arXiv:1803.09918v1 [cs.IT] 27 Mar 2018 1642865. emomn maesse otasi utpestreams hybrid multiple a transmit considers to support work can system Subsequent mmWave and stream. chain data (RF) one frequency only one uses which systems mmWave [2]–[4]. several date to obstacles, In proposed these been systems. mmWave have address of to deployment limitations the order hardware for and obstacles sparsity, signifi- major channel However, loss, [1]. path multiplexing enables degrees large cant and which higher gain a area, more beamforming of small support of potentially a deployment to in the systems elements mmWave for allow of band number waveleng mmWave shorter communication the the large at Indeed, gains. a f throughput potential of the significant represents existence frequencies mmWave The at bandwidth [1]. solutions ing ilmtrwv mWv)cmuiain prtn nthe in 30 operating communications (mmWave) millimeter-wave ob aifidb xliigapehr fnwtechnologies, new of plethora a exploiting as by deemed satisfied be to o ohsmercadaymti hnes h numerical NOMA The to channels. findings. compared analytical asymmetric rates the and demonstrate user achievable computations each symmetric seco higher to the both power to In for optimal quality. allocates leads CSI channel which full better with RAMA experience assigne is case, that power less channels, chann users when results the NOMA asymmetric symmetric to Further, than for analytical rate rate. for sum RAMA direction Our better sum that achieves and the of indicates used. terms result only CSI is in analytical and partial NOMA user required outperforms with specific RAMA not that a is for indicate CSI arrival case, ( information of first state channel the full cons and In are partial at with cases signal RAMA different i.e., intended inter-us Two an user’s technique. 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(5G) generation th ∗∗ .I I. eateto lcrclEgneig nvriyo South of University Engineering, Electrical of Department NTRODUCTION ∗ aiMehrpouyan Hani , maeSystems mmWave idered, umbers hthe th CSI). nfig- able sed. ∗ are ths in- nMr nvriyo London, of University Mary en nd els ue or er ai Matolak David , aeUniversity, tate le is d ssonta imthbtenteues hne vector channel it users’ [11], beamforming the analog In between resolution users. finite mismatch and paired that toward shown beam is directional technique beamforming a randomly (BS) random radiates station a base The designs systems. mmWave mmWave-NOMA [10]–[14]. [10] for studied in in been work NOMA has The of mmWave-NOMA, i.e., integration systems, the recently, nications, t at applied Subsequently, . is [9]. the (SIC) [8], receiver at coding cancellation domain superposition interference power performs power successive the the NOMA in in fact, (SC) realized In time, is in [7]. NOMA realized domain domain, are code spectral that orthogo or techniques enhance frequency, Unlike (OMA) [6]. to access [5], 5G multiple scenarios multi-user for in another non-orthogonal technique efficiency as systems, considered enabling also these been promising has to (NOMA) array addition access antenna multiple of lens In a concept switches. to introduced connected the via are is [4], chains RF (MIMO) In several where multi-output [3]. chains multi-input RF beamspace several exploiting by ito em ihoeR hi 1] 1] h unique The [16]. shifters. phase [15], of ra- chain multiple RF of one transmission with the beams support diation can that transmitter the antennas at chain RF structure. one receiver requiring simple NOMA, same and outperform the to at takes that antennas while scheme reconfigurable access works, multiple of prior new advantage a the at propose to costly will of we contrast be here, use can in which Hence, the number amplifiers frequencies. large power and a mmWave and with receiver along shifters chain phase the RF of one the at or in at chains complexity resulted RF come multiple higher all has have of gain [10]–[14] this costs efficiency, works bandwidth the maximizing proposed Although been has [14]. algorithm