# Design and Performance Analysis of Hardware Realization of 3 GPP Physical Layer for 5G Cell Search
## 2 Specifications of 5G CS and Literature Review
### 5g Cs PHY  
We consider the n78 frequency band (3300-3800 MHz) in the frequency range 1, i.e., FR1 (410-7125 MHz) as it is being widely chosen for initial deployment of the 5G networks [5, 6]. As per the 3 GPP specifications, the maximum transmission bandwidth in the n78 band is 100 MHz, and sub-carriers (SC) spacing (SCS) is fixed to 30 kHz for SS [17]. Thus, the maximum number of SC in the n78 band is 3276. In 5G, a resource block (RB) is the smallest bandwidth unit for resource allocation and 1 RB consists of 12 SCs. Thus, the maximum number of RBs available in the n78 band is 273. The 5G PHY is based on orthogonal frequency division multiplexing (OFDM) based waveform modulation [25]. Each OFDM symbol consists of the number of SCs which must be a power of two due to IFFT/FFT operations. This results in 4096 SCs per OFDM symbol in n78 [17]. In the time domain, each frame duration is 10 ms, and it consists of 10 sub-frames. Each sub-frame consists of 2 slots, and each slot consists of 14 OFDM symbols. Then, a single frame of 10 ms comprises 280 OFDM symbols. Then, the symbol duration is 33.33 \(\upmu\)s with a cyclic prefix size of 2.86 \(\upmu\)s for the first symbol of each slot and 2.34 \(\upmu\)s for the remaining 13 symbols. Different size of cyclic prefix allows a common frame structure for multiple SCS newly introduced in 5G [5, 25]. The SS signals are transmitted in a burst, known as SS burst (SSB), and the size, duration, and periodicity of the SSB depend on the operating frequency range. For n78, SSB is transmitted in every other frame, and each SSB comprises 8 SS [7, 8, 9, 10, 16, 18]. In a frame, the starting OFDM symbol of the SS is [4, 8, 16, 20, 32, 36, 44, 48]. The duration of each SS is 4 OFDM symbols which means SSB spans over 52 OFDM symbols in a frame of 280 symbols. Each SS consists of 240 sub-carriers (SC) in the frequency domain, i.e., 20 resource blocks (RBs) and 4 OFDM symbols in the time domain [7, 8, 9, 10, 16, 18]. As shown in Figure 1, the middle 127 SC of the first and third OFDM symbols are occupied by PSS and SSS, respectively. Since PSS and SSS are the first signals detected by UE during IA, they are carefully designed to enable blind detection with high reliability. 3 GPP has adopted m-sequences to generate PSS \(d_{PSS}(n)\) and SSS \(d_{SSS}(n)\), \(0\leq n<127\)[16]. The rest of the 113 SCs of the first symbol are fixed to zero. The PSS and SSS allow the UE to detect the physical cell ID (PCI). In 5G, there are 3 candidate PSS sequences and 336 candidate SSS sequences which means the PCI range is from 0 to 1007 [16, 18]. In the third symbol, there are 7 upper and 6 lower SC adjacent to the SSS fixed to zero, and the remaining SCs are \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Word Length**} & \multicolumn{3}{c}{\(D_{PSS}\)} \\ \cline{3-5}  & & **1** & **6** & **10** \\ \hline \multirow{3}{*}{**Execution Time**} & **SPFL (32 bits)** & 29.3 & 19.2 & 19.1 \\ \cline{2-5}  & **Fixed Point (32,2)** & **13.3** & 6.9 & 6.85 \\ \cline{2-5}  & **Fixed Point (24,2)** & **13.3** & **6.8** & **6.84** \\ \hline \multirow{3}{*}{**On Chip Memory** **(18 KB BRAMs)**} & **SPFL (32 bits)** & \(156\) & 108 & 100 \\ \cline{2-5}  & **Fixed Point (32,2)** & \(144\) & 106 & 96 \\ \cline{2-5}  & **Fixed Point (24,2)** & **108** & **82** & **80** \\ \hline \multirow{3}{*}{**Embedded** **Multipliers** **(DSP48s)**} & **SPFL (32 bits)** & \(137\) & \(137\) & \(137\) \\ \cline{2-5}  & **Fixed Point (32,2)** & \(107\) & \(107\) & \(107\) \\ \cline{1-1} \cline{2-5}  & **Fixed Point (24,2)** & **104** & **104** & **104** \\ \hline \multirow{3}{*}{**6-input** **Look-Up-Table** **(LUT)**} & **SPFL (32 bits)** & 42.7 K & 42.6 K & 42.6 K \\ \cline{1-1} \cline{2-5}  & **Fixed Point (32,2)** & 41.5 K & 41.3 K & 41.3 K \\ \cline{1-1} \cline{2-5}  & **Fixed Point (24,2)** & **31.1 K** & **30.9 K** & **30.9 K** \\ \hline \hline \end{tabular}
\end{table}