channel estimation based method, where the number of

Monte Carlo trails is 1000000 (large number of runs is needed

to cater for the low Pfa). As the running time for the ML method

is prohibitive long, we do not include the ML method in this

comparison. The probability of detection at given Pfa versus

SNR is shown in Figure 3. The receiver operating characteristic

(ROC) curve is shown in Figure 4. Obviously, the proposed

FCCR method is substantially better than the channel

estimation based method.

Fig. 3. Probability of detection versus SNR

Fig. 4. Receiver operating characteristic (ROC) curve

B. Compare FCCR and ML on estimation accuracy

To compare FCCR with ML (minimizing cost function

equation (23) with known ℎi), we have done simulations based

on the 802.11ad waveform and the self-defined waveform. As

the ML method runs very slowly, we only use packet length of

0.013ms for the 802.11ad waveform with � = 2. For the same

reason, for the self-defined waveform, we choose a short packet

length of 0.9 ms and � = 2. To have a fair comparison, we have

chosen the number of searching points for FCCR and ML to be

the same. The comparisons of the two methods are shown in

Fig. 5 and Fig. 6, respectively. We see that FCCR achieves

almost the same performance as ML.

9

Fig. 5. Performance comparison of FCCR and ML (IEEE 802.11ad SC waveform)

Fig. 6. Performance comparison of FCCR and ML (self-defined waveform)

C. Compare FCCR and channel estimation based method

Now we compare the channel estimation based method

(channel est) and the proposed FCCR method. The minimum

mean square error (MMSE) algorithm [16, 17] is used for the

frequency domain channel estimation. After the MMSE

estimation, the limited length of the time domain channel (the

channel length is less than the CP length) is also used to boost

the channel estimation accuracy as follows. We turn the

estimated frequency channel into time domain by FFT and set

zeros to the taps with indices larger than the CP length. Then

we transform the time domain channel back to frequency

domain channel by an inverse FFT. Here we assume that the

transmitter and radar receiver are well isolated without

significant self-interference. The radar detection performances

for the first target are shown in Fig. 7 and Fig. 8 (respectively

for the 802.11ad waveform and the self-defined waveform) for

channel estimation based method and FCCR. Obviously,

FCCR is much more robust to the noise and has higher range

and speed accuracies. This is true at other parameters as well.

Thus in the following, to save space, we will not consider the

channel estimation based method any more.

D. Compare FCCR and separated range-speed method

Next, we compare FCCR and the separated range-speed

method (Section IV.C). The average absolute errors are shown

in Fig. 9 with the same settings as those in Fig. 7. It is no wonder

that FCCR is much better than the separated method at low

SNR, as FCCR is an approximation to the ML. However, the

separated method reduces the memory size to only 1/8 of that

for FCCR. The cumulative distribution function (CDF) of the

absolute range and speed errors are shown in Fig. 10 and Fig.

11 respectively for SNR=-34dB and SNR=-20dB. At -34dB

SNR, the range error of separated method still has about 10%

chance to exceed the bound �56

�= 0.04 m, while that of FCCR

is always within the bound. The speed errors of both methods

have certain chances to exceed the bound �

��5= 0.41 m/s. At -

20dB SNR, the estimation errors of both methods are within the

bounds. Note that, due to the limited sampling rate, the

estimated range error is not continuous.

E. Performances at different levels of self-interference

To test the robustness of the FCCR method to the self-

interference, we have done simulations with different self-

interference strengths. The estimation performances are shown

in Fig. 12 respectively for interferences free (-int0), 20dB

interference (-int20dB) and 50dB interference (-int50dB),

where the ranges of the targets are in the interval [0.5, 10] m.

As the self-interference is assumed at range 0, its impact to the

real targets which is at least 0.5 meters away is not significant,

when the interference strength is less than 20dB. However, if

the interference strength is too strong, the impact can be

significant. In fact, as shown in the figure, with the interference

power increased to 50 dB, the estimation performance has

become completely unreliable at short range targets.

Fig. 7. Performance comparison of FCCR and channel estimation based method (IEEE 802.11ad SC waveform)

10

Fig. 8. Performance comparison of FCCR and channel estimation based method (self-defined waveform)

Fig. 9. Performance comparison of FCCR and separated method (IEEE 802.11ad SC waveform)

Fig. 10. CDF of the absolute erors (SNR=-34dB)

Fig. 11. CDF of the absolute erors (SNR=-20dB)

Fig. 12. Detection performances with different interference levels (IEEE 802.11ad SC waveform)

For the self-defined waveform, the radar detection

performances for interference free and 30dB interference are

shown in Fig. 13 with FCCR method, where the ranges of the

targets are in the interval [3.1, 175] m. With 30 dB self-

interference, the range detection performances only degrade

slightly (about 2dB degrade), while the speed detection

performances degraded considerably. However, further

increasing the interference power will make the detection

completely unreliable for short range targets.

11

Fig. 13. Detection performances with different interferences (self-defined waveform)

VII. CONCLUSION AND FUTURE RESEARCH

In this paper, a low complexity method called “Fast Cyclic

Correlation Radar” (FCCR) is proposed for joint range and

speed detection/estimation. The algorithm is derived from the

ML principle. The method produces a RDM by cyclic

correlation at each block and then FFT along the blocks. Based

on the RDM, existing CFAR detection algorithms can be

readily used for target range and speed detection. The

performance of the FCCR is compared with the channel

estimation based method and ML method through extensive

simulations, which shows that FCCR is substantially better than

the channel estimation based method and has almost the same

performance as the ML method.

Future research topics include: (1) self-interference

avoidance/cancellation in both analog and digital domain; (2)

efficient implementation based on software defined radio [5].

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