efficiency. systems mmWave beamforming in energy analog the and maximize in allocation NOMA to for power order joint a in hy- Newly, for provided algorithm studied allocation been is power has NOMA A [13], systems. th In mmWave-MIMO than [12]. more brid chains is RF users RF of served number of of limited number number the a to result, with a NOMA, served As be chains. and can MIMO users pro- beamspace more [12], ensure of in combination work the The poses systems. mmWave-MIMO in NOMA 1 nodrt ev oeuesi Gwrls commu- 5G in users more serve to order In eety hr a enanwcaso reconfigurable of class new a been has there Recently, iierslto nlgbafrigi u oteueo fin a of use the to due is beamforming analog resolution Finite { mojtabaahmadialm,hanimehrpouyan Carolina, ∗∗ uhaPan Cunhua , { matolak { c.pan,maged.elkashlan } @cec.sc.edu † ae Elkashlan Maged , 1 } ipie utilizing simplifies @boisestate.edu } @qmul.ac.uk † t number ite nal he e property that distinguishes the system in [15], [16] from prior (a) Spherical RFRF TransceiverTransciever Chain Chain Dielectric Lens Far-Field art is that the proposed reconfigurable antenna architecture Mixer PA Pencil Beams can support multiple simultaneous orthogonal reconfigurable beams via one RF chain. Inspired by this class of antennas, this Duplexer paper proposes a fresh multiple access technique for mmWave Network Beam Selection Beam reconfigurable antenna systems which is called reconfigurable Mixer LNA Tapered multiple access (RAMA). We consider a scenario in Antenna Feeds which a single BS is equipped with a mmWave reconfigurable antenna and each beam of the antenna serves one user where Fig. 1. Schematic of the reconfigurable antenna steering multiple beams. The antenna is composed of a spherical lens fed with a number of tapered slot the users are not aligned with the same direction. Given antenna feeds. Each feed generates a beam in a given direction in the far that the limitation on the RF circuitry of the antenna [15] field [15]. results in the division of the transmitted power amongst the beams, the current state-of-the-art in mmWave-NOMA would only five outputs that are connected to the input ports of five not operate efficiently in such a setting. To enhance the TSA feeds. Accordingly, the network divides power of the performance of multiple access schemes in the mmWave band output signal of the RF chain equally or unequally amongst and also overcome this fundamental limit for reconfigurable five TSA feeds. antennas, unlike NOMA, RAMA aims to transmit only the It is mentioned that the reconfigurable antennas steer re- intended signal of each user. To accommodate this technique, configurable independent beams. This steering is achieved we will consider two cases, RAMA with partial channel state by selecting the appropriate TSA feed. Also, recall that we information (CSI) and RAMA with full CSI. In the first case, assume that the transmitter has knowledge of the DoA of channel gain information is not required and only the direction the users. Accordingly, by appropriately steering the beams, of arrival (DoA) for a specific user is used. Our results the reconfigurable antenna can manipulate the phase of the indicate that with partial CSI and for symmetric channels, received signal at the user terminal. Therefore, steering mul- RAMA outperforms NOMA in terms of sum rate. Further, the tiple reconfigurable independent beams and routing the power analytical result indicates that RAMA for asymmetric channels amongst those beams are two properties of the reconfigurable achieves better sum rate than NOMA when less power is antennas. assigned to a user that experiences a better channel quality. In the second case, RAMA with full CSI allocates optimal power B. Review of NOMA to each user which leads to higher achievable rates compared to NOMA for both symmetric and asymmetric channels. Our In this paper, we consider the downlink of a single commu- extensive numerical computations demonstrate the analytical nication cell with a BS in the center that serves multiple users. findings. The BS and users are provided with a signal omnidirectional Notations: Hereafter, j = √ 1. Also, E[ ] and denote antennas. For simplicity, the number of users is restricted to the expected value and amplitude− value of (·), respectively.| · | two where the users are not aligned with the same direction, · i.e., there is an angle gap between the users. Let the BS have signals si (i = 1, 2) for User i, where II. SYSTEM MODEL AND NOMA 2 E[ si ]=1, with power transmission pi. The sum of pis, for In this section, first we introduce the reconfigurable antenna i =1| |, 2, equals to p. According to the principle of the NOMA systems and their properties. Then, NOMA technique for a downlink, at the transmitter, s1 and s2 are superposition coded BS and multiple users is described. Finally, NOMA for the as reconfigurable antennas is investigated. x = √p1s1 + √p2s2. (1) A. Reconfigurable antenna systems Hence, the received signal at the ith user, for i = 1, 2, is A reconfigurable antenna can support multiple reconfig- given by urable orthogonal radiation beams. To accomplish this, a yi = xhi + ni (√p1s1 + √p2s2)hi + ni, (2) spherical dielectric lens is fed with multiple tapered slot ≡ where h is the complex channel gain between the BS and User antennas (TSAs), as shown in Fig. 1. The combination of each i i, and n denotes the additive white Gaussian noise with power TSA feed and the lens produces highly directive beams in far i σ2. At the receiver, each user performs the SIC process to field [15], [16]. That is, each TSA feed generates a beam in i decode the desired signal. The optimal decoding order depends a given direction in the far field. Therefore, a reconfigurable on the channel gain. Without loss of generality, let us assume antenna system is a multi-beam antenna capable of generating that User 1 have better channel gain, i.e., h 2/σ2 h 2/σ2, M 1 independent beams where M is the number of TSA 1 1 2 2 which gives p p . | | ≥ | | feeds.≫ Only the feed antennas that generate the beams in the 1 2 After applying≤ SIC, the achievable rate for NOMA for User desired directions need to be excited. To this end, the output i can be determined as of the RF chain is connected to a beam selection network (see 2 N p1|h1| Fig. 1). The network has one input port that is connected to R = log (1 + 2 ), 1 2 σ1 2 2 (3) the RF chain and M output ports that are connected to the M  N p2|h2| /σ2 R2 = log2(1 + 2 2 ). TSA feeds [15]. For instance, in Fig. 1, the network selects  p1|h2| /σ2 +1  This result indicates that power allocation greatly affects the Allocated power to user 1

Allocated power to user 2 Power achievable rate for each user. For example, an improper power Time/Frequency/Code allocation does now allow User 1 to decode s2 correctly, which User 1 s 1 5p 0. in turn does not allow for the interference from User 2 to be ¢ ...,s2, s1 RF £ 0.5p s2 successfully eliminated. Im

User 2

Re Network Selection Beam TSA feed C. NOMA for the reconfigurable antennas Phase ej¡ Detector 8-PSK constellation Suppose that a BS is equipped with the described recon- figurable antenna system and aims to simultaneously serve Fig. 2. Schematic of the BS for reconfigurable antenna multiple access technique with partial CSI and equal power division amongst the TSA feeds. two users by using NOMA. The reconfigurable antenna steers It is assumed that the signals s1 and s2 are selected form 8-PSK constellation two beams by feeding two TSAs. Each TSA serves one user which is equipped with a single . The superposition coding of si with allocated power pi is defined A. RAMA with Partial CSI in (1). Users 1 and 2 receive the following signals as Let us assume that the BS utilizes a reconfigurable antenna and has partial CSI, i.e., knows the DoA of users. Thus, power z1 = √αxh1 + n1 √α(√p1s1 + √p2s2)h1 + n1, ≡ is allocated equally for each user, i.e., z2 = √1 αxh2 + n2 √1 α(√p1s1 + √p2s2)h2 + n2, ( − ≡ − (4) p1 = p2 =0.5p. (6) respectively, where factor α (0, 1) is due to the power ∈ Our main objective is to suppress inter-user interference. To division in the reconfigurable antennas. When α = 0.5, this end, we aim to transmit only the intended signal for each it means the power is divided equally between two TSAs. user at the same time/frequency/code blocks. The intended Thus, each user receives only a portion of the power of the signals for Users 1 and 2 are s and s , respectively. Let us transmitted signal x. 1 2 assume that si, for i = 1, 2, is drawn from a phase shift Consider the same order for the channel gains, i.e, E 2 2 2 2 2 keying (PSK) constellation and [ si ]=1. Accordingly, s2 h1 /σ1 h2 σ2 . An error-free SIC process results in the can be expressed in terms of s as| | achievable| | ≥ rate | | for each user as 1 2 j∆θ NR αp1|h1| s2 = s1e , (7) R = log (1 + 2 ), 1 2 σ1 2 2 (5)  NR (1−α)p2|h2| /σ2 where ∆θ denotes the difference between the phases of s and R2 = log2(1 + 2 2 ). 1  (1−α)p1|h2| /σ2 +1 s2. Similar to (1), the power of the transmitted signal, x, is Obviously, signal to noise ratio (SNR) for User 1 and signal assumed to be p. to interference plus noise ratio (SINR) for User 2 in (5) Unlike NOMA, in RAMA only one of the signals, say s1, is less than that of the NOMA given in (3). As a result, is upconverted by the RF chain block and the whole power combining NOMA with reconfigurable antennas will reduce p is allocated to that signal before the power division step. the achievable user rate when considering the same channel Therefore, x is given by gains, power allocation, and noise power. It is noteworthy that for reconfigurable antenna-NOMA the definition of power x = √ps1. (8) allocation is different from power division. Power allocation is a strategy which is used in NOMA. While, power division It is clear that the superposition coded signal in (1) and the is one of the properties of the reconfigurable antennas that signal in (8) carry the same average power p. The proposed divides power of the superposition coded signal among two multiple access technique for the signal in (8) is shown in TSAs. Fig. 2. The phase detector block calculates the phase difference j∆θ In brief, when users are not aligned in the same direction, between s1 and s2, e . Moreover, as shown in Fig. 2, the the reconfigurable antennas cannot harvest the benefits of beam selection network selects two TSA feeds as highlighted NOMA due to the power division property. Whereas, when with black color based on the users’ DoA. For simplicity, we users are located on the same direction, the reconfigurable an- call them TSA 1 and TSA 2. The network divides the power tenna steers only one beam to serve users which means power equally between TSA 1 and TSA 2. That is, the signal of TSAs division is not required. In this case, reconfigurable antenna- 1 and 2 is given by √0.5ps1. NOMA and NOMA in Subsection II.B achieve identical sum The signal intended for TSA 1 is the desired signal for rate performance. User 1. To transmit the signal intended for User 2 via TSA 2 we take advantage of the reconfigurable antennas. Thanks to properties of reconfigurable antennas, signal at each TSA III. RECONFIGURABLE ANTENNA MULTIPLE ACCESS can independently be rotated with an arbitrary angle. Using In this section, a novel multiple access technique for the this proper, the beam selection network multiplies the signal reconfigurable antenna systems is proposed. The technique in corresponding to TSA 2 with ej∆θ. This results in the j∆θ which we call RAMA takes advantage of the reconfigurable transmitted signal via TSA 2 to be √0.5ps1e = √0.5ps2 antenna and directional transmission in mmWave bands. which is the desired signal for User 2. Since transmission 2 2 2 2 is directional in mmWave bands, each user receives only its Case II: p h1 /σ1 p h2 /σ2. Here, this case is called intended signal as asymmetric channel| | [5].≥ That| | is, we assume that the channel gain for User 1 is stronger than User 2. It can be shown that z = √0.5ps h + n , 1 1 1 1 (9) for asymmetric channels, RAMA-I achieves higher sum rate (z2 = √0.5ps2h2 + n2. than NOMA when the power isproperly allocated for Users 1 and 23. To proof this claim, we have It is noteworthy that, here, we assume that there is no interference that is imposed from the signal intended for User p h 2 p h 2/σ2 N log 1 1 log 2 2 2 Rsum = 2(1 + | 2 | )+ 2(1 + | 2 | 2 ) 1 on User 2 and vice versa. This assumption is very well σ1 p1 h2 /σ2 +1 2 |2 | 2 justified since the structure of the proposed lens based slotted (a) p h p h /σ log 1 1 2 2 2 reconfigurable antenna results in very directional beams with = 2 (1 + | 2 | )(1 + | 2 | 2 ) σ p1 h2 /σ +1 very limited sidelobes. Moreover, due to significant pathloss 1 | | 2 (b) p h 2 p h 2  and shadowing at mmWave frequencies we do not expect the 1 1 2 2 log2 (1 + | 2 | )(1 + | 2 | ) , (13) signals from the sidelobes to reach the unintended user2. We ≤ σ1 σ2  also highlight that in contrast to NOMA, full CSI and the where p1 and p2 are allocated power for Users 1 and 2, re- SIC process are not required at the receiver. Furthermore, in spectively. Also, the (a) follows from log2a + log2b = log2ab, 2 2 RAMA power allocation and power division carry the same and the (b) is a result of p1 h2 /σ2 > 0 . Using (13) and N | R,I| concept, such that the routed power for TSA 1 (or 2) is the (10), the inequality Rsum Rsum holds when the following same as the allocated power for User 1 (or 2). condition follows ≤ The achievable rate of RAMA for each user under equal 2 2 2 2 p1 h1 p2 h2 p h1 p h2 power allocation is obtained as (1 + | 2 | )(1 + | 2 | ) (1 + | 2| )(1 + | 2| ). σ1 σ2 ≤ 2σ1 2σ2 2 R,I p|h1| (14) R = log (1 + 2 ), 1 2 2σ1 2 (10)  R,I p|h2| Obviously, for p1/p (0, 0.5] the inequality holds which R2 = log2(1 + 2σ2 ). ∈  2 indicates that User 1 should have lower power than User 2. Although this range is not tight, it gives a considerable Let us denote RAMA with partial CSI by RAMA-I. It is valuable to compare the sum rate of NOMA and RAMA-I. To insight. This result implies that with proper power allocation in this end, we consider two extreme cases as follows. By defini- NOMA, RAMA-I attains higher sum rate. However, RAMA-I N N N may not achieve user fairness when channel gain of one of tion, sum rate for NOMA and RAMA-I are Rsum = R1 +R2 R,I R,I R,I N N the users is significantly greater than that of other user. In this and Rsum = R1 + R2 , respectively, where R1 and R2 R,I R,I case, the allocated power for user with strong channel gain are defined in (3) and R1 and R2 are defined in (10). 2 2 2 2 should be far less than other user and equal power allocation Case I: p h1 /σ1 = p h2 /σ2. In his paper is case is called symmetric| | channel [5].| | That is, the two users have the would not lead to user fairness. same SNR. In this case, RAMA-I always achieves higher sum rate than NOMA. B. RAMA with full CSI To show this, we calculate the sum rate for NOMA and Assume that full CSI is available at the BS. Furthermore, the RAMA. For NOMA, the sum rate can be calculated as BS can unequally allocate the power between two users. For 2 2 2 N p1 h1 p2 h2 /σ2 signals s1 and s2 that are chosen from a QAM constellation Rsum = log2 1+ | 2 | + log2 1+ | | 2 E 2 σ p h 2/σ +1 and [ si ]=1, the relationship between two arbitrary signals 1 1 2 2 | | 2 | 2 | 2 selected from the constellation is given by (a) p h  p h /σ  = log 1+ 1| 1| 1+ 2| 2| 2 2 2 2 2 j∆θ σ1 p1 h2 /σ2 +1 s2 = s1se¯ (15)  2 2 | |  p1 h1 p2 h2  = log 1+ | | + | | where s¯ denotes s / s . For RAMA with full CSI, the 2 σ2 σ2 2 1 1 2 transmitted signal is| defined| | | as 2 (b) p h  = log 1+ | | . (11) 2 2 x = p′s ( p + p s¯2)s , (16) σ 1 ≡ 1 2 1  The (a) follows from log2a + log2b = log2ab and the (b) which obviously hasp the samep average power as the signal in 2 2 2 2 2 2 follows the assumption that h /σ = h1 /σ = h2 /σ (1). It is assumed that p and p are the allocated power for | | | | 1 | | 2 1 2 and p1 + p2 = p. User 1 and User 2, respectively. For simplicity, we consider Also, for RAMA-I, we follow the same steps as in NOMA. that our power allocation strategy is exactly the same as Hence, it is obtained as NOMA. Fig. 3 depicts the schematic of the reconfigurable p h 2 p2 h 4 antenna for the RAMA. The phase detector and s¯ calculator RR,I = log 1+ | | + | | . (12) blocks calculate ej∆θ and s¯, respectively. The beam selection sum 2 σ2 4σ4 network first selects two suitable TSA feeds, TSA 1 and TSA 2 4 4 N R,I  Since p h /4σ > 0, it gives R Rsum . 2 which are highlighted with black color in Fig. 3, based on | | sum ≤ 2 3 2 2 2 2 Detail analysis of the impact of sidelobes on inter-user interference in To achieve user fairness in NOMA, when |h1| /σ1 ≥|h2| /σ2 we have RAMA is subject of future research. p1 ≤ p2 [5]. h olwn eak r norder: in are remarks following The NOMA. as same the fairness repcieo hi hne odto.Ta is, That NOMA condition. than channel rate their sum of higher irrespective achieves RAMA-II, by denoted respectively. where ec,teitreec-rercie inl o sr a 1 as Users attained for are signals 2 received signal interference-free intended the the Hence, 2, multiplying User by For built 1. is TSA from transmit to ready oe loainsrtg.Tesga o sr1, User for signal The strategy. allocation power i.3 ceai fteB o eofiual nen multip antenna allocation. reconfigurable power for unequal BS and the signals CSI that of full regarding Schematic technique 3. 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Sum rate (bits/s/Hz) p | 10 15 20 iue4()ilsrtssmrt efrac essasym- versus performance rate sum illustrates 4.(b) Figure • iue4()rpeet u aevru ymti channel symmetric versus rate sum represents 4.(a) Figure mul- proposed the of performance the evaluates section This h 0 5 1 02 30 20 10 0 -10 1 p te utpeacs ehiusi eodtesoeof scope the RAMA- with beyond via RAMA paper. is served this techniques of access be Integration multiple will considered other RAMA-NOMA. cluster are or direction Each OMA same cluster. the a Accordingly, on would as NOMA. located RAMA or users OMA direction, of the same one with the combined in be When aligned NOMA. for are alternative users an not is technique RAMA | 1 2 /p /σ RAMA NOMA 1 2 |h 1 = ) 1 / | 2 ( V N IV. =|h p / aeII Case ( (a) | 4 h p u aeo AAIi lasbte than better always is RAMA-I of rate sum , | 2 2 h | | 2 2 1 (dB) UMERICAL /σ | 2 /σ ( 2 2 uscinIIA thg einof region high At III.A. Subsection p ) | 1 2 for , h ) 1 / | ( 2 p /σ | p h C 1 1 2 2 aeI Case /p aeII Case OMPUTATIONS | )

Sum rate (bits/s/Hz) 2 / 10 15 20 /σ ( 0 5 ≤ p 04 60 40 20 0 | 2 2 h (p|h 1 ) RAMA-I, p NOMA, p NOMA, p NOMA, p 2 For . uscinIII.A. Subsection / | hne aifisthe satisfies channel 2 2 1 e.g., , | /σ 2 / 1 1 1 2 2 p 1 2 1 /p =3/4 /p =1/2 /p =1/4 )/(p|h ) /p =1/2 1 (b) /p sntlarge not is p 1 2 3 = | /p 2 / 2 2 / 1 = mmetric ) (dB) 4 que. and ere / n 2 e , First, we show that NOMA is not suitable technique for

5 1 serving the users for the reconfigurable antenna systems. Then, by wisely using the properties of reconfigurable antennas, a 4 0.8 novel multiple access technique called RAMA is designed

3 0.6 by assuming partial CSI and full CSI. The proposed RAMA provides mmWave reconfigurable antenna system with an 2 0.4 inter-user interference-free user serving. That is, the users with

1 OMA 0.2 OMA higher allocated power do not required to decode signals of NOMA NOMA RAMA-II RAMA-II other users. It is shown that for symmetric channels RAMA- 0 0 0 2 4 0 5 10 I outperforms NOMA for an arbitrary p1 in terms of sum Achievable rate for User 2 (bits/s/Hz) Achievable rate for User 2 (bits/s/Hz) rate for User 1 (bits/s/Hz) Achievable rate for User 1 (bits/s/Hz) rate. Also, for asymmetric channels RAMA-I demonstrates (a) (b) better sum rate performance if approximately more than half Fig. 5. Achievable rate region of user 1 and 2 for (a) symmetric channel of the power is allocated to User 2. Further, RAMA-II always 2 2 = 15 = 1 2 with p|hi| /σi dB for i , and (b) asymmetric channel with achieves higher sum rate than NOMA. Numerical computa- 2 2 = 30 2 2 = 0 p|h1| /σ1 dB and p|h2| /σ2 dB. tions support our analytical investigations.

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